JPRS ID: 10110 TRANSLATION MAN AND SPACE ASTRONAVIGATION BY VALERIY FEDEROVICH BYKOVSKIY, ET AL.
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10 November 1981
Translation
MAN AND SPACE ASTRONAVIGATION
By
Valeriy Fedorovich Bykovskiy, et al.
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t~Y)k U!~'F'It'I.~1i t'NE' t)~l.\
JPRS L/10110
10 November 1981
MAIV AiVD SPACE ASTRO~JaVIGATIOPJ
Moscow CHELOVEK I KOSMICHESKAYA ASTRONAVIGATSIYA in Russian 1979
(signed to press 26 Jan 79) pp 26, 3171, 103207, 220222
[Annotation, introduction, Chapters 2, 3, 5, 6, 7 and table of
 contents from book "Man anc"�. Space Astronavigation", by Valeriy
Fedorovich Bykovskiy, Leonid Pavlovich Grimak, Yevgeniy Aleksandrovich
Ivanov et al., edited by V. F. Bykovskiy, candidate of engineering
sciences, pilot~casmonaut of the USSR, V. P. Merkulov, doctor of
engineering sciences and L. S. Khachatur'yants, doctor of inedical
sciences, Izdatel'stvo "Mashinostroyeniye", 1700 copies, 224 pages,
illustrated]
CONTENTS
Annotation 1
Introducti.on ...�.�.��~.~~�.~���~~~~~~~~~~~~~~��~~~~~~��~��~��~~~~�����~s� 2
Chapter 2. Man in the System of Space Astronavigation S
Chaoter 3. Problems of Engineering Ysychology in Development of Visual
Optica]. Means of Space Astronavigation 22
Chapter 5. Modeling Conditions of OperatorAstronaut Performance in
Solving Astronavigation Problems 41
Chapter 6. Evaluation of Effectiveness of Astronavigation Systems
With a Human Operator 59
Chapter 7. Method for Overall E~aluation and Forecasting Quality of
Operator Performance in Solving Astronavigation Problems (According to
Ct?aracteristics of His Psychophysiological State) 117
Table oL Contents 133
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~ANNOTATION
'(TextJ This book deals with the inception of astronavigation; it demonstrates the
; link between aviation and space astronavigation. There is discussion of the
j equipment for space astronavigation, methods of assess~ng the accuracy of various
; astronavigation technique~. Analysis is made of cosmonaut work during spa~e
flights.
~i
This book is ir.tended for engineering and technical work.ers involved in development
~ ar~d use of systems of navigation and control of manned space flights.
Ij
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(
i
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INTRODUCTION
Celestial navigation is an ancient acience that mankind used to solve numerous
~ractical problems for many centuries. The famous seafarer, Christopher Columbus,
= who discovered America, realized even then, in 1492, the great importance of
astronomy in determining the,location of a ship at sea. He said: "There is only
one errorfree seafaring calculationastronomic; fortunate ie the one who is
familiar with it" [47]. Without trie help of celeatial navigation it would be
extremely diff icult for man to orient himaelf, not only in the open sea but, in !
many cases, on land as well. ;
For a long time, celestial navigation was an area of applied astronomy. With the
development of all types of transportation and, in particular, aviation, astro
 navigation gradually developed into an independent branch of science dealing with
the patterns and methods of spatial orientation with the help ~f heavenly bodies.
Aviation astronomy is a relatively young discipline, which took over many methods
from maritime astronomy. However, because of the differences in aviation, as
compared to ships (for example, higher speeds), these methoda underwent substantial
refinement and changes.
For example, it is considerably more complicated to measure the altitude of heavenly
bodies above r;~e planet's horizon in aviation. The reasons for this are, in the
first place, the great distance from the horizon, which makes it difficult to
 superimpose precise~.y the image of such a body on the horizon due to atmospheric
haze; in the second place, inaccurate knowledge about the aircraft~s altitude
above the surface of the earth and irregularity of earthts topography at the hori
zon, as well as bumpiness of aircraft in some cases, which makes it difficult to
take precise readings. These differencea are so aignificant that they led to the
use in aviation of aextants with an artificial horizon, which is formed on the
basis of diverae pendulums, often of the liquid type. In order to reduce reading
errors due to bumpy flight, special integral averaging devices are also used. In
addition, by now some highprecision automatic and automated (i.e., those operating
with the participation of an aircraft navigator) navigation systema have been
developed and constructed, which permit continuous determination of the geographic
coordinates of an aircraft in flight; automatic astronomic course instruments,
astrocorrectors for inertial navigation systems and many others krere also
developed.
Launching in the Soviet Union of the Vostok spacecraft manned by Yurty Gagarin
inaugurated the era of manned space flights. As time pasaes, the duration of
space flights is increasing and thei~ programs are growing more complex. The
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knowhow gained in flying aboard modern sircraft and manned spacecraft showed the
great importance of operational and accurate navigation.support. Tl~~e increasing
complexity of space flight programs makes it necessary to develop and use autonomic
[selfcontained] ways and means of space navigation involving the us~ of modern on
board computer equipment.
It i~ a pressing task to pursue studies for development and improvement of the
effectiveness of ways and means of astronomic navigation of manned spacecraft. In
this regard, cosmonautics must define the duties of a spacecra~t navigator, his role
and place when performing the main operations for autonomous navigation.
There are a number of distinctions to solving problems of celestial guidance of
spacecraft, and they affect the professional performance of cosmonauts.
The navigation methods that are guided by the sun, stars and planets, which are
very accurate and unrelated to distance or duration of flight are quite promising.
_ Astronavigation systems are autonomous in nature, and they require no additional
infozmation from groundbased equipment. They can operate at inf initely long dis
tances from earth. These systems, which use heavenly bodies as reference points,
, are quite resistant to possible artificial interference.
Development of celestial guidance systems is a complex techn�3ca1 task, and it re
quires work on a wide range of interrelated problems referable to optica, light
engineering, precision mechanics and a number of other branches of modern science
and technology. The difficulty of navigation support of spacecraft flights lies
in the fact that each flight must provide for laying out the optimum tra3ectories
for efficient performance of the specif.ied assignment with specif ied energy re
sources. This means that there is a rigid flight schedule which is planned on
earth for each mission. However, because of errora in guidance [into.orbit?J, use
~ of corrective maneuv~rs and possibility of "overshooting" in flight, it becomes
necessary to have autonomous calculation of many navigational data abbard the
spacecraft. In this regard, the eff iciency of performing the set assignment
aboard a manned spacecraft will depend significantly on the ~har;attesie,tics�of'its
navigational equipment and the crew's ability to solve navigation problems at
different stages of a fl~ght, �
In recent times, development of navigation equipment resulted in the use of inertial
navigation systems (INS) with and without platform. Those without platform have
several advantages over those with them. Development of such systems involving the
use of inertial elements based on new physical principles will make it possible to
create inertial systems that will provide for a high degree of precision in deter
mining the pilotingnavigational and orbital parameters of flight.
Pressing problems of theory of inertial systems have been studied comprehensively
by Soviet and foreign authors [2, 36, 42, 66].
, The requirement that accuracy of inertial navigation systems had to be improved
i first led to an effort to make use of classical statiatical methods, such as the
, least squares or maximum plausibility method. Subsequently, to improve the
accuracy of inertial navigation, recurrent methods of statistical evaluation became
popular. Analysis of the margin of error of inertia:l elements (accelerometers,
gyroscopes) revealed that it is impossible at the present tima to assure the ne
cessary precision of solving navigation prcblems by inertial systems with or without
platforms without using additional external information.
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The following sensors of externai informaLion can be used to r_orrect inerti.al navi ~
gation systems aboard manned spacecraft: autiomatic aetronavigational devices (astro !
telescopes); Doppler flight speed and altitude indicator; unit for determining the
direction ef the local vertical (IK [infrared?J vertical, radio vertical); viaual ;
 optic device for determining directions on celestial reference points (optical ;
sight);.optical visual 3evices for determining the a?tir.ude of heavenly bodi.es. .
~
 Space flights will continue to be unique events for a long time, and the capabili !
~ ties of spacecraft will rem3in limited. For this reason, developers of space equ~p ;
ment will be faced for a long time with the requirements of low weight, small size ~
and low energy consumption. In this respect, the use of optical visual means of ;
correction (sights and sextants) is the most acceptable variant. The expediency of
sucti devices is also due to the fac~ that the operatorcosmonaut can determine with ,
their help, independently and without communication with earth, not only the coor
dinates of the position of his spacecraft, but check [monitor, control] such navi
_ gational parameters as the direction of the local vertical and altitude of flight.
For a long time, man aboard a spacecraft will remain the principal link in a semi
automated system of selfcontained astronavigation.
As we know, the psychophysiological functions of a cosmonaut change during flight,
and this is manifested the most obviously by the change in sensoz~imotor fine
coordination functions, which constitute the foundation of professional skill in
astronavigational orientation [38, 73, 75).
A designer who plans and designs any system that operates with the participation i
of a human operator must take into conaideration the psychophysiological capabilities
of man, not only under conditions of normal function, but with exposure to different
space flight factors which alter the level of his work capacity.
Thus, space astronavigation of today is based on many branches of knowledge,
which at first glance often appear to be very far removed from one another. For
this reason, this monograph is the coll~ctive work of various specialistsengineers
and psychophysiologists, cosmonauts and physicians, psychologists, mathematicians
and methodologists.
The authors concentrated primarily on shedding light on questions of improving ,
the efficiency of operation of a semiautomated syetem of selfcontained astronavi ~
gation and formation of recommendatians on optimizing its operation.
~
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CHAPTER 2. MAN IN THE SYSTEM OF SPACE ASTRONAVIGATION
2.1. Structure of Cosmonaut's Work in Astronavigation System
At the present time, the opinion has been established that complete automation
of solving space astronavigation probleme is not efficient. It is imperative to
include an element that integrates all other elements to assure the operation of
a complex navigation system as a whole. In modern navigation systems, man is such
an element, since his mental properties enable him to best solve problems of integ
ration. Expressly man organizes and coordinates the operation of all elements in
the system, uniting them into a single whole [53, 74].
' Whil.e automatic calculations are used in a navig~tion systetn, the main observations
must still be made and finalized by man. Man is the principal element in all
= possible approaches with respect to performing reserve functions in solvii~g naviga
tion problems (of both observation and calculation). Moreover, the human operator
has definite advantages in solving a r~umber of special problems of space astro
navigation. ~ .
Thus, it has now become apparent that it is impossible to de~velop either the main
or ancillary navigation system without taking into conaideration the capabilities
of the human operator.
Development of equipment, with which the operator worka, must be preceded by.�analysis
of the structure of his activities in~solving a specif ic problem. In space astro
navigation, one of the main operations performed by man is taking astronomical
measurements. The entire operation requirF;d for this can be illustrated with an
 abstract algorithm scheme (Figure 20). Aiter receiving an order for an astro
 navigational operation, the cosmonaut displays "instrument zero." Then he identi
 fies the specified reference points (01). If the reference point is not identi
fied (n) he works with the next reference points (02); if it is identified (logic
condition (n) not met), he performs the next operation (aiming at reference point)
to which the corresponding needle comes. After sighting [aimingl,superposition of
both reference points and taking readings (P, S, C), the cosmonaut must provide
for performance of arithmetic operations (K).
A second operation can be performed to increase the reliability of the results of
solving the astronavigation problem, starting with action "0," to which goes a
needle w3th the number 7. Consequently, man's visual and motor analyzers are the
psychophysiological basis of this work, as well as his operative memory which
is instrumental in identification, guidance, reading instruments and calculations.
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~ r,9 > s J 4~4s.~ a ~ e ,
Z~C 10 T~ 8n1 ~wt1 Pg~ S~~Caf K6fi ~rT
. , y . .
Operator Actions Predicate Logical conditions
xC issuing order y "0" data are ncarmal
0 removal of instrument "0" n r~ference point not
idenr if ied
O1 idzntification of reference point q reference point in cross
~ hairs
02 identification o� reserve m reference points super
reference point imposed
P sighting measurement device on a parameters do not exceed
reference point range of inean static
series
S convergence of both reference 
points
C reading instrument b correct performance o~
actions
K mathematical operations w always false logical
condition
J f inding coordinates  ~
Figure 20. Abatract algorithmic scheme for solving astronavigation problem
� (variant): actions and logical conditions
 2.2. The Cosmonaut's Visual Analyzer During Flight
The cosmonaut's sight is the decisive factor in a number of cases in solving problems
of autonomous astronavigation. This applies, first of all, to operations such as
measuring angular distances between celestial bodies, between them and the planet's
horizon, between objects on the planet's surface and its ~ horizon, etc. In all
cases, regardless of the design and parameters of astronomic measuring instru
ments, the cosmonaut uses the main physiological functions of sight: acuity, dis
crimination, sensitivity to light and time parameCers of visual perception. Of
course, proper manufacture of ineasurement instruments increases the accuracy and
reliability of the cosmonaut's work, but none of the listed visual functions is ever
excluded from his work.
It srould be noted that before publication of the first results of studying visual
functions during space flights, the designers and develop~rs of astromeasurement in
struments For manned spacecraft used data from groundbased experiments. However,
before there were flights into space it was not known what changes could occur in
vision iz~ space. Assumptions were expounded that absence of gravity could cause
deformation of the eyeball and alter the functional capabilities of the visual
analyzer. It was expected that the motor system of the eye would lose, to some
extent, coordination of movements that deveZoped in the course of life, as a
result of which there would be disturbances of viaual functions, deterioration
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,
of depth vision, change in processes of accommodation and convergence, etc. All
this had to be checked before man would fly into space.
The first experiments were conducted with aircraft with the use of brief weightless
 ness. American specialists reported a decrease in acuity of vision b~ an average
of 6% during such flights [18]. Some interesting data were also obtained by Soviet
medical men. Thus, L. A. KitayevSmyk [46], observed enlargement, vagueness and
distortion of visible objects during brief weightlessness. In his study of color
perception he found that there was heightened sensitivity to brightness of colors,
particularly yellow. Some of his operators observed a purple halo around luminous
objects.
Studies revealed that visual acuity diminished with onset of weightlessness, but
with further exposure to this state it was restored in some subjeets or even ex
ceeded the initial level. These studies were started with the Voskhod spacecraft,
then continued aboard Voskhod2, Soyu ~3, 4, 5, 6, 7, 8 and 9. They con
sisted of testing visual acuity, visual discrimination or contrast capacity, color
vision and a certain general characteristic of sight, which included both the
abovementioned functions and some of the time cha.racteristics of vision. We
named the latter general function of vision the operational efficiency of vision
[work capacityJ. The studies were conducted by means of apzcially developed
tabular tests with the use of lined patterns and ob~ects of different colors and
contrast [75].
According to our data, the duration of flights aboard Soyuz spacecraft was adequate
for analysis of the dynamics of visual functions. We found that noticeable changes
occurred in these functions within the first 23 days of space flight. The studies
revealed that, while visual functions K diminished by 530~6 during the first day~
of flight, as compared to the preflight level, there was subsequent restoration
_ as a function of flight duration (n orbital passes), which was indicative of
development by the cosmonauts of certain adaptive or compensatory mechanisms
(Figure 2I). Starting with the 40th50th passes, this process starts to be affected
by other factors, which again lead to some decline of visual functions thoug;h not
as significant as at the start of the flight. The maximum decline occurred in the
70th80th orbital passes.
 Subsequently, visual functions improved
~ again, and it is expected that they
would remain more stable than in the
" 1 period between the 30th and 60th passes.
2u ~ After a considerable period of time,
~ l there could be another monotonous de
cline of all of the body's functional
capacities, including sight. We cannot
s rl'~ ,2 state definitely how long this would
1:1 last until a sufficient number of appro
_ 2~0 16 :~6 .f4 4? s0.sg n priate studies is conducted during long
Figure 21. ~ term space flights.
Changes in visual functions K as related
_ to duration of flight (npasses) The nature of visual problems, which are
1) operational visual efficiency solved most often with the use of stars
2) visual acuity or other luminous point sources, is
important to working with _
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astromeasuring instruments. It is also known that the operator's vise~al acuity, ~
contra~t sensitivity and photosensitivity play a substantial role in solving such ;
problems. Only experiments could show how these parameters of vision would change ~
' during space flights. A special technique was developed for this purpose, wbich
involved the use of point light sources of graded intensity located on. earth's
surface.
We conducted an experiment with the use of such a groundbased visual test during ii
the flight of the Voskhod spacecraft in October 1965. A special lighting situation ~
was created on the ground in a desert region, i.e., far from city and village
lights that would hinder the work of the cosmonaut. It consisted of t'hree strips '
of lights, each of which consisted of six point sources of light and one reference
light, which was very bright, for certain detection of the strip.
Floodlights with up to 60� angle of beam divergence, powered by a mobile pro~ector
power plant were used as lights. Such pro~ectors can provide a light with intenaity
of the order of Jfl = 0.2 Mcd. Illumination E created in the ob~erver's pupil at
 a distance L from the floodlight at orbital altitude H, with atmospheric transmittance
Ta and craft's port transmittance [transparency] Tp, can be calculated with the
following formula:
E = JoHTa'[pL3 ,
For the expected flight conditions, the following values of these parameters could
be expected: H= 200 km, L= 400 km, '[a = 0.8 and Tp = 0.75. In this case, ~
E= 0.4 ulux. With such illumination of the pupil from a point source and ;
with adequate light adaptation, the eye sees this light source in the form of a ;
star of about the first magnitude. If we consider, however, that six auch lights 4
will be concentrated in each strip, we can be sure that the distance of L= 400 km ~
is not the maximum when atmospheric conditiona are good and there is a good level
of dark adaptation.
_ Types A and B flares were discussed as another light source. They provide light
intensity Jo in the range o~ 5 to 15 Mcd. Measurement of illumination generated
at an altitude of 1000 m by burning flares revealed that the intensity of light
from these types of flares constituted 45 and 10 Mcd, respectively.
By making calculations analogous to thoae described above, we will.find that !
intensity of light on ths cosmonaut's pupil at a distance of L= 400 km is E_
S ulux and E= 10 ulux, respectively. We used lights created by flares for the
experiment conducted during the flight of the Voskhod apacecraft.
The angular distances between lights diminished because of the dist~rtions of
perspective when the cosmonauts observed the light strips. If we use Z to de~ig ~
nate the ho~izontal distance to the lighte, H for altitude of flight and ~ for the
linear distance between the lights on the ground, the angular distance Da (j.n
 angular minutes) between the lights, as observed by the cosmonauts, can be ob
tained with the following equation:
~u : : ~ ~:in arc~G fl l 3 ~3~5. .   _ _
, H^
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If the minimum angular distance between lights observed by the cosmonaut consti
tutes ~o~in, his visual acuity will be V= 1/Do~in (for point sources).
During the experiment, the flares were lit 2 min before the spacecraft flew over
the lights. At this time, the distance between the manned spacecraft and lights
was about 1000 km and Voskhod was so oriented that the axis of the porthole
through which spacecraft commander V. M. Komarov looked out was directed forward
and tilted by an angle of the order of 60� in relation to earth's surface~ The
cosmonaut saw earth's horizon in the very top part of the porthole and the rushing
surf ace of the earth in the middle and at the bottom. V, M. Komarov adapted to
the dark for 810 min before approaching the region of the lights.
V. M. Komarov observed all three light strips a.*_ a distance of 400 1an and recognized
their location from the familiar configuration, which he immediately reported over
radio. For 1 nin, he observed the lights continuously until they left his field
of vision. At the last stage of the overflight, the cosmonaut counted them and
reported that he saw 12 separate lights.
At the time Voskhod flew over the area of the lights, these lights were photogxaphed
continuously from an aircraft flying on the same course and staying constantly on
the line that connected the spacecraft and light strip. Concurrently, measurements
were taken of the light intensity from an aircraft flying at an altitude of 100p u?.
 All this made it possible to check visibiliry of the lights to the cosmonaut,
since cloud cond~tions constituted 23 points (at an altitude of 67 km) and
visibility was 20 1~ in the area where the lights were used at the time the
spacecraft flew over it. Moreov~r, the measurements gavc~ us an idea about the
intensity of the lights.
In analyzing the results of this experiment, let us consider two aspects of the
cosmonaut's visual activities. The first is the visual search for the point
sources of light on the dark side of earth. The cosmonaut performed this task
quite well. He not only saw the lighting situation, but identified it. As we
indicated above, the glare of the lights at the time they were detected consti
tuted 5 ulux for type A flares and 10 }ll.ux for type B. They appeared like stars
of 1 and 1,58 stellar magnitude, i.e., about the same as the hrightest stars in
the skyCanopus and Sirius.
In the absence of interfering light sources, the detection problem was not difficult.
However, there is usualty a difference in time of visual detection of photic
stimuli. In the process of the search, the operator either does not look where
the stimulus is situated, and then detection time increases, or else he looks by
chance expressly at the spot where the stimulus is located and then the search
time is signific arn.ly reduced. For this reason, the fact that the cosmonaut
saw the lights at a distance of 400 km is primarily of evaluational value, showing
 the order of magnitude determining conditions that are suffici.ent for this visual
problem.
The second aspect is determination of the cosmonaut's visuel acuity from ground
based lights. It was based on his counting the total number of lights he saw
separ~tely. V. M. Komarov made such a count at the last phase of the flight, when
the direction of the beam of vision of the lights constituted an angle of about
60� in relation to the plane of the horizon. He counted 12 separate lights in all
3 strips. From this, calculation was made of maximum angles1.5 to 2.0', which
corresponds to visual acuity of 0.7 to 0.5 units.
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In evaluating the results, it should be noted that visual acuity determin~d from :
point sources situated against a black background is always lower by an average
of 24 times than when measured by the conventional method (Landolt rings) [13J. ~
If we consider that the visual acuity of V. M. Komarov measured by the lined
patterns constituted 1.41.5 on the ground and underwent virtually no change during
the flight, the obtained decline of visual acuity when.measured by point sources ,
of light conforms well with the abovementioned range, constituting about 2.5fold. ~
The studies revealed that there were relatively minor changes in the main physiolo
gical functions of sight during the space flight. The levels thereof, which ranged
from S to 3040%, depending on the physiological function, were not high enough to
be detected by the cosmonauts. This gives us sQme idea about the distinctions of
psychology of visual perception, which is based on comparison of photic stimuli
(simultaneously or after short intervals), rather than perceptiun of their absolute
parameters. For this reason, the work capacity of .xhe!:vz~txal anal.yzer . diminishes
 during a space flight by a magnitude of second order smallness, as compared to the
work capacity of different physiological functions of sight given in this chapter,
since the ratio of increment of photic stimulus ~S to its value S, to which the
visual analyzer reacts, will remain virtually unct?anged if visual sensitivity to
this stimulus is diminished, for example, by a~6. In this case, the following
ratio applies:
~S = a~S/100
S  aS/100
and after conversion:
~S(1  a/100) N ~S ~
_ S(1  a/100) S
i.e., again the same initial ratio, distorted only due to nonlinearity of visual
perception as a function of magnitude of stimulus.
2.3. Photometric conditions Under Which Gosmonauts Solve Astronavigation
Problems
The photometric conditions under which a cosmonaut has to take angle measurements
for astronavigation difier substantially from the conditions under which the same
 tasks are performed in shipping and aviation astronomy.
Knowledge and comprehensive consideration of these conditions con~titute a manda
tory prerequisite for the cosmonaut~s proper performance.
'rhe sun is the chief source of light during orbital and interplanetary flights.
However, the composition of its radiation differs appreciably from that present
near earth's surface because of the protective effect of the atmosphere. The '
radiant energy of the sun, which filla the space near the sun, includes the entire
range of the electromagnetic spectrum, from long radiowaves and including short
radiowaves, infrared, visible and ultraviolet rays, extenc?ing to the region of x
rays and gamma rays, bordering on cosmic rays. The earth's atmosphere is "trans
_ parent" only for a narrow segment of this spectrum. Man is welladapted to radi
_ ations of this segment. The result of Che radiation, including radiowaves, has
some deleterious effect on man, which is determined by its intensity, in addition
to frequency. As shown by the experimental studies of ~he last 2 decades, which
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were conducted with rockets and artificial earth satellites, the shortwave part of
 the solar radiation ~pectrum contains rather intensive ultraviolet (at altitudes of
300 to 100 km) and x (at less than 100 km) rays. The energy of the visible spectrum
_ does not differ in space in overall intensity and spectrum from the on~ on earth, so
' that no special protection against it is required. Radiation in the infrared (IR)
part of the spectrum is hazardous in some cases, in view of ~Usence of absorpti~n
in the atmosphere essentially due to ~~ater vapor, since it can be absorbed markedly
by bodies and heat them. In particular, IR radiation has the unpleasant property
~ of having a harmful effect on the cornea and other transparent media of the eye.
 It has been demonstrated that prolonged exposure to IR rays could cause cataracts,
i.e., opacity of the lens. In this respect, short IR rays are of particular signi
ficance, since they can penetrate through the cornea and aqueous humor of the
anterior chamber of the eye.
X and ultraviolet (UL') rays are even more dangerous to sight. It is known that UV
radiation causes inflammatory processes in the conjunctiva and cornea. The distinc
tion of such lesions is that the morbid symgtoms of inflammatory processes (sharp
pain, burning of the eyes) do not appear right away, but 67 h or more after exposure
to W.
_ The foregoing must convince one that the first prerequisite for a navigatorcosmo
naut to work well when taking astronomic measurements is to protect his vision from
the deleterious effects of x, UV and IR rays from the sun, including reflected
radiation.
In addition, determination must be made of lewels of brightness, contrast, linear,
time and other illumination conditions that provide for optimum measurement quality.
Because of the wide diversity of elements that could be used as bases for astro
measurements, it is not expedient to solve this problem in its general form. The
elements involved may be as follows: ob~ects of small angular size and brightness
against the background of the stellar sky (stars, planets, artificial earth satel
lites); objects against the background of the dark side of earth (cities, light
signals from earth, reference lights, artificial earth satellites); objects on
earth's surface illuminated by the sun (cities, seas, rivers, artif.icial installa
tions, et~:.); ob~ects on the sunlit surface of the moon (craters, "seas," mountains);
horizons of. earth, tY~e moon and planeta in the eola.r system, and other objects.
Let us consider the photometric characteristics of some of the above~isted objects.
Of course, stars a~zd planets are and will continue to be the most frequently used
objects for spac:e astronavigation. In view of the fact that the angular dimPnsions
of these objects are much smaller than the angular resolution of the eye, they
appear as point sources and are characterized by the magnitude of brightness [or
glare] E. Stellar brightness is estimated as the illumination it produces on the
observer's pupil near the boundary of earth's atmosphere. In addition, stellar
magnitude m is a gauge that determines the brightnesa of a star or other light
source. The scale of stellar magnitudes is determined by the equation m=13.89 
2.5 log Em, where F,m is illumination from the star's brightness m produced on the
pupil of the obseroer (in lux).
Minimal illumination on the observer's pupil, which enables him to see the star,
is called threshold. This threshold glare [brightness] is a variable that depends
on viewing conditions. These conditions should include, firstof all, brightness of
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the background against which the star is viewed, degree of dark adaptation of
vision, fullness of accommodation of the eye to infinity, approximate knowledge ,
by the observer of the location of the star, presence of other stars in the field
of vision, light sensitivity of the eyes, experience of the observer in finding
a dim st~r and, in particular, ability to detect it with lateral vision, abilitq
to provide optimum motor activity of the eye during the search and many other ;
factors. This is why reports about visibility during orbital flights are sometimes ;
so contradictory, particularly when flying over the daytime side of earth. One
of the most important of the above conditions ia background brightness Bb. We
know that, while threshold brightness is about~Ethr = l ulux with an absolutely
black background, with a background of Bb = 0.01 ucd/m2, threshold br~,ght~ess already
constitutes 10 ulux, i.e., it increases by 10 times. Thus, the faintest star that
the eye sees against the background of a moonless nig;ht sky is a star of the sixth
magnitude. These are average data, and they could change substantially for different
observers in either the direction of increase or decrease of threshold brightness,For
 example, the results of our studiea revealed that the number of stars viewed in the
triangle of a, S and d stars in the Dolphin constellation ranges from 4 to 13
for different observers, which corr~aponds to a change in brfghtness,`of more than one
stellar magnttude.
The dependence of threshold brightness on brightn~ss of adaptation background has
been the subject of numerous comprehensive studies. There were sometimes rather
wide discrepancies between data of different authors. Apparently this is attri
butable to differences in setting up experiments and, in particular, differences
in level of dark adaptation of operators, which does not end entirely even after
5060 min or more, as well as substantial differences in light sensitivity of
different individuals. Nevertheless, we shall submit as tentative data the re
sults obtained by Luizov [54] on determination of threshold brightness of a point
source as related to brightness of the background:
Threshold brightness [glare], ulux 0.0203 0.0225 0.025 0.0288 0.0571
Bright~ess of background, ucd/m2 0.032 0.32 3.2 32.0 320.0
Stars could be viewed in space against a background other than absolutely black
wtien, for example, there is an "atmosphere" around the spacecra�t that is formed
by exhaust from jet engines with angular orientation. The brightness of these
gases in the sun's rays could, in extreme cases, be of the order of l0U cd/m2 or
= more, and could hinder viewing stars even of the first stellar magnitude. In
 view of the possibility of poorer visibility of stars, one should effect the
angular orientation of the spacecraft in sufficient time for the abovementioned
atmsophere to dis~ipate before undertaking astronomic measurements.
Spacecraft illuminated by the sun and viewed from great distances may not necessarily
differ in any way from stars with regard to their appearance. Indeed, if the
spacecraft is 10 m in size, already at a distance of 35 km it cannot be distin
guished from a star, and its glare will be determined by the phase of illumina
tion by the sun and aspect , in addition to dimensions anci reflective properties
 of its surface. Let us consider a spacecraft in the form of a sphere 10 m in
diameter with a diffuse coefficient of reflection of 0.3 and illumination by
the sun's lat,eral light (1/4 phase). For this case, its brightness will have the
values listed below:
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.
Threshold glare of spacecraft, ulux 10,000 2500 800 400 100 4 1 0.01
Distance to spacecraft, km 10 20 35 50 100 500 1000 10,000
As we see, the glare [brightnessj of the spacecraft at a distance of several tens
 or even hundreds of kilometers will be many times greater than the brightness of
navigational stars. This warrants the statement that there must be several neutral
filters in sextants to ~qualize the brightness needed for reliable and accurate
measurement of angles between a star (planet) and the spacecraft. This ap.plies in
 particular to the case o� measuring angles when the distances to the object are
less than 20 km, when it would appear elongated'to'the viewer. It must be stipulated
that, for distances of 35...100 km sucii an object could also appear elongated, even
though ttie angular dimension is considerably smaller than the eye's resolution.
This phenomenon occurs due to irradiatian of stimulation of retinal regions of the
eye that are adjacent to the one on which there ia the image of the star. It is
known that the greater the irradiation, w~ich also means the size~of the luminous
object, the greater its brightness. Let u~ t.ry to estimate the visible angular
diameter of a star as a function of its brightness. Let us consider that the
following are the main causes of irradiation: diffraction of light on the margin
of the pupil; aber~ation of optical media af the eye, particularly the marginal
regions of t~e cornea and lens; scatter of light in media of the eye; scatter of
light in layers of the retina; additional expansion of the circle of scatter.due
to the large receptiv?. fietds af the retina.
The large number of factors causin~ th~ irxadiation phenomenon warrants the assump
tion that the most probable law of distribution of illuminati9n from a star on the
retina according to its angular diameter wi11 be the narmal Zaw, i.e.:
FIY)= ~ yln e T' ,
where y is angular distance from the center o~ the image of the star and Q is the
parameter of the normal law.
Let us assume that rhere is a G~reahold level of illumination of the pupil Eo,
below which there is no sensation of light in the eye. We can then write down
the following equation:
 �
� Q `E`~~ e 2a+= c )El~t � _
 from which we obtain the angular diameter of the circle of irradiation in the
~ form of :
~ yi=2a Yl In f_'/Eo. _
In view of the fact that the diameter of the irradiat~on circle is close to 1' for
a star of the sixth magnitude and taking Eo = 5 nlux, we obtain Q= 0.4'. Under
these conditions, we shall have:
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O,8 li? F ~
'i ~ .i�?u~
Calculations using this formula yielded the following results: ~
Illumination on the pupil, ulux Q.O11 Q:07 O.1Z Q.45_ 1 10 100 1000 ;
 Diameter of irradiation circle, angular min 1 1.84 2.12 2.4 2.6 3.12 3.55 3.95 i
~
i
As we see from the submitted data, the angular diameter of the circle of irradiation
increases, though slowly, to values that could yield.an inadmissibly high magnitude
of astronomical measurement error. This confirms the desirability of reducing
 glare of the ob~ect for more accura*_e superposition of the image of the ob~ect in
 the sextant over the star. However, it should be borne in mind that marked reduc
tion of brightness of stars, the distance between which is being measured, makes it
difficult to work with a sextant and increases measuring error. One could there
fore believe that there is~an optimum level of brightnesa that leads to minimal
reading error. Its specific level will depend, to some extent, on the design of
the sextant, operator working conditions and other factors. Nevertheless this
level is of the order of 10 ulux. In conclusion, let us mention that all of the
foregoing ref ers to the naked eye. However, inclusion in the sextant system of i
= diopter systems, calculation of their optimum parameters, transfer functions,
 coefficients af absorption of light filters, etc., should be based entirely on the
above comments.
We shall now cite a few photometric characteristics~of the moon as an object of
 astronavigational measurements. The moon does not have an atmosphere, and this
makes it much easier to measure angular distances between stars and the moon's
horizon. However, it must be borne in mind that the brightness of the moon's
surface illuminated by the sun (full moon) constitutes about 5000 cd/m2, i.e., it
is to grsat ior astronomical readings.
The increase in angular dimension of the moon during flight elicited the sub~ective
= impression of increase in its lbxightness. Thus, one should consider it quite
desirable to use an absorbing light filter in astronomical measuring instruments.
The lunar luminous constant, i,e., illumination of the full moon at a distance
equaling the mean distance between the earth and moon, is 0.3 lux. Hence, the
dark side of earth ill.uminated by a full moon would have a mean brightness of
0.03 to 0.07 cd/m2, depending on the cloud cover over the ear.th's surface. At
this level of brightness, there is 53fold reduction of resolution of vision, as
compared to the usual level. However, use of rapid diopter instruments in
angle measuring instruments makes it possible to measure angles between space
objects and ob~ects on the dark side of earth illuminated by a full moon rather ,
effectively for 12 days a month.
The lunar disk illuminated by earth, the socalled earthshine, can l~e used with ~
even more success. The bri~htness of the moon's earthshine can constitute up to
 0.4 cd/m2, i.e., about 10 times greater than that of earth. There is reason to
believe that use of the moon's horizon illuminated by earth for astronomic measure
ments may be wiser in many cases than the horizon illuminated by the sun.
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Let us discuss some of the parameters of the sun as an object of astronomic measure
ments. The brightness of its surface constitutes a mean of about 2000 Mcd/m2. It
is higher in the center of the solar disk, where iC reaches 2500 Mcd/m2, whereas
on the margins it is somewhat lower1300 Mcd/m2. The sun is surrounded by an at
mosphere, the thicknes~ of which is $o small that it does not affect accuracy of
readings at distances equaling the average distance to earth, Venus and even Mercury.
During interplanetary flights, the brightness of artifi.cial space vehicles at differ
ent distances from the sun can be readily calculated, conaidering the fact that *.~e
spherical intensity of solar light is 3.0�1027 cd, whereas absorption of light in
space equals zero. The dimensions of such objects, the phases of their illumina
tion by the sun, foreshortening and mean brightness coefficients of their surfaces
 should be known.
When designing astronavigation systems for a spacecraft, it should also be borne in.
mind that astronavigational observations aboard a spacecraft are difficult because
of the diverse background spots.; The~sonrcea of these apots could be the sun,
moon and earth. In addition, the inside light sources and reflection from parts
_ uf the spacecraft also make astronavigational observations difficult.
The magnitude of background spots reflected by radiation from the earth's atmas
phere is determined by the equation 3.14 SBT'y2, where S is the area of the ,
instruments input aperture of the instrument, B is background brightness at the
 input of the instrument, is the transmission eoefficient and Y is the angle of
the instrument's field of visiono
Hence, we see that the magnitude of background spots ~ increases proportionately to
the square of angle of visual field Y. Thus, background spots have the most sub
stantial effect on observations demling with identification of navigational
 reference points, when the width of the astronavigation instrument visual f ield is
~ at a maximum.
The navigation instruments must have a visual field of at least 40� for certain
 identificarion of navigational landmarks. With such width of the visual field,
the spot from earth's atmosphere could be so large that some navigational stars
 would not be distinguished against its background.
   . .
  .
A laboratory experiment was conducted to assess the effect of light reflected fr.om
 earth's atmosphere on discernibility of stars. During the experiment, a background
spot from earth's atmosphere was simulated and an astronavigation instrument used
with 40� width of visual field. Maximum discernible stel~lar magnitudes were
obtained as a function of their angular distance from earth's horizon. Thus,
with 20, 30, 40 and 50� angles between the star and earth's horizon, the maximum
discernible stellar magnitudes constitute +0.7, +1.5, +2.0 and +2.5, respectively.
According to the foregoing, only stars of the first order of magnitude or brighter
are discerned at angular distances of less than 30� from earth's horizon. If we
consider that it is desirable to use atars of the third and second magnitude for
high accuracy of astronavigational readings, it becomes apparent that optimum
accuracy of astronavigational measurements is possible at angles of at least 4050�
from earth's horizon.
Foreign specialists believe that, becaus.e there is no atmosphere near the moon,
conditions would be more favorable for astronavigational readings near its horizon.
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however, when landing on the illuminated side of th~ moor~ near the terminator,
there is a rather high probability of lateral glare [spot] from the Sun in the
window [porthole]. Such exposure makes it substantially more difficult to iden
tify navigational landmarks. Attenuation of the effect of lateral exposure
[spots) is achieved, as shown by missions on the�Apollo program, by using naviga
tional instruments of the periscope type which have a rather large aperture
(S~600 cm2). Such instruments make it possible to exclude the intermediate environ
ment of the window from the optical system.
A dirty window pane has an adverse effect on astronomic observations. '
The outside panes are most often soiled by the waste from propulsion systems, ,
particularly the attitude engines that are usually situated in the im�nediate
vicinity of windows. According to the report of the crew of Apollo 7, discharge
of liquid. waste caused fc~rmation of crystal cloud~ that made astronomic observa
tion very difficult for several minutea.
According to the studies of American specialists, outgasing of the sil�icone
seal of panes was the chief cause of a dull film on the window panes. The
size of the dull spot on the window can change over a wide range, including
complete coverage of the window. The size of the spot,diminishes when the
window is illuminated by solar rays. This phenomenon was used by the crew of i
Apollo 8 to improve observation of landmarks on the moon's surface. In preparing
for subsequent missions aboard the Apollo, all seals for window panes were submitted
to prior outgasing on the ground, and this was quite effective in preventing ;
dirty windows.
2.4. Motor Analyzer and Operative Memory of Cosmonauts in Flight
. During space flights, weightlessness is a specific factor that affects the cosmo
naut's motor analyzer. It can be maintained that no other analyzer system of man
is subject to such changes in weightlessness as the motor analyzer.
Studies of coordination of movements and motor activity in weightlessness were
started on man long before the first manned space flight. At first, experiments
were conducted in socalled Roman towers, highspeed elevators and in water. The
subjects' task was essentially to superimpose images of obs~rved objects. Differ
ent data were obtained by different authors. Thus, according to the findings of
 Lomanako [92]9 drastic increase in seattered hits was observed at the moment of
weightlessness, whereas this was not observed in the experiments of V. S.
Gurfinkel' anc. P. ~C. Isakov [32]. We must believe that the brie� duration of
weightlessness did not enable different authors to analyze performance under
~ identical conditions. The test cor.ducted by L. A. KitayevSmyk [45] during
~ weightlessness in an aircraft revealed that the accurac}r of superposition dimi
nished, the shift occurring upward and to the right.
A. A. Leonov and V. I. Lebedev described the results of studies of coordination
during brief weightlessness, in which they used a special coordinograph instrument
[51]. They found that the sFeed of motor acts diminished in some cosmonauts in
weightlessness. In subsequent flights, the speed of performance of this test was
the same as obtained on the ground.
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Authors who studied the effects of atable weightlesaness devoted much attention to
writing ski11, the stability and individual diatinctione of which are wellknown,
in the study of fine coordination. Thus, according to Yu. M. Volynkin (19], who
analyzed the handwriting of B. B. Yegorov during flight, there was a.51~6 increase
in time of writing some complex elementa, whereas the increase constituted about
12% for simpler ones (numbers, signature).
_ _ _
~perations involved in manual control of the spacecraft wer~ found to be the most
impaired. For this reason, during the first missions, all manual control systems
were backed up by automatic ones to improve reliability.
At the same time, analysis of the_time spent on these operations revealed that
it was longer a.t the start of a flight than in subsequent passes or training on th.e
grour~d.
It is known that operating a telegraph key is the basis of radiotelegraphic
communication. This activity involves finely coordinated hand movements. In this
case, the quality of transmission of information depends on proprioceptive sensi
bility and time predicting [gauging?] function. Analysis of this form of cosmonaut
activity during actual flight could contribute much to the demonstration of the
distinctions of motor analyzer function in weightlessness.
Let us analyze the radiograms of P. I. Belyayev during his flight aboard Voskhod2
spacecraft. Figure 22 illustrates the time graphs of different symbols in the
Morse code taken from radiograms referable to the first passes and those sent
shortly before the end of the flight [75]. For the sake of comparison, also
illustrated are the same values selected from radio texts transmitted by P. I.
Belyayev during training on the ground. As can~be seen from the graphs, the
motor part of the skill of radiotelegraphic communication underwent considerable
changes, particularly at the first stage of the flight.
Experiments dealing with the dynamics of motor function of cosmonauts were started
during the fiight of the Voskhod2 spacecraft and were continued aboard all
spacecraft of the Soyuz type and Salyut orbital station.
Incidentally, let us note that, with increase in requirements of accuracy of man
machine systems, the means of relaying command information is becoming increasingly
complicated, with increase in number of display equipment, and in structure of
data decoding. Analysis of command motor impulses of cosmonauts pertaining to
control of the spacecraft and navigation systems leads us to assume tha~: the
tracking reaction (pursuit and compensatory), simple operator reactions, reactions
of choice and complex associative forecasting rea~tions could serve as the psycho
physiological correlates of these movements. r`'or this reason, the experimental
paychophysiological part of the scientific programs of space flights was planned
on the basis of these considerations [80, 30,�41]. The results of studies of
man's dynamic characteristics are particularly important for further optimization
of control systems of future, maneuverable spacecraft, making eoft landings on
other planets, docking, etc. For this reason, a model control system was used
for the first time aboard Voakhod2. The ob~ect of the studies consisted of the
abovementioned operator functions included in the model control (tracking) aystem
during exposure to space flight factors and, first of all, prolonged and stable
weightlessness.
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 . _ _ .  _
. ~ Usually, ane uses visual displays and, ~
~,s less often,audio indicators in studies
. of the tracking process. The difference ~
0,1 , between input and output signals expressed ~
in different ways is always considered the ;
�/i ~ ,
quantitative.gauge of the tracking process,
% while the operator's task is to reduce to
1'' a minimum the mismatch between signals. '
1~ The function of this error over~a specific !
n ~ period of time is a characteristic of ;
 Background Flight operator performance. ;
Figure 22. There is parti.~ularly broad coverage in !
Main parameters of radio messages of the literature (unrelated to space flights)
P. I. Nelyayev on the ground (back of studies of human behavior in tracking ~
ground) and in space systems as rela~ted to m.r::ber of control ~
I) duration of interval levers, characteristics of input signal,
II) duration of dash damping of regul.atory units, effects of
III) duration of dot some noi.aes, etc. In describing tracking ~
 systems, many authors refer to theory of !
communication in closed servosystems, considering them as models of.the man
_ machine tracking system. This thesis was very convenient for psychologists,
who had difficulties~in their studies in offering accurate~descriptions of the
system, while servomeehanism theory ia a method of mathematical analysis where
the output of a complex system ia described as a function of input aignals, so
that its functional characteristics can be established.
Thus, examination of the relation of input signal to output signal (change of j.nput
signal by the system) or transfer functions of the system is the sub~ect of such
studies. However, this generally involves the use of very complicated and cumber
some equipment, which is difficult to use on spacecraft. For this reason,.the
authors developed a functional system of a tracki,,,g process recorder (TPR) and
 des~igned a special miniaturized recorder.
In order to create a selfcontained tracking system, ~e rir~Pd the method of visual ~
d~.sp?.~3~ with graphic recording of the output signal. The input signals were put ~ ;
on the tape of a tapefeeding mechanism, in the form of a sin~a.soid differing in
frequency and other curves. The output signal was recorded by a pen recorder
finder, which was closely linked with the control lever. It was possible to study ;
the operator's reactions dL~ring immediate and deferred feedback, i.e., there was ,
simulation of an inertial control system. The contrast of the gresented curve :
constituted about 0.85. The shape of the curvss, their order and duration were
the same at all stages of the experiment. The tape was fed at a stable rate of
S mm/s.
Each measurement of a reaction consisted of 50 einusoidal signals, 12 squarewave
_ pulses collected in alternating order and signals of random processes in two
segments, i.e., there was sufficient digital material for statistical processing on
a computer. The study of dynamic characteristics of the operator in these experi
ments made it possible to define the following, which we know from automatic ;
control theory: amplitudefrequency characteristic A(w); phasefrequency charac
teristic ~(w), autocorrelation function R, coefficient of reciprocal eorrelation r,
transfer function and certain other characteristics of the operator as a dynamic
element of a control system.
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TY?e cosmonauts worked with a TPR under laboratory conditiona, in a training space
, craft to fulfill a flight program, in a spacecraft during the prelaunching period
and in flight. Reactions'were measured 34 timea at all atages of the study, with
the exception of those conducted in flight. Each measurement of the reaction con
sisted of 50 sinusoidal signals and 22 squarewave pulses gathered in random order.�
Analysis of all of the obtained data, as well as of frequency characteristics, led
us in virtually all cases to describing the dynamic properties of an operator
engaged in tracking by means of the following equation:
R,ra (a7'tP ? 1) 
11'' ~
 i~~:r i)(7',p  1; '
_ whexe W(p7 is the operator's transfer function, T is operator reaction time, T1 is
. the time constant characterizing the lag in the operator's oculomotor system, a is
 the coefficient characterizing the degree of participation of psychophysiological
mechanisms of anticipation, T2 is the time constant for delay in operator's decision
making, k is the amplification factor and p is the Laplace Crati~fozm,argt~ment.
According to analysis of transfer function, the damping coefficient changes in
� flight in the range of 0.11.0. Its optimum value is 0.7.
Analysis of amplitudefrequency and phasefrequency characteristics of the operator
as a dynamic element of a control system revealed that the quality of tracking
higher frequency sinusoid signals ~rorsens, particula~l.y 3n flight. For example,
noticeable changes in amplitudefrequency cha~acteristics during flight occurred
already when working with a signal having a frequency of 34 rad/s. Analysis of
phasefrequency characteristics showed that changes start_at input__signal frequency
= of the order of 12 rad/s, and in this case the magnitude of change was greater.
Experiments revealed that there was an increase in duration of the transient process
by a mean of 1.52.0 times for the operator to ad~ust a solitary mismatch during
space flight. It is not possible to define this time mare accurately because of
substantial dispersion, which increased even more in flight, constituting 0,35 s2,
which corresponds to 45% in relation to ~ean value of the transient process and
almost 75% according to standard measurement error. Moreover, it~ the course of
the flight we observed a tendency toward mono~~nous increase in duration of the
transient process, which was apparently related to progressive fatigue and adapta
tion of the neuromotor system to weightlessness, when its overall tonus diminished
 more and more with increase in duration of rhe ~~.ight. This occurred in particular
when no intensive physical exercise was performed.
It should be noted that the abovementioned high dispersion of duration of the
transient process, which occurred during space flight, was a~ttributable to some
extent to the less convenient ~onditions of working with the inatrument than on
the ground. For this reason, the design of astronomic measuring instruments
must meet several special conditions to asaur~ better and faster work with them.
In particular, an important prerequisite is to have the aetronomic measuring
instrument wellsecured aboard the spacecraft. The gear ratios of lever movements,
magnification of the sighting telescope and its luminous power wiJ.3. have an appre
ciable effect on accuracy of astronomic readings. As ahown by the results of
experimental studies, the brightneas of atars or space vehicles [ob~ects]_ between
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which the angles are measured should be at least +1 stellar magnitude, otherwise ~
there could be a marked increase in lag [value of in the expression fur W(p)] and ~
hence in work time. Such an effect can be the result of a wide difference b2tween }
brightness levels of two stars, the images of which are superimposed for the f
measiirements. In this case, adaptation of the eye becomes established at a I
certain mean level between the two stars, and for this reason the less bright star
would be perceived as being dimmer than if it were alone in the field of vision.
For this reason, by virtue of the wellknown law [54], the inertial properties ~
of the eye would be more pronounced. '
To sum up the analysis of our experimental data, we can see that there are two f
types of changes in nature of oculomotor coordination which is the most responsible
for accuracy of astronomic measurements during a space flight, as compared to
terrestrial canditi~ns: in the first place, extension of all processes occurring
in the operator's motor sphere and, in the second place, increased instability of
work, which is manifested by increase in dispersfon of mistakes in oculomotor
coordination. These two factors together would,~of course, diminish accuracy of
astronomic readings in flights. This decline constitutes a mean of "'S0%. It must
be borne in mind that further refinement of the deaign of astronomic measuring
instruments, as well as of inetho3ology of conditioning and training cosmonauts be ;
fore flights could improve substantially the accuracy of astronomic measurements.
p i~ ~ ,
Z K ~
J ?
~o sT ~ .
 SQ o1? 3
~ ~
30 0,06 ~
, , ~ 1 J S 7 9 11 13 15 1l Flight
ZO k0 60 h Training
Figure 23. Figure 24.
 Change in reliability of operative memory Change in reliability of operative memory
 PoP as a function of duration of space during training and 1day space flights
 flight (mean data) (Kgeneral coeff icient of quality of
1) background data obtained from labo operative memory)
ratory experiments 1) data for cosmonaut A
2) data obtained in training spacecraft 2) data for cosmonaut B
3) data obtained during training 3) data fc~r cosmonaut C
As has been shown previausly [73J, operative memory is the atructural basis of
operator performance in an extrapolation system. For this reason, during the
flights aboard Voskhod2 and Soyuz6 spacecraft we atudied the dynamics of cosmo
nauts' operative memory, comparing it to the parameters obtained on the ground
" and in a training spacecraft.
Figure 23 illustrates the mean reaults of testing operative memory of eubjects
while fulfilling programs of longterm space flights (8 experiments, 16 sub~ects,
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240 measurements). Analysis of the submitted data confirmed the agsumption we pre
viously expounded that there is an adaptation phasp in dynamics of psychophysiologi
cal functions. It was demonstrated that, under the experimental conditions,
operative memory diminished on the first day of flight and held, with some vari
ation, at 3545~ of the control level to th e end of the experiment. Longer experi
ments did not alter the previously obtained data. Thus, in the course of a 70dP.y
experiment, it was also possible to single out the adaptation phase of changes in
operative memory and persistent change in this funct:'.on in the next phases.
During preparations for performing the
PoP~~  scientif ic research program in f light,
_ .
Fp_ _ _ l. each cosmonaut participated in 1216
_ i. _ ~ ~ training sessions, during which 70100
~ i r measurements were taken of tests charac
~ terizing the functional level of operative
~ ~ memory [75]. In all casea, a stable
 ~ ~   ~ ~ "plateau" was reached for this form of
 o activit which served as the control
Y.
0 10~ 40 bD n background. Figure 24 illustrates the
 Backgraund Flight findings referable to a 1day flight
Figure 25. (B. B. Yegorov, P. I: Belyayev and A. A.
 Comparative characteri.stics of opera Leonov) and Figure 25 to a manyday
tive memory at different stages of flight (G. S. Shonin, V. N. Kubasov).
manyday space flight (Popreliability
of operative memory) As can be seen from the results illus
trated in these figures, starting with
the fifth and sixth training sessions the general coefficient of performance quality
became set at one level and did not undergo appreciable changes thereafter. The
highest coefficient was found for B. B. Yegorov, The same figure illuatrates
results obtained during a space flight (using mean data for the flight as a whole).
A decline was inherent in this coefficient (most marked in B. B. Yegorov) during
 the flight.
In ~he case of tt~,e mult~.day flight, there wae fluctuation of reliability of operative
memory :.haracterizing the adaptation phase of flight and phase of established work
capacity. The results indicate that space flight facto�Ls, particula.:ly prolongPd
' weigh~le~,s:~ess, d:iminish lability of inemory, which can b~ clasaified as operative
according to all of its characteristics. The fact that operative memory diminishes
should also be taken into consideration when forecasting performance of tasks deal
ing with identification of navigational stars and orientation in the process of
taking astronamic readir~gso
~
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CHAPTETt 3. PROSI~FMS OF ENGINEERING PSYCHOLOGY IN DEVELOPMENT OF VISUAL,OPTICAL
MEANS OF SPACE ASTRONAVIGATION ~
3.1. Use o� Optical Visual Devices
_ At the present time, increasing preference is being given to selfcontained naviga
tion equipment for space flights. As the programs of space exploration grow more
complicated, the importance of autonomous navigation systems will increase, the
class of problems solved with use thereof will expand, and there will be an increase ,
in requirements of their accuracy, speed and reliability.
Several specialized visual optical riavigation instrumenta for manned spacecraft
have already been developed, both in our country and abro ad. Some of our instru
. ments have undergone trials aboard Soyuz series spacecraft and the Salyut orbital ;
station. Some experience in using opticovisual navigation instruments was gained
during preparations for and participation in spa~ce flights. For this reason, we
are able to solve problems of navigation using existing optical devices and work i
out the main specifications for future instruments and systems. ~ ,
In developing opticovisual means of space astronavigation, it is very important
to take into conside.ration the experience gained during actual space flights. For
example, considerable attention was devoted to teeting astronavigation systems
and observation of navigational landmarks during fYights aboard American spacecraft
on the Gemini program.
Several na.vigation experiments were conducted.
1. Observing setting of stars beyond earth's horizon on the dark side of the orbit.
The experimer~t was conducted by the crews of Gemini 7, Gemini ~0 an3 G~mini 11.
It was estabZished that stars of less than 1.5 stellar magnitude could not be seen
in open space through the light filter of the space suit. ~
2. Photography of ob~ects on earth's surface.
In this experiment, the crew of Gemini 5(Conrad and Cooper) detected rather
small objects (individual ships, aircraft) on earth.
3. Measurement of "starstar" and "starobject" (carrier rocket stage) angles.
This experiment was performed by the crews of Gemini 4, Gemini 6 and Gemini 7. It
was also conducted during the flight aboard Apollo 7 in 1968. The crew of this
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spacecraft succeeded in viewing the last stage of the carrier rocket by means of
a sextant at a distance of up to 550 1~.
4. Observation of special markinga laid out on earth. As such markings, 16 white
strips were u~ed, which were paved with plaster (Larado, Texas), as well as shell
rock (Carnarvon, Australia). The target indication of these signs was perfonued by
means of smoke signals. The crew of Gemini 5 and Gemini 6 were able to observe
these signs at a diatance of 640 km.
The program of astronavigation experiments performed by the crew of the Apollo in~
cluded most of the experiments that had been previously conducted aboard Gemini.
The technical tasks included the following: elimination of spcts; development of
devices that would permit observation of navigational stars on the day side of
orbit; providing for high light transmiseion. �
When methodological problems are solved, it will be possible to make the f inal
choice of observation objects (navigation landmarks) and methoda for processing the
obtained information in order to assure optimum efficiency of the astronavigation
system. �
The statements of the cosmonauts also revealed that they set up many engineering
psychological problems, the solut~.on of which would permit development of an
optimal ergatic operatorinstrument system. The following tasks should be in
cluded here: choice of optimum coefficient of magnification; determination of �
size of visual field for certain identification of navigational landmarks; providing
for the necessary accuracy of readings; development of optimum system to stop the
image from "wandering" [running], and generally speaking developing a piece of
equipment that takes into cansideration the dynamics of the objec.t (manned space
craft), etc.
3.2. Specifications for Space Sextants
The effects of space flight f actors on man, as part of the system of spa~e astro
navigation, the accumulated experience with space flights, as well as groundbased
studies, enable us to formulate, even now, several specific requirements of optico
visual instruments for space astronavigation.
Let us discuss sev~ral general requirements of space sextants.
1. Presence of two sighting lines. The fact of the matter is that one
cannot use pendulum verticals to create the datum point base in sextants. Use of
other types of verticals leads either to great errors and increase in dimensions
and weight that are not acceptable for opticovisual equipment, or loss of autonomy
of the system. For this reason, stars are used as the datum base in developing space
sextants, since they are an excellent datum base because of their very distant
location [35]. But stars carry no informatio~ about the location of a manned
spacecraft. As a result, it is necessary to add a second sighting channel to the
sextant to measure the direction of the navigational landmark (neareat celestial
body). We shall ca~l such a twochannel sextant a sfghtaextant (SS). The angle
measured with the SS between directions to the star and landmark defines the aur
; face of the spacecraft position and constitutes primary navigational informetion.
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Thus, a twochannel optical system, which permits simultaneous viewing of two ;
� sighted objects, must be used in a space sextant. '
`
2. Visual field of sextant. It was established experimentally that the
 sextant's field of vision should be about 40� for certain detection and identifi
cation of navigational stars and landmarks. If a small visual field is chosen for ~
some reason or other, there must be provisions for high viewing speed. '
3. Sextant magnif ication. We know that sighting is improved with increase
in sextant magnification. However, it is necessary to reduce the sextant~s visual ,
f ield to increase magnification with retention of dimensions of the instrument ;
within a wise range. As a result, the task ~f detecting navigational stars and '
terrestrial landmarks, and to measure angles between them from a spacecraf t could
become quite difficult. For this reason, in preparing the specif ications for
the sextant, it is necessary to search for compromises in selecting magnif ication
and field.
 Below are the results of laboratory studies of accuracy of astronomi:, readings as
a function of sextant magnification [82]:
Sextant magnification 2.5 6 8 12 16 20
Root mean square error of sighting, angular s 22 15 12 8 6 5
The more precise results of astronomic readings are attributable mainly to in
crease in angular distance between images of the sighted objects.
These data indicate that accuracy of readings increases by almost 32% when magnifi .
cation is increased from 2.5 to 6. On the other hand, an increase in magnifica
tion from 10 to 20 increases accuracy by only 15~, but worsens significantly the
conditions for identifying stars, which we mentioned above, and makes mEasurement
difficult due to the high angular rate of movement and shaking of the image of
the stars in the eyepiece when taking readings with a sextant that is not secured.
~ Analytical studies revealed that to assure encountera of spacecraft in orbit,
the permissible error of readings when using a sextant as a selfcontained means
~ of navigation would be of the order of 10' [35]. For this reason, there should
be over 8fold magnification of the sextant telescope for these purposes.
4. Multifunction. There are many natural sensors of navigational information
(stars, sun, moon, earth, etc.) in space. For this reason, a space sextant must
maice it possible to observe and sight them, in spi~te of the wide scatter of their
illumination characteristics. The cosmonaut muat be able to adapt to changes in
flight conditions. This makes it necessary to provide filtsrs differing in
optical density.
5. Multimodality. Since the space sextant could be ~ised, on the one hand, as
a means of correcting the inertial navigation system and, on the other hand, as a
spare navigation tool, it must have provisions for automatic and manual collection
of navigational information. For automatic collection, precision sensors of
angles of rotation of the main mirrors of the space sextant must be inetalled,
and they must be linked with an alphanumeric computer.
To increase the reliability of the navigation system, there must also be provisions
for the feasibility of reading data by man, directly from dials [dial devices].
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6. Mechanism to stop ima.ge "wandering." As shown by different studies,
the dynamic characteristics of the manned spacecraft affect the accuracy of ineasur
_ ing navigational parameters. This has the most adverse effect when sighting land
marks on the surface of a planet in nearplanet navigation. In this case, "wander
ing" of the image must be compensated by meana of some sort of electromechanical
drive operating automatically from signals computed hy an alphanumeric computer
on the basis of information from the INS [inertial guidance system?]. In this
case, the operator would work under conditions where the visible "wandering" [or
running] of the image is determined solely by errors of compensation. The reading
accuracy then increases significantly.
7. Connection with timer [time sensor, clock]. The high speed of the space
craft makes it necessary to be extremely accurate in checking the time of taking
angular measurements. While, for example, timing errors of 1 s could lead to an
error of several tens or hundreds of ffieters in determining the location of a ship
or aircraft, the same error would cause a difference of 70008000 m in locating
an orbiting spacecraft. For this reason, apace sextants muat be connected to a
chronometer that permits fixing the time of taking angle measurements.
 8. Compensation of systematic sighting errors. This requirement means that
there must be thorough examination of each inatrument during exposure to factors
that affect its characteristics.
For example, the uneven surface of the window glass, presence of a wedgelike angle
between two surfaces of window glasses, as well as distortion of glass surface
due to pressure difference on both sides of the cabin, are factors that affect
distortion of object sighting lines. The difference in refraction coefficient of
the environment in which light spreads (space, interior of spacecraft) is a
fourth factor that is not directly related to the window.
Distortion of the surface of window glass, a wedgeshaped angle and pressure
gradient can be demonstrated both analytically and experimentally. Knowing the
 characteristics of glass, angle of incidence and location of beams hitting the
glass, one can eliminate such errors within a range of up to 1".
One can estimate the correction for the difference in refraction if one knowe
the measured angle, pressure and temperature in the spacecraft, as well as
 direction of sighting lines in relation to the surface of the window glass.
Other similar errors must be evaluated and compensated in an analogous fashion.
9. Utmost simplicity, reliability and long operating time.
10. M~.nimum dimensions, weigh~ and energy consumption. Specific requirements
for sextants can be formulated oniy with due consideration of the functions they
perform on a specific manned spacecraft.
For example, the requirements for the sextant used to conduct experiments aboard
Gemini 12 were formulated as followa:
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Precision +10' ~
Maximum weight 6 pounds ~
Maximum length along main sighting line 7.5 inches
Eyepiece use normal and away from eyes when working ~
with space helmet visor closed
~
~
Information obtained in the course of experimental studies enabled the 1~ASA~� ~
Research Center in Ames to define the specifications for a space sextant to be I
used for orbital flights around earth and to the moon [99, 101]. These require '
ments were as follows: ~
i
Magnification 8x (normal eyepiece)
Magnification 4.6x(eyepiece with attachment) ,
Telescope visual f ield angle 7�
Sextant's margin of error (overall) no more than +10' '
Moving mirror actuation 1 and 5� per turn of handle
Range of ineasurements 6 to 70� '
System of sextant with two lines of sight
Weight of ~extant ~ 2.7 kg (aelected rather arbitrarily)
In addition, there were several requirements, such as a chronometer on the sextant ~
with a button to start it and delivery of a synchronizing pulse at the moment of t
~
reading the angle on the onboard recorder or computer, filters of different optical
_ density for simultaneous sighting of ob,jects differing in brightness, need to ~
illuminate the angle counter and eyepiece hairs, mechanical angle counter. There ~
 was special mention of the fact that the cosmonaut muat be able to work with the ~
sextant when the space helmet is closed, as well as with a guardfilter used in !
an emergency situation. The latter required an additional attachment for the �
eyepiece, so that it could be at a distance of at least 57.5 cm from the eye. ;
i
New space sextants are being developed on the basis of the above requirements. At ~
first such work was pursued on the basis of existing aviation and maritime sextants. '
The changes made in their design were uaually directed toward making work easier
with them for cosmonauts during flight and increasing sextant accuracy [1, 881. :
However, there are already some original instruments that are based on new prin
ciples.
The functional diagram ard main design features of a apecial type of space sextant
have been published [88]. It was indicated that use of a mirror made of beryllium,
_ which precluded the effect of temperature fluctuations on accuracy of readings, as
well as high quality of manufacturing the drive gears for the mirror, resulted in
a margin of error in Che sextant not exceeding 10". Moskowitz et al. [95] describe
the design and drawings for a apace sextant consisting of 3 telescopes with visual
field angles of 40, 7 and 1�. The aextant is equipped with a spectrometer that '
permits measurement of Doppler shift of spectral lines in the radiation from
sighted stars, which permits calculation of radial velocity of the epacecraft. The
weight of such a sextant is estimated at about 2.7 kg, while the margin of error
does not exceed 1".
Let us consider the construction of one type of space sightsextant, which was
developed with consideration of the aboveformul.ated requirements and is a visual
optical instrument for autonomic determination of the coordinates of the craft's
location [99, 101].
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The epace sightaextant, a diagram of which is illuetrated in Figure 26, ie a
combin~.tion in one inetrument of an optical sight and sextant, and it coneists
of the following: a) Opt i cal mechanical sight cansi~ting of the main sight
mirror with sensors of directional angles of terrestrial (lunar) landmarks,
sight window (4), optical system of sight (5 and 7), mechanism for controlling
position of main sight mirror and at~tomatic setting of "wandering" of image of
earth's (moon's) surface (8), binocular viewing system (9), eyepieces of binocular
system of aight (10 and 1 Z); b) mechanical optical sextant instrument consisting
of sextant window (1), main sextant mirror (2) with sensors of angles of direc
tion to celestial bodies, stationary semitranaparent mirror (17); optical system
of sextant (15 and 16), mechanism for controlling position ~f main sextant mirror
(14), monocular system of viewing the sky (13), sextant eyepiece (12).
1' ?1 1R
11
B ,
~
l/ rp ~
\ 7
Star i
_ .
? 7 'r S' 6 1 �
. J ` , �
Terrestrial
landmark
Figure 26. Diagram of space sightsextanC...__
_ . .
1) sextant window 9) binocular viewing system
2) main mirror of sextan t 10, 11) eyepieces of binocular vision system
3) main mirror of sight 12) sextant eyepiece
4) sight window 13) monocular system for viewing sky
5) optical system of sight 14) mechanism to contro_~.position of
' 6) housing main mirror of sextant
7) optical system of sight 15, 16) optical system of se~ctant
8) mechanism to control position of 17) stationary semitransparent mirror
main sight mirror
The task for the operatorastronaut is to superimpose identified images of naviga
tional heavenly bodies and the terrestrial (lunar) landmark over the center of the
visual field of the spac e aextant. When these imagea are visually auperimposed
 over the center of the in struments field and a apecial button is depressed, there
is automatic reading and storage of readings of sensors of the anglea of poaition
of main mirrors of the sextant, and the time of the measurement is recorded.
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During a space flight, astronomic measurements are made wtaen the "wandering" of '
the image in the field of the sextant is stopped in order to facilitate the
process of identification by the operatorastronaut of navigational stars and
landmarks. Image "wandering" is stopped automatically by using the algorithme for ~
selection of navigational stars and landmarks on t~ie onboard.digital computer and ~
adjusting the main mirrors of the sextant in the direction of specified stars and
~
landmarks.
In this mode of work1 the operatorastronaut is given only the task of eliminating ~
mismatch and superposing the images of the star and terrestrial (lunar) landmark
over the center of the sextant's field.
To work with such instruments, the astronauts muet be able to correctly choose the
navigation parameter to be measured in a given situation, i.e., he must know appro
ximately what their characteristics are and have stable professional skill,
developed on earth, in taking measurements.
3.3. Navigational Parameters Measured With Space Sextants and Measurement
Errors
At the present time, the following navigation~l parameters can be measured with
space sextants: angle between directione of navigational star and landmark on
a planet's surface; angle between directions of navigational star and artificial
 satellite of planet, as well as probe released from a spacecraft; angle between f
directions of navigational star and centers of planet or its satellite (vertical
of earth, moon, etc.); angle between directions of navigational star and visible
planet horizon; angle between directions of two landmarks on surface of planet,
in the centers of two artificial satellites or two planets; angle between vertical
to the planet and landmark on its surface; angular diameter of celestial body (sun,
earth, moon and other artificial or natural bodies).
In addition, other angular values can be measured, as well as the rate of change
in these values, Doppler shift of spectral lines in radiation from sighted stars,
 etc.
We shall discuss navigational measurements involving the use of an artificial
problem on the basis of foreign investigations.
Astronomic measurements of "probestar," "probeterrestrial landmark" and "probe
lunar landmark" are based on releasing an artificial probe from a spacecraft and
subsequent measurement by the astronaut, using a sextant, of the angular position
of the probe in relation to identified navigational stars or terrestrial (lunar)
landmarks. The method of selfcontained navigation, which is based on the
release of an artificial probe, makes use of the effecta of the gravity fields of
earth and the moon on movement of the artificial probe and spacecraft.
In view of the fact that this method does not require mandatory viewing of tez�res
trial (lunar) landmarks, astronomic readings can be taken when the earth's surface
is covered with clouds. However, when taking astronomic measurements by this
method, some time is required for stabilization of the probe by the gravity field
of earth (moon). For this reason, when there is a shortage of time for astronomic
readings, use is made of other stars and landmarks.
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Thus, the use of an artificial probe combined with natural navigational stars and
landmarks solves the problem of astronavigation aboard manned spacecraft, not
only in orbital flight, but in flights from the earth to the moon and back, in
the absence of vieibility of te~restrial landtaarks.
Any of the abavementioned navigational parameters measured from a manned spacecraft
determines the surface, in each point of which it will be the same ~t a given point
in time. To put it differently, the measured parameter determines the surface of
the position of the spacecraft or geometric location of points of its possible
_ position characterized by constancy of the measured parameter.
Since measurements of a parameter are made with some element of error under the
influence of different causes, the position surfaces obtained in measuring naviga
tional parameters deviate from the actual ones. One can determine the link between
navigation measurement errors and errora in determining poaition surfaces by
using the concept of gradient of ineasured function.
 As we know [20J, the linear displacement of position surface in the direction of
the normal is determined by the equation ~n = ~0/g, i.e., it depends on error of
measuring parameter 0 and modulus of gradi~nt g.
If function 0 ls specified analytically in a rectangular system of coordinates,
0= 0(x,z~,z), the n~lmerical value of th~ gradient modulus is determined with
the formula:
t�` ~ ld~l rlx!!{(llU ~~fj'{~,1J9,'r~zf'~
Analogously, the error of determining the surface of the spacecraft position and
error manifested by change in navigational parameter 0 are related by the equation
~p = ~0/g. B}r using this correlation, one can estimate the error of determination
of surfaces of the spacecraft position when measuring various navigational .
parameters.
When measuring angle 0 between a navigational star and landmark on a planet's surface,
the equation for surface of spacecraft position in a topocentric system of coordi
nates OXYZ, whose Z axis coincides with the direction to the star and the beginning
of the coordinates is at the location of the selected navigational landmark
(Figure 27) will be written in the form of x2 + y2  z2 tan2 0= 0; the gradient of
this position surface is~g = cos 0/z; the error of determining the position surface
is:
Op ~ ~O � z0OIC08 O
9
Measurement of angle O1 between the direction of the navigational star and arti
ficial earth satellite also determines the conical sur~face of position. The
difference is that the apex of this cone is at the location of the artificial earth
satellite at the time of the measurement. In the rectangular system of coordinates
O1X1Y1Z1(Figure 28) related Elinked] to the artificial earth satellite (the axis of
this system is oriented along the line that connects the satellite and star), the
equation for this surface will be written down as x12 + y12  zi2 tanz O1 = 0. The
error of determining position surface of the spacecraft when measuring this para
meter with error DO1 will be determined from the equation ~pl ~ ~0~/gl a z~~01/coa ~1. ~
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:
~ ~ !
. / ~ . ~
~
F
~ . � ` ~
~ ~ ,
j ~ ~
1 `
. ~~ta a' ~
t ~
~
. / ,
~ ' ~ ,
/ '
X 1 ~ ~ _~n' .
\ ` ~ Y \
`
Figure 27. y
 Surface of spacecraft position deter l
mined by angle between directions of :
landmark on planet's surface and etar Figure 29. ;
Surfac~ of spacecraft poaition deter
 mined by angle between vertical to '
planet and direction of star '
~
The angle between the vertical to the
planet and direction of navigational
j star 02 ~lso .determines the coni.cal
sur�ace of position. The apex of this
! ' cone will be in the center of the
� 1~ planet, ~!hile the axis of rotation coin
~;,~b~ cides with the line that connects the
star with the center of the planet.
e~ ~
In a geocentric system of coordinates
02X2Y2Z2 (Figure 29), axis Z2.of which
coincides with the direction of the
x star from the center of earth, the ~
' � equation for this surface will be
y written down as:
~ ,
' xz � y~  t~~ 92 p.
The error of determining the surface of i
Figure 28. apacecraft pos~tion will be found with ~
Surface of spacecraft position deter� the equation ~p2 = 002/g2 = z2~02/cos 02� ~
mined by angle between direction of ,
navigational artificial earth satellite The surface of spacecraft poaition, when i
and star m2asuring the angle between the naviga
tional atar and visible planet horizon 03 ~
is also a right circular cone (Figure 30). The apex of this cone is on the line
connecting the star with the middle of the planet at distance za from its center:
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Rn
zo a
sin 0~
where Rn is planet radius.
The equation for this surface in a rectangular system of coordinates Oa~sYsZa~ the
start of which coincides with the apex of the cone and whose Z3 axis is in the
direction of the line connecting the planet center to the star, has the following
 appearance: x32 + z~32  z32 tan2 Q3 = 0. The gradient of this position surface is
determined with the equation g3 = coa ~3~zg~ while error of determining position
surface is ~
, ~e;~ 23JB3
i ap3 = B3  ~~s ' ~
When measuring angle Oy between the directions of two landmarks O1 and 02 on the
surface of a planet or angle between directions of centers of two planets }~1 and n2,
the distance between which is commensurable to the distance to the spacecraft, de
termination is made of the position surface that is a cyclide obtained by rotating
the arc of the circumference about axes 0102 (Figure 31a) or nln2 (Figure 31b),
which connect either two landmarks on the surf ace of a planet or the centers of
two planets (celestial bodies).
The cyclide equation is Z2 = R12 + R22  2R1R2 cos y, where R1, RZ are distances
from centers of celestial bodies ~landmarks) to the spacecraft, ~ is the distance
between centers (landmar.ks). The coordinates of the landmarks or centers of
celestial bodies and distances between them are known.
In a rectangular system of c~ordinates FI1XqYyZ4, related to one of the planeta n
(for example, earth), Z2 = xn2 + yn2 + zn2, where x~t, y~i, zn are coordinates
defining the position of li2 (for example, the moon)~in relation to IF1 (earth) at
the time of ineasuring parameter Q.
The distances between II1 and II2 and the spacecraft are determiried accordingly by
the following equations:
; _ ~li ,ra ; J4 ~ z.i;
i.~d.t~' ;iy~J~' ; i_az~'.
after differentiation, we shall have the equation for the value of gradient g4 =
 Z/R1R2� The error of determining position aurface is:
.  ~J~s~~ia,~~='k~1~_~L~II.
Analogously, when measuring angle Os between navigational landmarke on a planet's
 aurface and the vertical to it, determination is made of poaition surface in the
form of a cyclide, which is cbtained by rotating the arc of the circumference
about the axis that links the center of the planet with the landmark (Figure 32).
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~
'i
~
. .
_ !
_ ,
= The equation for this surface has the ;
following appearance: Rn2 = Rs2 + Ra2 
~ 2R~Rq cos 05. i
r
r
IJ ~.1
f~ For earth in a geocentric system of 4
coordinates OSX5YSZ5~ this equation can '
,;1, be written down on the basis of the '
~
~ "~y~~ fact that '
i
 :

~
yl  R3=x5T~ST Z5+ ~
" ~f '
n
. , ~y � Ri=.x~~m)5 ; t~Jsy~~` ~ (zszm},
~ ,
: :
  R~~=x~.,_y~, ,
x, ~
, .
/
~
where Rp is the earth's radius in the
r; f ollowing':f orm : *
'
. .   
,  _
:
�,_ym=zm=x;fiy~=z?; (xsxm~!~ ; (y;ym~~(z;z~l~
~XS}ysfzs) ~(:~s=xm~tl~lsy~~'t(zszm?'`~ cos 9;. '
0.; Y1
 After differentiation, we shall have
the equation for determining the
gradient: g5 = RoIRsR4�
Figure 30.
Surface of spacecraft position deter The error of determination of position
mined by altitude of star in relation surface is:
to visible horizon of planet ~O5R3R4
~p 5 = RG .
Measurement of angular diameter of cosmic body 06 determines the position surface
in the form of a aphere with its center in the center of the cosmic body (Figur2 33). ~
The radius of this sphere is: ;
~
 R sin 0 2` Rr co~?ec O6/2.
6
 If we measure the angular diameter of earth, the equation for surface of spacecraft
poaition corresponding to this navigational aystem of coordinatea will have the
following appearances x62 + y62 + x62 s Ro2 cosec2 06/2. f
~
The flaw of determining the surface of spacecraft position when measuring angular '
diameter of earth ~pe is determined with the formula:
*Subscript "m" i{~ formulas may refer t~ landmark ("or" in Ruasian).
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.
B'
F, / l1, , Y R:
. n
~ y` ~r
.
~ p, ,c~. xa .
~ x .
_ ~ Y4
' . b~ .
a
Figure 31. Surface of spacecraft position determined by angle between
directions of two terreatrial landmarks or centers of two planets
 _ 
h_~
~ ~Bb _ R1Bfi Rr, cosec ~6,~
 R ' ~Ps  _ .
f ~I, ~ 1 r.+~ 9a12 8h
2 _1
r f 1, R . :
/
I ~ ~ v,
1 ~ ~
I~' ~s1 ~ The errors of determination of surfaces
~ '~ti ' of spacecraft position when measuring
y/ any other navigational parameters can
i be defined in an analogous manner.
~
The above equations for errors of deter
Figure 32. mination of postition surfaces when
Surfac~ of spacecraft position deter measuring various navigational para
mined by angle between vertical to meters enable us to conduct a comparative
planet surface and direction of naviga analysis of the potential accuracy of
tional landmark readings made under different conditions.
It must be borne in mind that the choice
of a given navigational parameter in
each specific instance should be made not only on the basis of the conditien of
maximum gradient of the surface of spacecraft position determined by this parameter,
but of the requirement of minimum error of the measured navigational paramercer. The
latter could include various components for any parameter. For example, when measur
ing the angular diameter of earth, measurement error would include operator error,
instrument error, errors appearing beca~ise earth is not spherical and the�line of
the visible horizon is blurred, etc. Thus, use of a specific navigational para
meter should be preceded by comprehensive analysis thereof. It must also be taken
into consideration that at least three navigational parametere muat be measured
for direct determination of spacecraft coordinatea with the use of position surface.
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3.4. Methods of Evaluating Potential Accuracy of Solving Astronavigation Problems ~
i.
With a Space Sextant ~
As we ~ave already sta ted, Che accuracy of solving astronavigation problems whett '
using a space sightsextant is affected both by error of sextant reading and type ~
of reading taken. Moreover, accuracy of solving problems of space navigation also ;
depends on the selected set of types of angular measurements and .geometric loca :
tion of the manned spacecraft in relation to sighted stars and landmark3. ;
 We shall discuss below the methods of
~ estimating the potential accuracy of
solving astronavigation problems with
~ ` a manual [handheld] space sextant. ~
s~A~S
i ;
In processing the astronomic measurements, ,
/ a~~ we shall assume that the approximate lo
 ~ cation of the spacecraft is known; then
~`1~ ~ the astronavigation problem is reduced
~ , .
i ` ~ ~ to finding deviations of the spacecraft ,
/ ~ from the base orbit of flight. For
~ \ this reason, for any type of astronomic
~ ~ ~ measurement, the matrix equation of
I ~ 't
~ ~ ~ r6; ; link between deviations of ineasured
R' J 
~ j parameter q wi*_h location r can be
/ written down in the following form [10]: i
xe
% aa = na~ c3.~>
\ R / .
where h is the vectorrow [or line] that
~ depends on the type of astronomic measure
~igur e 33. ment and characterizes the correlation
 Surfa~e of spacecraft position deter between measurement errors and errors in
mined by angular diame ter of planet determining the coordinates of the space
vehicle. Let us demonstrate this for
(celestial body) [AESartificial earth different types of astronomic measure
satell~te] ~ ments. ;
"Starterrestrial landmark" type of ineasurement '
According to Figure 34, we can write down: .
rt,r? _ r cos(A1 + 0) (3.2) '
~
 where r is the vector of the location of the spacecraf t in relation to the center
 of the earth; n is the unit vector of direction of identified navi~ational
star, A1 is the angle between the lines of sighting the star and terxestrial land
mark, 0 is the angle between the direction of the landmark and local vertical.
By differentiating (3.2.), we shall obtain
_ _ _ _ _ .  '
;~~lr~r[lit �~ u cn~ ' ~
~,p~ ,
; ~
i
where a2 and bi are parameters of the model of the operator which take into con
sideration the linear component of man's reaction to an input signal presented to ~
him on a display. The "remainder" in the quasilinear model reflects the degree '
of inadequacy of a linear model for man's actual characteristics when working
in a given system, under given concrete conditions. ;
After choosing the structure of the mathematical model of an ergatic system to be ~
of the (6.1) type, the task of identification is reduced to experimental determina
tion of its parameters, evaluation of parametera. It must be noted that, although
we know of many diffes~ent identificat~on methods, most of them were not developed
to the stage of concrete algorithms for estimation of parar.ieters and structure of
an object on a real time scale; for thia reason, it is atill a pressing task to
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conduct research to upgrade these methods in the direction of improving accuracy
and speed of evaluation, particularly as related to ergatic systems.
We shall describe one of the effective methods of identification that is used on a
real time scale. This method amounts in essence to conversion of a differential
= equation equivalent in the time area to a transfer function (6.1) to a system of
linear algebraic nonstationary equations and then to recurrent solution of this system.
In the time area, transfer function (6.1) corresponds to a differential equation of
the following appearance:
_ 
~1 ,r,,~,i \1 G..'~''drrl
~l' ' ~ _ , (6.2)
~ , ;~t ~ ~ .
.errJ
_ where u(t) and z~(t) are input and output signals of the ob~ect, respectively; ay and
b~ are unknown parameters of the object, one of which, for example aa, can be con
sidered to equal one. In this case, the vector of unknown parameters h is an Z
dimensional vector (Z = n+rn+l):
hT =[ai~ a2~ an~ ho~ bi~ bnl (6.3)
The task at the first stage of identification is ta fArm algebraic equations in
relation to coordinates of unknown vector h. When there are unknowns, the coeffi
cients should be the observed coordinates of the ob~ect.
Let us introduce the following designations:
J (t ) =='k ( ~  
ay~r~ d"a~r) ~ ~ ,
 ~f �~~1(11,..., dt" t :
~ , r~ (t)=~~~., (r);
du ~r~ e�'a (r~ (6.4)
' d~ `~n+'! ~~,r..., df'" ~l ~t~i
~Ttr)==[�~~ll)...~~(~)I (l~:n.{�~}1), ,
With consideration of designations (6.4), the differential equation (6.2) for
discrete points in ti.me k can be submitted in the form of an algebraic equation:
' ~,(k) _ ~T(k)h (6.5)
Let us call such a transformed model the ideal canonical model. It does not take
into consideration conversion and measurement errors. These errors can be taken
into consideration in a canonical model of the following appearance:
~(k) _ ~T(k)h + n(k) (6.6)
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where n(k) is discrepancy, which is also called noise. The discrepancy could be ;
attributable to measurement errors, errors of approximation of a real object in a ~
linear model and other factors. ~
By measuring t~(k) and ~(k) at successive points in time and using one of the iterative ~
computing algorithms, we can estimate parameter vector h, the coordinates of which ,
are, according to (6.3), coefficients of differential equation (6.2). The difficulty
lies in the fact that ~ae need to know the derivatives of the input (to the m order)
and output (to the n order) signals. Under real conditions, repeated direct differ
entiation is not effective because of Che interference superimposed on input and
output signals.
To avoid direct differentiation of signals, let us turn to the other observed coordi
nates of the object on the basis of the method of additional filtration [21]. For
this, let us use certain ancillary operatorfilters with the same transfer functions
F(p) on the observed input u(t) and output z~(t) signals of the object. With the
proper choice of filters, all of the phase coordinates of signals are observable
~ at their outputs and are found to be related in the fashion of (6.5) to vector h
determined by~equation (6.3). "
Using the Laplace transform for equation (6.2) and then multiplying it by function ;
F(p), all poles of~which are to the.left of the imaginary axis of plane p, we shall
have: ~
n i Q ~dQJ~ ` ~
F ~P1 a~ PrY (P) ~ P~_. 9 ( ) +o ~ _
rt f Q~'
r _~i a..., (6.7)
? ~ ~ `
=F ~n~ ~,b, n~~~p~  _~,u,rt )io ~ �
( dr
r u i
where refers to the initial conditiccns of variables. In this equation, the
= terms that depend on base conditions of variables t~(t) and u(t) and their deriva
tives are extinguished [damped] in the time region, and the less the time of
the transfer processes of filters F(p), the faster this damping occurs:
lim L...~ jF~~~ ~ p!.a (d
ar'i/(t) ~ +Q
~ ~ � 1 +u~
v1 ,
I
and liir, f.~;'F . pl ~ p~~ ~d "fi =0 with t~o:;,
. ~ r.l dt  +o}
r : ,
where L'1 is the symbol for the inverse transform of Laplace. ,
Thus, by performing the inverse Laplace transform in equation (6.7) and disregard
ing the influence of base conditions, we shall obtain the main equation for the
method of additional filtration:
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,~~~~.t`~,,,,;,j (6.8)
1 dt` jF rpi ,~i~1 ~ l, dt~ ~ftpi
~ . ~ ~I .
f i~' 1r)
where i'_~ p; F; p.,,
~ ~ dr' ;~'!v,
anci ;'"(r>~ __/i~~l~p~rl%F~;l~~'r
l. ~~r' F
(6.9)
are the phase coordinateg at the output of the additional filters when signals y(t)
and u(t), respectively, are fed to their inputs.
We assume that in equation (6.8) ao = 1 and introduce the following designations:
~y.~:~F~;,~
f,~uir) 1, ~ ~l"yt~l
 1 . < < .  . . l ==.n ~f
L ~i~ 1t~cvi ~rr�~ ~rcn~
~u ~~~f(~)"tn1;Ij:
 r,~,~ rt> ~ ~ r_?_~ _ c6.lo>
~ Jt' ~E, 1 ~t' .I,~~N, ";'fl;
~ . L t ..i i ~n
With consider~tion of these designations, equation (6.8) for discrete points in
time k is put into canonical form (6.5):
~,(k) _ ~T (k)h
Here, ~(k) and vectox coordinates ~(k) are converted phase coordinates of model
(6.2) observed at the outputs of the �ilters r(p) at discrete points in time k.
Let us discuss the requirements of the structure and parameters of the additional
filt~rs.
In order to obtain estl.mates of all Z coeff icients of the object's transfer func
tion by the method of addj.tional filtration, we must observe the appropriate number
of phase coordinates at the outputs of the additiona~ filters. This condition is
satisfied if ttie order oE the transfer function of additional filters F(p) is not
lower than the order of the object's transfer function. Thus, taking into consider
ation the requirement that execution must be simple, we determine the structure of
the additional filters. In selecting the parameters of these filters, one shotrld
proceed from the level of highfrequency interference. The higher this level, the
narrower tiie bandpass of the filters must be. One must also bear in mind that
reduction of the bandpass prolongsthe transient processes due to the nonzero
base conditions.
 Figure 69 illustrates, as an example, the block diagram for conversion of phase
coor.dinates for parametric identification of an object, the model of which is
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described by a second order transfer function. For such an object, the order of
transfer function of additional filters should be at least two. The block diagram
illustrates ttiird order filters F(p).
a rtl p p ,vt~l
W(vl = 'v_
�tGz ` Q~P ' ~
do F du
! ra~ 1 (PJ r j 9
~1P ' ~:P 'ci0 ' ~ ~~P '~:l'''~ip r ~
y�j ~y�~"~t~~~~vl ~4~t~~ ~dirtJ v ~t1= d~v?ltl ~ dV~~tl ~~~_~y(~ll~ :
1 dc dc ~p~
.
Figure 69. Block diagram for conversion of second ~rder model of a dynamic
object to canonical form
Gutput signal ~(k) of the transformed model (6.5) is formed by measuring at successive
points in time k the output signal af filter F(p) connected to the output of the
object. To form the coordinates of fourdimensional vector ~(k) one uses discrete
measurements of two ~hase coordinates of the filter connected to the object's output
and two phase coordinates of input filter F(p). Additional filters can be executed
in analog or digital form.
The second stage of solving the problem of parametric identification is to calculate
the parameters of a nonstationarX object when the structure of its model is specified.
In the general case, we shall discuss the model reduced to canonical form (6.6). The
algorithms for calculating estimates of parameters of nonstationary objeets must
define the parameters of its model in the course of functioning of the ob3ect. Such
IDodels were named ada~tive [76].
The adaptive approach to solving the estimation problem makes it pos~ible to track
the changing vector of object ~,arameters as information is received about input and
output variables of the object. The simplest way to do this is to use recurrence
algorithms to calculate the estimates of parameters.
Recurrence algorithms, which do not require repeated pracessing of the entire
sequence of observations at every step, permits evaluation of the object's para
meters in real time. Recurrent or interative estimation provides a solution in
the form of a sequence of vectors, which are formed by means of a uniform process
the iteration process.
. In each calculation of estimates, iterative algorithms can malce use either of
only incoming information about input and output vari.ables of the object, or of
 preceding information~as well. In the latter case, the algorithm should retain
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prior information (i.e., it should have a memory). The volume of information used
to obtain a new estimate of parameters determines the depth of algorithm memory.
Recurrence algorithms can be divided into three groups i~ relation to this feature.
The first group consists of algorithms without memory, which do not store the
results of prior observations, and they are often called singlestep ones. They
use onethe lastset of ineasurements of input and output variables of the object
to calculate estimates of parameters. The depth of their memory, which we shall
~efer to hereafter as S, equals one.
The second group refers'to algorithm with memory of 2F2 (6p35)
7. If condition (6.35) is not fulfilled, vector ~(k) and scalar t~(k) are replaced
on the basis of the data of the new step in rueasuring input and outpu~ variables
of the object.
8. Calculations of items 26 [above] are repeated.
The values of ~ and ~ are changed until a vector ~ is found, with which condition
(6.35) is fulfilled.
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9. Calculations are made using equations (6.31) and (6.34).
The values of ~ and ~ are also chaaged in subsequent cycles of the recurrent pro
cedure for determining vector zs(k)�.
The abovedescribed method for lowering the effect of noise [interfereace] on
accuracy of estimation makes it posaible to perform calculations for any iaput and
output variables of the object, even when they are closely timed. It permits
gathering only the signals that cause less influeace of interference. Control of
interference is effected without making the algorithm more complicated o~ increasing
the digital computer memory required for procesaing it. ~
The astronavigational researchtraining unit described in the preceding section
enabled us to conduct an experimeatal atudy of the method of identification of
dynamic characteristica of navigation aad control systems that we have discusaed.
This study was conducted in the form of solving several teet problems. We shall.
discuss some of them.
Problem 1. Aaalysis of effect of deptn of inemory of estimation algorithm
oa its operating apeed;
~ A comparison is made of identification time for algorithms differing in
memory depth. Identif ication time is determined by the ~teration n~ber
starting wfth which the norsalized mean square e~rror of estimati.on does~
nat exceed 1�~. Input vectors ~(k) are formed from a noncorrelated pseudo
random sequence with unit dispersion. The zero vector is takea as the
initial esrimate of the vector of object parametere.
Table 6.1 lista th~ results of determinatioa of identification time for
a stationary ob~ect with parameter vector dimensionality Z~ 5. We used
estimation algorithms with memory depth S~ 1, 3, 3 and 4. We obtained
12 estimates of identif ication time k(0.01) for each algorithm with
different processiag of random input vector ~(k). The mean identification
time Itm (0.01), which was calculated from 12 ruas, is liated for each of
the four algorithms in the last column of Table 6.1. Table 6.2 lists ana
logous data on identif ication time, but for a process�with dimensionality
Z= 4 of the vector of parameters. ~
Table 6.1. Results of determining identification time (s) of stationary process
~ with Z s 5 dimensionality of parameter vector
~ ; ~ , ~ , , ` k..;
~ 5' I~ j ~ ~ s`, I s i:: j I~,~I
( 1 I Y i 3.~ i ,3~+ ~ :3' ~ ~ 33 ~ 3~ ~ �i:s ' ~2 ~ ~ i 4�3 I '?9 !`f ~
~ ' ~ ~ ~ ~ ~ ' ~ I ~ I�s~
,
1 � ~ ~ 1 (
' ~ ~ I
? I 2U i 2~~ I 3~ ( 3.i ~ 3l I 2i I':~ I 3!3 ~ 39 > 3+) i�~6 ~'~9 I
~ I , I I j ~ I i i` ~
~ 3 I t; i lu i~3n !:g I~?~; I 2,l I 31 } 2:i ; 15 i 13 j 16 ~?r~ I
~ I ; ~ I I ,
~ ; I I , I
~ i3 i g I y i 7! 9 I'J I i4 ;U j:? 9
, , ~ ,
 
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Table 6.2. Results of determining identification time (s) of stationary process
 with Z= 4 dimensionality of parameter vector
' c i II 2 I.~ .i' t�i �~`b I 7 I R I 4 I ~0 I It I I^ I(kII111
i
1 ~ 2'' I tG I`l:, . I 3:, I:j:~ ( 2l I:.'4 I Y2 ~ 3l I 2'l I:'1 I 33 I 2ri
2 I 11 I 12 I 19 I 19 ( IG I 13 I 22 I l4 I 18 ~ l~ I`?3 I 2f) ( 17
i
~;l I~i I N I I1 I ~ I lU (!3 ~ 11 I 7 I 13 ( 12 I Ifi I IU i lU
~
Table 6.3. Results of determiningmean identification time (s) for procesaes
with Z= 5 and Z= 4 dimensionality of parameter vector
       
Mean identification time_k~ _(0.01) _ _ _
_ _ t   i ! ; i
' Corre      I  _
; ~ .
'lation . , , ~ : . i ~ ~ .
time , ; ' ~
~  ii , I , ~ ~ i `1~ i ~r; I i I I~)
~
, ) ` ; ~ 1 I 'U }~I I1 ~ r ~
I  I  1' I1!!' IIS`i I
The obtained data are indicative of monotonous increase in speed of
running estimation a1Kor~thms with increase in depth of their memory
and decrease in dimensionali[y of the vector of estimated parameters.
Problem 2. Analysis of the influence of statistical characteristics of
input signal on operating speed of estimation algorithms.
The set~up of this problem is the same as the first, but in addition there
is change in time of correlation of the pseudorandom sequence, from
which input vectors ~(k) are formed.
Table 6.3 lists the results of determination of inean identification~time
f or processes with Z= 5 and Z= 4 dimensionality of parameter vector.
These data enable us to derive an important conclusion: correlation time
of input sequence has very little influence on operating rate of multi
step algorithms. Expressly this property of multistep algorithms deter
 mines, to a significant.extent, the success of using them under condi
tions of passive identification.
Problem 3. Identification of dynamic process with optimization of the
structure of model thereof.
This problem was formulated to check the efficiency [work capacity] of
identification algorithms when the structure of the model of the process
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is IlOC rigidly set. It is only known that the model is described by a
transfer function oE the (6.1) type and its maximum possible order n~~
is known. In this case, the identification system functions as follows.
 For all variants of models in the range of n~nmax and m~mmax, determina
tion is made of established values of estimates of parameters. The
minimum mathematical e::r~ctation of square of discrepancy between process
output and model output is a criterion f.or choice of optimum model struc
ture. In practice, calculation is made of the sum of squares of dis.
crepancy for each possible structure over a certain finite interval of
time. The minimum of these values indicates the structure and parameters
of the optimum model of the process.
Table 6.4.lists the results of defining the structure and parameters of
a process described by transfer function
Y ~f 1 ' f~
IC,�  .
l~ ~r~i . .
Identif ication is made on the assumption that rt~ax  2�
Table 6.4. Results of determining struc~ure and parameters of process
Model ?~cP~ I~ ~Ptimality I R~rke
criterion
:~,'11 I 1,3,i�lU~ ~ .
_ti_4:i_. I ~10� 10~
1 FI,Gtip
_ _  I .
f'~...~~~gp 1,4s� 10~ �
1F1,43p . I
fi,ll�~
8,14 � lU"=
1 ~ l,y~~p i U,'l~=p
fi=i"';�~~~!' ~ g;. ~ps Optimum model
ti ~ ~~r?/' t,u3P "
~_fi,1Jl 'r'~ fit/, : u,u7:r I
  I,~ifi.~~14
i l f I,!?.'/~ !~','I,i'~~ ~
Analysis o: the data listed in Table 6.4 shows that it is possible to
define pa.rameters of the process with adequate accuracy even when the
structure of its model is not rigidly specif ied.
= Problem ~r. Parametric identification of a twocoor3inate ergatic tracking
system.
T~e purpose of the experiment was to determine the effect of operator
proficiency ["degree of training"] on the dynamic parameters of a tracking
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 system of whic:h he is a part. The tracking system had two channels, hori
zontal and vertical. Determination was made of time constants for each
channel (Th, T~) during work of three different operators.
The results of parametric identification of the twocoordinate ergatic
tracking system are illustrated in Figure 71. This figure shows that
the estimates of time constanrs of the system are localized in region 1
with the best trained operator, and this corresponds to the lowest time
constants. Evaluation of the system with the least trained operator
corresponds torhe highest values for time con.stants, and they are localized
in region 3. The region of localization of evaluation of the system with
the average operator, 2, corresponds to average time constants. In addi
tion, this figure shows two regions for each operator, the one that is
farther away from the start of the coordinates corresponding to the first
performance of the tracking problem, while the region situated closer to the
start of the coordinates corresponds to performance of the task after 10
training sessions.
T~ ~ s
o~
 , _ o
J �
_ ~
~
t
~
~
~ _,.~1 9
t.~. L~ '
' ' 
~ I Th~ s
Figure 71. Results of parametric identif ication of twocoordinate ergatic
 tracking system
The results we obtained enable us to conclude that it is possible to use parametric
identificatior. to obtain estimates of efficiency of ergatic tracking systems.
6.3. Methods of Estimating Time Characteristics of the Process of Taking
Astronomic Measurements ~
Time criteria can be used to evaluate level of operator training for astronomic
 readings by means of a space sextant. The time required for an operator to take
astromeasurements is a random parameter, and to estimate it one can use the law
= of distribution of probabilities, which yields numerical characteristicsmathema
tical expectation, dispersion, etc.
The operatorsextant element of the system of autonomic navigation is characterized
by extreme complexity of internal and external correlations. For this reason,
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statistical data about ttie time and accuracy of astromeasurements durin~ a real
space flight would be the most reliable. However, there are some difficulties
involved in obtaining such statistical data. For.this reason, the most expedient
thing is to obtain the necessary statistical characteristics of astromeasurements
with simulation of a space flight.
The algorithm for processing time parameters of operator's astromeasurements could
be based on the mathematical model of R. Bush [16], in which time T of performance
of astromeasurements by an op~rator is described by gamma distribution:
~ c i (QP~ ~Y t~~~i~~1~ki C "��(S `~~i~) (6.36)
(11 I)1
with T>,Tmin~ where R and p are parameters of gamma distribution, '[min is minimum
time of astromeasurement by the operator determined by the technical capabilities
of the sextant and physiological parameters of the operator and pn is a parameter
that depends on the number of operator training [practice] sessions.
To determine the values of R,~p, Tmin in equation (6.36), let us put pn = 1 and
introduce the designation:
:~~~TTm~n~� (6.3~
Then equation (6.36) can be written down in the following form:
cA.k~
 Y(.ri  c'. (6.38)
I.l~  1 j I
.r 0 '
 On the basis of (6.38), let us write the integral distribution of observed values
in the form of an incomplete gamma function:
,    .
_ 1' ~ . e r " . (6.39)
Integral (6.39) is solved on the basis of tables [62]. Since the value of x here
depends on three unknown parameters, as a rule there are three set values for the
upper range of the integral (6.39) in the form of percentage points of distribution.
Let us propose, for example, a 10% ula, 25~6 u25 and 75% u~5 shares of integral
distribution. Then, using the tables [62] with the selected R, we find the values
of integral distribution (6.39) for ulo. ~2s~ u~s and solve the equation:
, ,
' ~6�40~
Let u~ select from the experimental data the time of operator performance of astro
 measurements that aquals thr~ae ~ralues of percentage shares of Tlo, T25 and T75,
and calculate:
~.s  r~ (6.41)
. E .
~i ~ " ~I'~
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Susrct?lri}; fur the val.ue ~f (obtained from the table for a given R) that is closest
to the result of calc~~lating E from experimental data, we find the sought parameter
R of gamma distribution. The values of parameters p, '[min and pn of gamma distribu
ti~~n (6.3fi) :~re c~ilc�ul~itc~d from the f~1law.in~ squatianH:
st,.;  rr ~S
l' _ " ' ;
T75 C_S
u:
Tnf~n _.T~~_ ~TiS T~I== T~~~5 ; ~6.42~
tt; . ~.5
/1 V,n ~~t ~ ~ ~  a.�~~.
where pl and a are constants determined from experimental data, n is the number of
practice series (cycles).
To obtain parameter pn, using (6.42) we determine in each trainit~g series the
median time of performance of astromeasurements by the operator using:
u~Ort  Q~ T50~ ~m I n~ ~
(6.43)
where Tson isthe median time spent by the operator on measurements ir~ the nth
training series. Then the estimate of parameter pn for this trair_ing series will
be:
I'/1 uso� ~t~l
(6.44)
where uso is the median tir.ie spent by the operator on astromeasurements in the first
training series.
We obtain parameter a from the equation:
. ~ , _ .
. ; , (6.45)
 where ~j is the number of practice sessions in the series.
The value of pl is determined using formula (6.44) with consideration of (6.43) for
values of time spent by the operator on astromeasurements in the first training
cycles.
_ Knowing parameters R, p, pn and Tmin of the law of distribution (6.36), we find
matt~ematical expectation m('r*) and dispersion 62('[*) of time spent by operator
on astromeasurements using the formulas:
_
iir T � r,~.  .
' (6.46)
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'Clic t1m~� :s~~t~ut by llie u~~er:~Lur c?u ar~tromeaeurements corresponding to probability uF
0.99 can be calculated on the basis of the following equation:
 ~ ~ . . r~ . (6.41)
where u99 is the value determined from tables corresponding to 0.99 probability and
the calculated value of parameter R of gamma distrib ut3on.
The effects of differ~nt space fligh.t factors on time spent by the operator on
measurements using a sextant can be evaluated in.the following manner. From the
experimental results, we calculate median time T50~ spent on astromeasurements by ~
the operator ~hen exposed to different space flight factors, then we find:
'r: 
JIM~
_ rt.,~w~,.. .l~ti~~~~  ~,~~~�1: P�~=_ , � (6.48)
us:~
We assume here that the ,characteristics of law of distribution f(T) change only
at the expense of parameter.pn~, i.e., parameters R, p and T~,n remain the same
as when taking astromeasurements without considering space flight factors. This
enables us to evaluate operator performance when there is a small volume of statis
tical data pertaining to the influence of different flight factors.
Thus, knowing the value of pn~, we can calculate mathematical expectation m(r*)~ and
dispersion Q2(r*) of time spent by operator on astromeasurements when affected by .
different space f~ight factors on the basis of the following equations:
Jll l[y _ ~ _'I" rm1n+ (Tr~~p" R + ~
~~/'ny ll~Pn~~~ ' ~6.49)
T~~�1'  Tm~u l ~ ~f:~r�
The data obtained from several experimental studies were processed ~y the above
described method. ~
First series of experiments. In the course of the experim~nts the following
time parameters were recorded: time spent by operator on astromeasurements in the
operatorsextant system, wtiich is the time ~rom the moment the signal is given to
start working to the momenC bearing is determined (when the operator depresses
button K); operatox reaction time, which is the time between giving the signal to
start working to the moment the operator starts to manipulate controls; time of
~ making decision that sighting is completed, which is the interval between the moment
the operator finishes handling the controls to the moment he depresses the button.
In the course of instruction, wl~ich occurred in 1 to 206 training cycles, it was
demonstrated that the time spent by the operator on measuremeiits in the last
 training cycles, 151205, changed negligible and was characterized by the following
parameters: vlo = 16.8 s; v25 = 17.5 s; v50 = 22.33 s; v~s = 27.5 s.
. Using equation (6.41) we calculate:
 _ ~ ''..=.~7,;, _ 1~,~~.
~ 17.r~ � ~ 1~~,~i
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F(1R nFFI('lAl, t 1~F. ONI Y
7'he clo5~~st to e= 14.'L will be a value of E calculated with R= 2. For this reason,
we Shall take R= 2. Using f.ormula (6.42) we make the following calculation:
u
T~nw  ~t~i.i....., ~ ~i'~~4~25~= � .
u75 u�~:
 d7, ,  ~'~~x  ('_'7,~ 17.5)= = I 1,7 s
~~,Gcs  o,JB
 Here u~s and u25 were taken from the tables with R= 2. Using (6.42) we calculate:
u:; u.,; ''.~~t u.`~K 0 17 1/3
,
~'t; t~.~5 ':%,~i  17,;i
Hence, the asymptotic distribution of time spent on astromeasurements with sextant
by the operator, without consideration of effects of space flight factors, taill
appear as:
jlr1:(?,I7(t),li (t.~ 11,71]e 0,~~~'~~~~witht~,, 11,7 s
Mathematical expectation and dispersion of time spent by trained operator on astro
measurements without consideration of space flight factors are:
i~r!t`) r~~~i~~ ~!{n: 11,7~~';'0,17 ''3,:i 6;
' ,'~t"'1 1~' 1?= ~U,li;~' . 6~~~;j S2
The time spent on astromeasurements by a trained operator with probability ~.99 is:
~ ~ t! _ ~~,t~~ i),;; ~~t~,~ S
The distribution of time spent by the operator on astromeasurements at different
stages of training can be written down as follows:
, i, ; I~ ~:.~'with t'. s
1
~
. , , , i ~ _ . ~ ~t.~i.� .f~ ~?u:;~.
where
In order to estinlate parameter a in (6.42), ~ae separate training into training
 series (Table 6.5). In Table 6.5, ~j is the number of practice sessions per series.
We calculate the value of pn using the following equation:
/~n= :~+Sp(t5t '..'(15) _Zmin ~
u5~1i ` Zu~ln
_ where u50 (151205) is the median time spent by the operator on astromeasurements
in the last training series, u5oi is the median time spent by the operator on astro
measurements in the ith training series.
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l~rom ~yuaCton (6.45), substttuting the values for n and pl, we obtain:
159.99 = 205  (1  0.234) lia
hence, a = 0.983.
Table 6.5. Parameters of distribution of time spent on astromeasurements
. . , _   i
Training uso, s pn pnx~ ' pn T99, s~
series ~ ~ _ j
    ,
' I ' I
i ~ ~i~ ~ ti~ ~ 11 '~.31 ' _1 .j{ ~ 11~~~jt~ ! i '
~ .i,~~'1 ' ~I~ : , . . l,:r I 11 ,.l':. ~ ~1111,1 {
i  i _ ' . ~
.~~r j .1 i ~.I . Ii~.Il~i . I ~1~1~11' ~ii.~~ I
i. i~ ~ _ ~ , il.~.:/i I .i._i�~ ' i V�~.. ~ .
' : , i 1 I ii~.h~ ~ :~!1 i
'~i~ i ' 
1 ' ~
~ ~t!: ,"~i ~ I ( U,7:,`i I 37,y U,~JI;i i1,~~
~ 1:1!. ..ii., ....i', ~ ~ . �i.) i !I,'.~lik ~ ~~~'i f
i i ~ ~
On the basis of the foregoing, we can calculate mathematical expectation and dis
persion at different stages of training using formulas (6.46) and (6.47).
Table 6.6 lists the parameters of distribution of reaction time and operator's
decision making time as to completion of astromeasurements with a sextant, without
the influence of space flight factors. '
Table 6.6. Parameters of distribution of reaction time and time of making
decision that astromeasurements are terminated ~
I I I N ev I ' ~
^ N ~ N ~ N N, ~ ~ N I W I _ i N i U~ ~ ,
Criterion , . ; . I _  _ ' : , ` 
i ; .
 ' ' ' ~ ~I
_ . . _ ~ i ~  ~ I
edCt.lOA time '~,.i�i'ii:~~~:~l:;~~:i.~~jll. I Ill,llflj,~7i; ~:'~i ~l_"~1.: ~:::1: I~~lia' .
, ~ 1~ j I
~   �    . . _ ,
@C1SlOII i'~~ 11i.'1~\'I, i~ ~'.f~ :i ~I~~~~~ill, :'I~ r I'~,~{`~,I
�I.,,nn
making time 1  I.. ~ ~I~~... _ i . ~ 
Table 6.Z. Parameters of distribution of time of astromeasurements by operator
under the influence of simulated space flighti factors
m: a~ t � II~I~S~~~m~_.) I.!'~~r/
Factor I N,~~r. I I (~V~' I,z, ~ I~~~
~.~oo�..  �0'~
I S~ s' ~i+i�'! , e'li'?
_ i,
Turning chair I u,!?~c 1:~:+,r,y 7t ,5 ;t~,5 I.n,i I 1_~, i~~
Weightlessness ~?,ic! :tu,.~ 1hu,y 7~,n 3u,:; :i,~~; 1r,:~~
Irregular situ ~~,~,i:i ;i:i,�t�1 '1�_>f ~3'~.3 ' ~_',~t ;1,`~8 30,9t
ation +
weightlessne~s
Irregular u,,iK I 3_~,~~~~ ~'I~.,l 7R.n ,ii :1,?7 '4?,JI
situation .
  _ ! . _ ~
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In these experiments, we examined the effects of different space fiight factors
on time spent by the operator on astromeasurements, as well as the effects of these
factors on reaction time and decisionmaking time as to end of guidance process
(Table 6.7). Analysis of Table 6.7 indicates that mathematical expectation m(T*)
under the influence of space factors was 3040% higher than the background value,
whereas dispersion ef astromeasurement time increased by more than 3 times. Table
6.8 lists the results of experimental studies of decisionmaking time referable to the
the end of the astromeasurement process. Analysis of the figures in this table indi
cates that the time required to make this decision increases by 100140% under the
_ influence of the different space flight factors. Table 6.9 lists the results of
experiments dealing with reaction time. Analysis of these data indicates that
reaction time increased by 100125% under zhe influence of the different space
flight factors.
Table 6.~. Parameters of distribution of operator's decisionmaking time as to
end of astromeasurement process
_   ~  i j ; _
~ ; , . ~ : ' ~ ~ r c. �p i
Factor ; ~ _ ;,.~,,,1. i~~(y, ~  ~ . ; :j  : )
; , , s , s ; : ~ ,;r ~ ~
, ~ ,   i
Chair turnir~g'~.~~~~ , . ' ~~,t: ~ :',7:3 Virtually no changei
~ . ; , ;
Weightless � '  ; _ ; 7. ' ;
Irregular ~
situation + , , i
weightlessn. ~
Irregular ~ ' ' . ~ I
situation . , ' ; , ;
Table 6.9. Parameters of distribution of operator's reaction time under the
influence of simulated space flight factors
_ 1 ' I . I  _ _ . .
. ~ i
i N ; ~ ~ !,�1 . ) 1 t
' ~ , I , ~ ) ~
Factor s2 s2 , I . ,
, ~
.
_ _
~ i ~ ~
Chair turnir~ ' . ' ' ~ ' ~ I ; 1, No change
i
Weightless , . . �r~ ~ _ .,r ' ~ ~ t?. ; I ~ , , ~
ness ; ; 1 ~ ~ I
Weightlessn. , t~'~ 3._ i~i.,,~~ , i ~
~ I
+ irregular ; ~ ~ I
situation : , , I '
Irregular . . , , , , t:: ! .~,r ; 1', , i
situation ;
Second series of experiments. Operators with professional skill participated in
tnis series of ex~~eriments.
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Unlike the first series of expeximents,
,T ~ in this ca~e astromeasurements were
taken on the basis of other than point
landmarks on the ground, and they were
identified from navigation stars. The
 xt, estimated time of performance of astro
measurements by the operators during
~ training is listed in Table 6.10. Ana
lysis of.these results indicates tliat
the changes in time parameters of astr~
~ nu . measurements by a professional operator
in the course of �instruction are close
, t~ the change in m('[*) for the entire
group~ of trainees. However, there was
~ considerably less scatter of values for
� time spent by professional operator on
~ , astromeasurements.
. .
~ ~ ~ Third series of experiments. In this
:i,, , ~ ~ series we evaluated the time character
~ . ,R istics of astronavigational operations
. ~ ~ ,F 7~h
r,~,� during simulation of a 3day flight in
i space. In preparing fQr the 3day experi
ment, operators were trained and each of
�1. ~ . them had 80 practice sessions.
1 6 16 26 36 46. 56 66 n
Figure 72. Analysis of the training results shows
that operators who had participated in
Changes in astromeasurement time as a experiments before (1 and 2 in Figure 12)
function of number of training sessions _ showed an insignificant loss of skill
is astromeasurement time) after a 6month break.
i, 2) operators who participated pre
viously in experiments For the sake of comparison, the sa~e
3, 4) operat.ors who did not partici figure illustrates changes in astro
pate in experiments before measurement time as related to training
5) operator with professional skill unskilled operators (curves 3 and 4) and
an operator with professional skill (curve 5), which show that the operator with
professional skill "moves up" to the trained level with more stability (less
scatter uf results as to time spent on astromeasurements).
Table 6.10. Parameters of distribution of time spent by operator on astromeasure
ments during training _
 I ; iS~ R ~ ~ ~ :n;:i. I �i.`i , I S ~ a I
u~ g i S: v. . 9 i ~ ; S I 3 82 I..
I_ . _ . .  !i
l7,'~ I I ''y ~ I ;t.~? ~ ?a.? j . ~~''i ~
i.. t . ,I  i
~ The time parameters of astromeasurements during the 3day experiment were determined
using the previously described method.
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~~a aFFtc~i.i, ~~sF ~tvt.v
Figure 73 illustrates the curves for changes in estimating mathematical expectation
of time spent by operator. on astromeasurements for each operator during the 3day
experiment (astromeasurements were taken during 8h shifts) and Figure 74 shows the
analogous functions for reaction time.
m(z,s 1it day 2d d` y I 3d day I
1u4 , , ~ , i ' ~ ' .
~ ~ i ~ ? i
ao I ~ ~ I I
g I i I
~ i i I
f~` ~ ~~K ~ ~ ! ~ I I i
s:, ' ~ ~ ~ i _ I I ~
f ~ ~ I .
I ~ ~~~L
JO ~ I~ 7' i ~
i8 ~ ~ ~ i I (
:F ~ ~ ~ ~ i i
t~ ~ ~ I , ~ I
( ~ I ' I ~ __1 t , ~
1Z 16 ?0 14 4 B 1? f6 10 14 4 B 12 /6 ?0 14 k. t, h
Figure 73. Changes in time spent on measurements during 3day experiment
_ (t time of day; m(T*) estimate of mathematical expectation of
astromea~urement time); 1, 2, 3operators
m(~~:,~, s lst day 2d day 3d day
I i I ~ I I I
I~,I ~ ; ! ~ ~ I I
~ ~ r ~ ~ ~ ~ i I
' 1 ~ ~ ~ .
~
r't ~ I i ~
I r ; ~ I I
I' , ' ' j~ I ' f ' ,
~ ~ I ~
j,;~ i~ I ' i I
~ ; ~ I
; i ; ~ i ~
I '
Y, 1 I ~
I' ~ / ~ I i ~~i ~
~ , ? +r ~ r ~
i ~ .
~ ~ , ~ ~ ~ , ~
i ~ ~ I ~ i ~
, _ . _1 _ . _ _  L _L_~ i
;n :0 To 4 d!? 15 .0 ?v ir R J.~ 1~ 10 7~r 4 t (h)
Figure 74. Changes in reaction time during 3day experiment; 1, 2, 3
operators
Figure 7~ illustrates the curves of change in estimation of mathematical expecta
tion of astromeasurement time m('[*) (curve 1) and reaction time m('[r) (curve 2)
in different training cycles n.
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~Y?a nr� t~~�t.~?i . t r~~ r~rn .v
p~f;o~~~~T`f lat day 2d dat 3d day
i l .fi ~ .
l,b Jti
r,.s ,rs~
1,4 .f4 /"'~x
Y
1.f .i1
l, I J7 x ,
/,1 3! M~ ? i '
10 )0 I
U9 : y
_ ~r. 7x .
1 15 JO 4S f0 7S 90 10S f?I ~ �
Figure 75. Functions of changes in estimates of mathematical expectation of
astromeasurement time and reaction time during 3day experiment
Analysis of the findings as to astromeasurement time shows that there.was an in
crease on the f irst day to 20%, as compared to the background. On the second and
third days, a~tromeasurement time diminished to the background level. Reactiot
time increased by 30% on the first day and then gradually increased.
6.4. Evaluation of.Effects of Difierent Space Flight Factors on Accuracy
of Astronomic Measurements
The accuracy of navigatia~ l readings made by an operator using a sextant is one of
~ the main parameters deter.:.ining the efficiency of the astronavigation system. For
this reason, one must make a quantitative evaluation of thi.s parameter of the astro
navigation ~rocess.
It is known that when taking astroreadings with a sextant it is virtually impossible
to obtain the true value of the measured angle. As a rule, various~errors are
contained in the readings, including instrument and operator errors. There can
be systematic errors and random ones that are caused by numerous factors that cannot
be taken into consideration.
The main cause of a systematir error is refraction of the atmosphere, astrodome and
windows. In addition, *?oncoi.~cidence with the initial pasition of the dial to the
initial position of the uairror or prism (error in dial zero) could be the cause of
systemati~ error. _
Systematic errors can be detected and excluded from the measurement results. For
example, when measuring from earth the anglzs between two stars ~'y) or between a
star and earth's horizon (h), the true values of these angles can be obtained
by calculation, using the equations
cos yo = sin dl sin d2 + cos 81 cos d2 cos(,al  a2)
wheie ya is the true angle between stars, dl, 82 is inclination of stars, al, a2
is right ascension of stars, and
sin ha = sin ~ sin 8+ cos ~ cos & cos (S~r  a+~)
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1~?1~ ~~f ~1't~ 1 ~i 1 ~ct' t1'VI \
wher~ ho is tlw ciu~ anblc UeLween the star and earth's horizon, ~ is the latitude
of the point at which the reading was taken, S is incltnation of the stars, S~r is
Greenwich sidereal time at the moment of reading, a is right ascension of the star
and a is longitude of the point at which the reading was taken.
At *he same time, :.hese angles could be measured several times by many operators,
and then we would have N measured values of angle yZ(h2), where i is the measure
ment number.
Knowing YZ and Yo we can determine the absolute error of the ith reading:
~YZ = Y o  Yi
When there is a large number of readings N, the following equation should apply:
1~ ~v, r~. ~
W
This statement is base3 on the following thesis of error theory: when there is
a large number of ineasurements, random errors of the same magnitude but different
sign are encountered at the same frequency.
Randam errors due to numerous factors that cause them to appear are distributed
according to the normal law (this is als~ confirmed in many experiments). Conse
quently, dispPrsion D or standard deviation 6 is the exhaustive estimate of
accuracy of astromeasurements after exclusion of systematic error.
_ The standard deviation for N readings can be calculated using the following
equation:
/'.v
/ ,~(10 1J'
~ ! ~
3 T ' . .
~r
With a low N, one uses the following equation to obtain an unshifted estimate:
/ ,
~ ~1'~i  1'i)~
i_�I
_ ~T _  N~ .
By using this quantitative estimate, one can demonstrate the influence of the
following factors on accuracy of astromeasurements: professional training of the
operator; weightlessness and confinement in a closed space; various factors (stress,
emergency situation, etc.); type of astronomic measurement taken, etc.
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I~r?R c1Fl~lt'IAL 11!;N; t1N1.1'
 In the results submitted below of testing the effect of the above factors on accuracy
of the operatorsextant system, we used the relative standard deviation (RSD) as a
criterion. This criterion was introduced to demon~trate the effect of a factor
under study, not only with regard to a specific instrument or visualization model
used, but to obtain generalized results.
 Table 6.11 lists the results of studying the effec~ of professional training of an
operator on accuracy of ineasuremenrS in the operatorsextant system. This table
shows that operators with stable professional skill (cosmonauts) take astronomic
readings with 23 times more accuracy than operators who are not specialists, who
had performed 100 to 140 such operations before the study.
Table 6.11. Relative standard deviation of errors in astromeasurements for
different t es of readin s �
Operator Star Star Star Landmark
star landmark horizon landmark
Unskilled operators 2.52 3.0 3.45 5.07
Cosmonautoperators 1.0 1.35 1.45 1.7
Table 6.12. Relative standard deviation of errors in astromeasurements for
different types of readings under the influence of simulated
s ace fli ht f actors
Factor Star Star Star Landmark
star landmark horizon landmark
None 1.0 1.19 1.67 2.53
Coriolis acceleration 1.37 1.46 2.04 2.81
~ Weightlessness 1.35 1.49 2.0 2.95
Weightlessness + irregular situation 1.76 1.89 2.27 3.35
Irregular situation 1.12 2.16 1.69 3.46
The results of testing the effects of various factors, using the method described
in section 5.5, are listed in Table 6.12. As can be seen, an irregular situation
simulated by the method of posthypnotic suggestion had the least effect on accuracy
of readings. The scatter of results is apparently attributed to differences in
mental stability of operators who participated in the experiments, It must be
 noted that there were cases when an operator was unable to take readings at all
in a simulated irregular situation.
The [ype of astronomic measurement is one the main factors determining th2
~ accuracy of readings (Tables 6.11 and 6.12).
The program of a 3day space flight was simulated, with concurrent recording of
physiological parameters and performance (including accuracy) to test the effect
of time spent in a closed and confined area (mockup of manned spacecraft cabin)
and hypnotically suggested partial weightlessneas on efficiency of t::e astronavi
gation system. Table 6.13 lists the relative RSD of reading errors that were
demonstrated in this experiment. Analysis of the data in this table shows that
the accuracy of astromeasurements on the first day of aimulated flight diminishes
Y~v a mean of 30%, after which there is ad~ustment to "flight" conditions.
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Table 6.13. Relative standard deviations of astromeasurement errors in
3;ia ex eriment
0 erator Back round First da Second da Third da
Uperator A 1.0 1.42 1.08 1.18
Uperator B 1.11 1.31 1.19 1.06
Operator C 0.89 1.07 1.24 1.04
Aversge operator 1.0 1.30 1.17 1.09
The results of these studies are indicative of the strong influenc~ of specif ic
space flight factors on accuracy of readings. Hence, it is mandatory to consider
these factors in designing systems of the operatorsextant type and in screening
_ operators. In view of the fact that these results were obtained under simulated
conditions and, therefore, constitute essentially a qualitative description of
the effects of the abavementioned factors, one should call the attention of re
searchers to obtaining strictly validated quantitative evaluatian of the degree
of their influence under real conditions.
6.5. Algorithm for Evaluating the Accuracy of Solving Astronavigation Problems
by the Recurrence Method
The main purpose of astronavigation is to define the navigational parameters of
 flight (coordinates of location, vectors of flight speed and direction angles).
In a manned spacecraft, this task can be performed by means of an inertial naviga
tion system and a space sextant, which is used to correct the latter (see Chapter 4).
In order to make corrections, one must first form an observation, i.e., obtain the
difference between measured values of some navigation parameter and value of the
same navigation parameter obtained with the ZNS [inertial navigation system].
Let us assume that the operatorcosmonaut uses the sextant to measure angle Om as
be~ween the direction of the terrestrial landmark C(~1~, a~) and navigationa~I
star S(d, a) (Figure 76).* The same angle Ocalc can be calculated using the on
board digital computer from the INS data usin g the equation:
(6.50)
where x, z are coordinates of location of the spacecraft in the inertial system
of coordinates OXYZ, calculated from INS data, ~lm~ ~lm are the geographic latitude
and longitude of the specified landmark [lm], 8 and a are inclination and right
ascension of the specified navigation star, Ro is the mean radius of earth 
cos alm = cos ~1~ cos J~1~; cos S1~ = co~ ~1~ sin alm;
 cos Ylm  sin ~lm; cos a* = cos d cos
cos y* = sin d; cos S* = cos d sin a.
variant of this problem is submitted above in a somewhat different form
~see Chapter 4).
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On the basis of the information obtained from the INS (Ocalc) and sextant (Omeas~
observation ~ is Ec~rmed as the difference between calculated and measured size
of angles, i.e.,
z= ~calc  ~ meas  ~~calc  ~~meas (6.51)
where ~Ocalc is the error that appears due to error of defining coordinates in INS
and ~Omeas is the error of ineasuring angle 0 with use of the sextant.
� To change finding (6.51) to the general
appearance of z= Hx + v, one must
submit calculation error ~Ocalc in the
' form of error of determination of coor
~ dinates of the location of the space
craft. For this purpose, let us take
\
~ ~~~Y~n ~~~i~% the partial derivatives for coordinate
. _ , ~0 h
, eleanents x, y and z:
, , .
_ r~?'f.,. i.._ y oo~ai~ = a~ + a� oz (6.52)
~  _J
~ � where
/ / ~;8 _ cos u*N A( (x  Ri, cus �i
dx N 1' N sin 0
' ~.i
i
~ rl9 c~'c ~+.N .11 (y Il~ cn~ ~ZII~
Figure 76. �  �
~A'I
Calculation of angle between direction of 'ti " ~
star and terrestrial landmar:c [ opland v~_ ~ ~ ~~1
~'~N + Ylid
~z N N ,~n 9  ;
 mark] _ . ~
,l l==(1~,~ rv~; ~c lm  x) c~~>s u" I I~n r~?~ .N) ~us H*
�1(h'ocu~~~lm ~)rusy*;
l~'Il~'o~_r�~~,,r.~i'~{(l~UCUS;;lm~j"~(R~~co,}'lm 'l~.
In matrix form, equation (6.52) has the following appearance:
~x
~~n ,~o ~
~Ocalc ~I dy ,,r ~ 9!; ' (6.53)
a,~
Substituting (6.53) in (6.51) and designating ~Omeas  we shall obtain, with
consideration of errors in determining flight speed:
_ j~ ~x
~J
Ju u0 ud
~ � _ L ,1 r_ .tiy_. 'J` ~ ~V~ v, (6.54)
I ~ y
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or in the general form of:
 fl.~'
where _ ( .J~. . Je _,ie0 ~ Ol ;
~ ~?J c~= I
.r.=(~.r 1~~.: ~1'..~Vl,~i't~~.
We assume that the statistical cha.racteristics of errrors v of astromeasurements
are known and governed by the conditions of:
M{7J} = 0; M{vvT} = R8(tT)
where M{...} is the symbol of mathematical expectation, R is the corrElation matrix
of error vector v and d(~T) is delta function.
The obtained observation z can be used to calculate estimates of ~rrors of deter
mination by means cf INS of navigational parameters x and covariation matrix of
dispersion of these estimates of errors P(t). Since there are measurement errors
when using a sextant in the astronavigation system, there will, of course, also
= be estimation eriors:
d~=xx
where Sx is absolute error of estimation of the vector of state nf errors of deter
 mination of navigation flight parame*_ers with the use of the INS.
Absolute error of estimating mistakes and standard de~~iations of these estimates
 of niistakes (square rootof diagonal elements of matrix P} could be the quantitative
indicat.ors of accuracy of the astronavigation system.
, On the basis of the foregoing, it can be stated that it is necessary to know the
real values of mistakes in determining coordinates x and th2ir estimates x, as well
as standard deviations af estimates Qx, in order to examine the accuracy of solving
astronavigation problems with the use of the INS az~d spac.e sextant.~ These values
can only be obtained by solving the enti.re navigation prob.lem. Use of mathematical
and ttalfscale models makes it possible to solve navigation problems on the ground.
The astronavigation research~raining unit (ARTU) described in Section 6.1 is a
good basis for this purpose.
The algorithm for e~timating accuracy of solving problemG of autonomous navigation
with the use of a spar.e sexrant is contained in the ARTU r_omputer system. The dis
~ tinctive feature of this navigation method is that the recurrence method is used
to process the results of n avigational readings with the use of the optimum
Kalman linear filter. Chapter 4 has a mathematical description of this method.
In view o� the limited storage provided in the ?.RTL' computer system, a simplified
mathematical model was developed to solve this problem. In particular, we simulated
the flight of a manned spacecraft in a circular orbit inthe ~uatorial plane, and
measurements wexe taken at a constant rate.
Figure 77 illustrates the block diagram of the model produced in the ARTU. The
contents of the different units of the mathematical model inputted in the computer
system of the ARTU are as follows.
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r~~1t ~~tN~ ~ ~~er. ~~~~1 ~
Computer
system Input
= Simulation chamber data
Solution of Solution of ~
 ' eq1p�u~~io s Initia]. moi~ition ~
 Simulator Wl~h idea3. condit W~~i rea~ ~
of Geles' . ~ initial ' it.condit. ,
tial condi~ions i
sphere . '
~
. , ~~work" H p I
~ ~ ~r. l~r� ~ I
 i~ jKSV~
~ ~ ~ i
atorr mockJ ~ ~
,~:r~~J L o ,
,"displa~ 1�m ~ Z, t' K. R
S ula~ Z) 2~
~ tor of ~
~ iearth'sl i
i surface.`
 lr   ~
x(t2/ Data ;
 _ . . . . .  ti ~ ) ut~ut ~
_ unit ~
Figure 77. Block diagram of mathematical model fcr evaluating accuracy of
solving astronavigation problems
 ~i.c~ ~r.c~ ~i.m~ ~r.m~ ideal and real calculated and measured navigational angles
_ in ith reading
H) linkage matrix
P) covariation error matrix
transiti~nal error matrix
ZZ) ith observation
x(t2/t2)) vector for estimating errors in determining coordinates
and speed of space~raft flight at'time t2 according to
_ readings made at time t2, inclusively
x(ti/t2_~) vector of estimates of mistakes in d~termining coordinates
and flight speed at time t2 according to readings taken at
greceding step (at time ti1)
ICZ) matrix of ~aeighted coefficients at time ti
R) covariation matrix of vector of mistakes in navigational
readings
1. Input data unit:
Ro = 6371.21 kmmean radius of earth;
H= 150 kmaltitude of spacecraft flight;
~ Ro H 6521821 sangular velocity of manned sp~cecraft;
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 ~1~ = 60� geographic latitude and longitude of
~1~ = 0�} location of terrestrial landmark;
. o
8a= 90�} coordinates of navigational star;
standard deviation of error of determining
QLO ~RO ~SO 210 ~}__lecation and flight speed at the point of
~VLO ~VRO ~VSO  1~ ~~S extraction in orbital system of coordinates;
Q~ = 1�standard deviation of ineasurement error
 2. Unit of initial conditions:
_ .r�~~__(~~,, f1; _r;,., _=.i�,,~;~.r,;: ~.ro ~L~, ~1.~,=c' .
'LG+
JN~,' U: J~ ~  J.~  =F, liru , ~k,,_:~Rn;
~
~�u=~~: ~~~o==;~~~, � ~=o   ~ r,  ~ n=c?so~
V l�" , ~'a4' .~~1~ ~V � .
~ MU ' r~ ~ xu l~ .r9 L~ L~~ l 1.6,
t: l� _ 1 � , l' ~l~' � ~l~' � i3 ~V . ~V . _ .
vNo' ~:P ~i~., y�u l y~,~ y;~ RU , RO i~R;,,
_  7. 1~?~/S
~'z,,~ , 91%Z~~ 1 ~SO "s~, ==:~i�s~�,
~ where OXYZ is the inertial system of coordinates ~(X and Y in the equatorial plane,
Z over the axis of earth`s rotation), O1LRS is the accompanying trihedron of
reference of the orbital system of coordinates (L along orbit, R along local verti
cal, S forms a right orthogonal trihedron with L and R), ~ are random numbers
distributed according to the normal law with M[~] = 0 and M[~2] = 1, B is the
 matrix of passage from orbital system of coordinates (O1LRS) to inertial system
(OXYZ):
r~~5~1 siu'~~ 0
/j si n !:3t ~~us !
~t 1)
O f 1 1
Subscripts H and p refer to ideal and real coordinates, respectively.
The value of the covariation matrix of mistakes in setting initial conditions
at the initial point ~n time has the following appearance:
. _ z
I
; ~
a
~'n = ' ~ .
~I'L
2
oVR
�
r oys ~
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1~()R OM~1('IAi, lltil~: ()NI,Y
3. U~itt fur solving equations of motion w:Lth ideal initial conditions:
xHZ = (Ro + H) cos ~t2;
~HZ = (Ro + H) sin ~t2;
zHZ=O
where tz = tZ_1 + h= ih; h is the m~asurement (observatiar.) frequency ["pitcb,"],
h= 5 min; i is the number of ineasurements taken, i.= 1, 2, 3, n.
4. Unit for solving equations of motion w~.th re~l initial conditions:
.rP; = .r~; ~x; _ ~Ro'~' ) cus ~t j Ax; ;
~Nr =l~; ~lr=~RoI tl) sin ~t; ~ ~~li~
,
~r~=~~r r~~~~= z~~
where are elements of errors in determining
 li~ p/~ coordinates in the OXYZ inertial ~
_0~ , ~ $ . system of coordinates;
' ~L ~ ~L ~I are elements of errors in coordinates
I and flight speed in the orbital :
_ =~S :_~p ~S l system of coordinates. �
~1V; ~
 a~~~, ~V ~
~_~l~S_, _~l'S I~.
The transition matrix of errrors of de~ermining coordinates and flight speed in the
orbital system of coordinates in the case of constant frequency of observation.s
can be written down as follows:
�_~c._l :.'s:3S'l: II !9s3!,!/tt~>_~~C 1;~ U i
s :.'(IC)'' S~~ (1
0 U U s~~
~l> ,
..?~C� 11 l,~ ''C! s
1 s, ~ (3~n t) ~i~!!c    ~.i
~ ~.1 i) !!.S ~ ~ C
where c= cos S2h; s= sin S~h.
Unit for calculating angle between ~.irection of terrestrial landmark and
navigational star.
As we have shown above, one ean calculate angle 0 between the dir~ctions of specified
terrestrial landmark and navigational star by using equation (6.50).
In order to obtain the value of the ideal calculated angle Oi.c in the equation
for M and N one must insert the values of coordinates xH, yH and zH, and to calculate
real angle Or.~ one must introduce xp, ~p and zp.
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t~?tt ~i ~�~r ~
6. Unit tor calculating linkage [connection] matrix.
~ The matrix for linkage af astronomic measurements H can be written in the following
form:
 f 1; _ ~X~ a ~c ~e z~ p 0 ~ } , 
~
' where
 i/uj,~C _ i uS il'" i1~~; .S~i (Rii CUS Q~ YR1~ ' .
~l.r Nr {.'~r; sin 6 i. C
~'~i_1�C____~~]=t~'j.tii;lR~.C_i~9~11~=I1:i/ , .
l!1 5;.~ i~ C
~:qi.C ,~,s1~`'_ '1!: (i~' '  1_]lq
 u_ .v; ~ i. c
7. Unit of optimum filter.
Calculation of optimum estimates of errors made in determining ;coordinates of loca
" tion and spacecraft flight speed is made in the computer system of the ARTU, on
the basis of solving the following matrix equations of the optimum linear filter
of Kalman:
, r, . t, . . i ~  /...r . . .
~ =~J~r.'~..~ %~~l~~;~, r. . . ~  k~,:
~r' ,  = i' ~ t ~  f~ l l. ~ . . �
r, ; .
. ! � I
` is vector of estimates of errors in
I determining coordinates and spacecraf t
 ~ .1.`~' i
, ~ flying speed in orbital system of
where ~i : I, ~ coordinates O1LRS at time tl (ith
; readin~ taken with space sextant
i,~�~ ~ tlirough time ti_1 inclusively;
 P(tZ~t2_1~ is the covariance matrix of errors in estimates of vector of system
stcitus at time ~~i calculated from information as of time t2_1 inclusively; P(t2/ti)
is ttie same with consideration of ~observation at time ti; K(t2) is the matrix of
weighted coefficients at time t2; R is the covariance matrix of the vector of
errors in navigational readings v. For a onedimensional measurement of "star
terrestrial landmark" the covariance matrix of errors in measurement of R equals
dispersion of errors of ineasurement [R] = 62; zi is the ith observation formed
on the basis of information obtained from t~ie INS (Or,~  Oi.c) and space sextant
(0  0�. and it is the actual difference between calculated and measured
angle ~ at time t2:
z2 = ~r.c  ~i.c + ~r.m  ~i.m = ~O1 + ~02
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NOR (1~~iC'lAl. I~;~F; (1NI.Y
where p01 is error of determini.ng angle 0 due to difference between real and ideal
vectors of spacecraft state and ~02 is o~rerall error, including operator error,
_ instrument error, error of converters, etc.
8. Printer unit.
The results of running the program for estimating the accuracy of solving navigation
problems by the recurrence method with use of the space sextant, the algorithm of
which was described above, the following are printed out:
Or.~real measured angle, to check proper choice by operator of specified
navigational stars and landmarks;
pQ22overall error of ith measurement, including operator error as one of
its elements;
pL2, pRi, pSi, pVL2, QV~, ~VS.Lerrr~rs in determining ccordinates and
~ ~ pacecraft~flyin~ speed in the O1LRS system of coordin.ates;
dLi, dR2, bS2, dVL2, dVRZ, dVSiabsolute errors in estimates of mistakes
made in determining coordinates and flying speed in O1LRS system of
coordinates, where:
b~L = ~L  ~L; dVL = OVL  ~VL;
 ~
SR = OR  ~R; 8VR = ~VR  ~VR;
b`~=pSpS; b`~VS=pVS~JS;
pL, ~R, ~S, ~VL, ~VR, ~VS are estimates of mistakes in determining coordinates and
 flying speed in the a1LRS system of coordinates; 8L, dR, Sg, ~b~,, ~b~g, 8VS are
standard de~~iations of estimates of errors in coordinates and flying speed in
O1LRS system of coordinates.
The above algorithm is used for. experimental evaluation of accuracy of solution by
cosmonautoperator of navigation problems by ttte recurrence metho+d with the use of
the space sextant:
~ The results obtained in the experimental studies with regard to estimates of accu
racy of determining the coordinates of spacecraft location b~L made by three
operators are illustrated in Figures 78, 79 and 80. Figure 78 illustrates t'.ie
estimates of error dL obtained when ~ubject A worked on the first (1, 2, 3) and
third (7, 8, 9) days of flight.
rigures 79 and 80 illustrate estimates of error dL obtained during work by subjects
B and C during the 3 days of flight (curves 19). Analysis of these results shows
that there is some scatter between estimates of accuracy of determination of
coordinates obtained during work by the same operator during differen ~ sessions
of solving astronavigation problems. Thus, this scatter constituted Bl~in  2~
and b`~max = 8 km for subject A in the 75th min of "flight." Figure 81 illustrates
errors averaged for each day in estimates of mistakes in determining coordinates
~L obtained for the work of subject A on the first (1) and third (2) days.
Figures 82 and 83 illustrate analogous results obtained for the performance of
subjects B and C in the 3 days (curves 1, 2, 3). These data ir.dicate that there
is no overt correlation between accuracy of evaluation of determination of coordi
nates and time of day in the 3day period. For all three subjects, the scatter of
mean daily estimates constituted 1.56 km.
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h()I2 ()MNIt'IA1. 1 ~tih: ()N1.Y
R ~ .
~ z
, ~ ~
f
, 1
. ~
~ ~ ~ ~ 1 .
st~. I~ ~ J
)J~ ~ ~
~ ~%r '
; ~ I /
~ , ,
; , i .
 ~
a , ,
, ~
; ~
~ /
~ j ; ~'/~a
: r' I \
, I ' ~r~~/ \
` ,
 I i ~ ~ \
~ j i ~ j
_ ~ \ ,T
i % _ 9
'r ~ ~ ~a
 ~ ~ . . ~
. S ~ c : s JJ JS ao 4S SO SS 60 fS 70 t~ min
Figure 78. Error in estimate of mistake in determining spacecraft coordinate
as a functi~n of navigation system operating time with 5min
intervals between readings, subject A
Figure 84 illustrates the estimates averaged for the entire 3~day experiment for
each operator (curve 1 for subject A, curve 2 for subject B and curve 3 for su~
ject C). From these curves we can see that the individual distinctions of
Lr.ained operators had little effect on accuracy of evaluations of determination ~
of coordinates of the spacecraft's location. The scatter of average values of aL
 in the 75th min of flight for the 3 days constituted 3S km.
On the whole, these experimental studias dealing with accuracy of determination of
coordinates of the spacecraft's position indicate that it is possible for a cosmo
nautopera~c~r to solve astronavigation problems using a sextant within the
avli.l.ablc time aLtc: adeyaate training, the absolute error being b~L  3... 5 km.
Otlier coordinates oi: tlle vector of evaluating errors have considerably lower
j abso].ute error factors. In order to improve the accuracy of solving astronaviga
tion problems it is necessary to upgrade the instrumental precision of the sextant
and increase the number of sessions of making astronavigational readings.
6.6. Standard Eva.luation of Operator Performance in Taking Astromeasurements
With a Sextant
For standard evaluation of the performance of different operators during training
on an ARTI1 Lor astronavigatianal measurements, it is expedient to select a proportion
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~ oi excellent, good, satisfactory and unsatisfactory ratings that would yield an
encouraging avera~e gradeo The initial parameters~for standard evaluation could
be the time and accuracy of operator's astrcnavigational measurements.
~
 i~k" ~
~5 ~ '
sV ~ . .
_ .s i..
 .
. , ~ ~
~ r .
~S i~,~_..~~
i / i;/~ .
r i i~l ~ ~
,
. js ~ ~ c
/ ~ r. '
I //~Y~ I ~ .
/ / c.
'S ~ /
\
70' ~ , / . e � .
~
I � ~ ~
r ~
~ i '`\.1
r,' / ~ ~
~ ~ ~ � /~y
i `O'~ _ ~ , JSZ
~ '  ~ S
,S iP 1~ 1:' ,~G �s 4~' SO ~S 60 6S ;0 t,min~
Figure 79. Error in estimate of mistake in determining spacecraft coordinate
as a function of navigation system operating time with 5min
intervals between readings, subject B ~
Let us discuss determination of the timerelated standard evaluation of operator.
training. According to the space flight conditions, available time Ta~ for
operator to take ~stromeasurements using a sextant and terrestrial landmarks c~n
be calculated on the basis of the following equation
T _ H~Ro + H~ tan ~6.56)
av ' R~ Y
where Ra is mean radius of earth, tI is altitude of orbital flight, V is orbital ~
velocity of flight and ~ is the angle of sighting terrestrial landmark along
flight course.
Table 6.14 lists the available sighting time for the terrestrial landmark, in
seconds, at different fli~;l~t altitudes and sighting angles.
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 E. rr~
SS ~
~
0 ~5 ;'C l3 JU JS v0 G3~ 3~0 S~ GJ 65 70 r, min
Figure 83. Daily averages of errors in estimating mistake in determining
spacecraft coordinate as a function of navigation systetn operating
time, subject C
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~ . ~1
. I
~~t.~ I
I
I \
{
i n~
`JI
{
r~! i /
. i ~
_ c
; i ~ ~
~ ~ ~ ~
.
~
?
/ l w` 1/ _ . _ .   / . \~:~r~~a'.
, ~ ~ ~ , ,
" ~ ~ . . , . , min
Figure 84. Errors in estimating mistakes of det~rmining spacecraft coordinates
as a function of navigation system operating time, averaged for
3 days of work
1) subject A 2) subject B 3) subject C
Table 6.14. Estimated time (seconds) of viewing terrestrial landmark at
 different flying altitudes and sighting angles
Sighting angle, degrees F1 ~,n altitude, km
100 200 300
 45 13 26.5 40.5
60 22.5 45.5 70
Considering the specifications of the space sextant, the time spent by the opera
tor on astromeasurements in orbital flight should not exceed 45 s. Operator
productivity diminislies when space flight factors (weightlessness, vestibular sti
mulation, negativ~ emotions, etc.) are present.
As St1UWi1 by the experimental studies of operator performance using a sextant with
simu.lation of space Elight factors (see Chapter 2), actual time for taking astro
navigational measurements could be increased by 3040%, as compared to training
on the grounci. Consequently, the time available to the operator for astromeasure
mznts in orbital flight should be reduced, for example, from 45 to 27 s. This
standardized evaluation of time is considered satisfactory.
As we have mentioned above (see 6.36), the experimental studies established that
the time spent by the operator on astromeasurements using a sextant can be des
_ cribed by a gamma distrib~ition:
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 (RPPnl> ~ [PPn~T  Tmin~ ~Ri eppn (TTm~) with T>T min
.f(T) _ { (6.57)
p with T~T min
where T;nin = 11.7 s, R= 2, p= 0.17 1/s and pn depends on operator proficienc}~
(for a welltrained operator pn = 1).
On the basis of (6.57), the probability that the operator will perform the astro
measurements in specified time Tsp can be determined from the formula:
TSP
 p(T  Tgp~ = f f~T~CZT C6.58)
Tmin
Integral (6.58) is linked with a partial gamma function and tabulated. Se~ting
Tsp = 27 s, let us calculate the value of u= p(TSp  Tmin~ = 0.17(2'7  11.7) = 2.6,
which corresponds to probability 0.720.73.
In order to determine the standard time corresponding to the "excellent" xating,
~ let us establish in the table a value of pn corresponding to probability of 0.5.
Time T5o = 22.7 corresponds to such a value of pn.
In order to determine the standard time corresponding to a"good" rating, let us
establish a quantile corresponding to probability:
0.7? + 0.5 _ 0.6
2
Then the standard time wil'�_ be T60  u60~P + Tmin = 1.84/0.17 + 11.7 = 23.5 s.
Thus, the time spent on astronavigational measurements by a welltrained operator
using a sextant can be rated as follows: "excellent"up to 18 s, "good"up to
'L2.5 s, "satisf actory"up to 27 s, "unsatisfactory"27 s or more.
in order to determine the expected average grade, let us mention that the total
number of "satisfactory," "good" and "excellent" ratings const~tutes 72%,
"excellent" constituting 50%, i.e., "satisfactory" and "good" make up 22%. On the
other hand, the total numher of "good" and "excellent" ratings constitutes 60`/�
then there will be 10% "good" ratings. Consequently, there will be 12% satisfactory
and l8% unsatisf actory ones.
Ultimat~ly, the expected score will be: 0.5�5+0.1�4+0.12�3+0.28.2 = 3.82. This is
low exl~ected average score.
To raise the average grade, let us select a quantile corresponding to probability
U.7 to establish the rime rated as "excellent." Then the quantile corresponding
to probability of good scores is:
0.73 + 0.7 _ 0.71
2
~ Hence, ttiere will be 70% excellent ratings, 1% good, 2% satisfactory and 27% un
satisfactory. The exp~cted mean score will be 0.7+0.01�4+0.02�3+0.27�2 = 4.14.
This is a rather high expected mean grade and it will be a stimulus for reducing
measurement time.
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Thus, the following standard ratings are established:
"excellent"to TeX = u~o/p + Tmin = 2�4/0.17 + 11.7 = 25.8 s;
"good"to z~d = u~i/P + Tmin = 2�5/0.17 + 11.7 = 26.4 s;
"satisfactory"to Tsa = u73Ip + Tmin � 2�6/0.17 + 11.7 = 27 s;
"unsatisfactory"over Tsa = 27 s.
Standard ratings of astromeasurement time during training can also be established
for untrained operators. The time spent by an operator on astromeasurements with
the established standards can be submit*ed as follows at different stages of
training:
_ "excellent"to TeX = u~o/ppn + '[min;
~~good"to T~d = u~ilPpn + Tmin~
"satisfactory"to TSa = u72/ppn + Tmin~
 "unsat~sfactory"over TSa. Pn = 1 an(1  Po).
We can determine the values of a and Po experimentally. As we have shown previously
(see Section 6.3), Pn = 1(0.974)nx(10.291) = 1(0.974)n�0.709; consequently,
by setting the number of practice sessions one can ca~culate Pn and determine the
standard time for the different ratings.
~ As an example, let us state that n= 10; then Plo = 1(0.974)10x0.709, while
standard time will be:
Y `4~11~7=='~J,,y s;
eX ~,t?�u,7~
_
r d  . ~ _';i~,i; S;
9 i, ; ~
�~,fi
tsa i l.i 31.3 s;
n, l; V,i!+
Iuns. ~ ;31,3 s.
Hence, there will be 70% excell.ent ratings, 1% each for good and satisfactory,
28% for unsatisfactory. The expected mean score will be:
U.7�7 + 0.01�4 + 0.01�3 + 0.'LS�2 = 4.13
This is a high enough expected average grade and it would serve as a stimulus for
r.educin~; 3Si:2'OiRe215lICCIiIC'I1C time.
Staudarclrating of accuracy of astromeasurements taken by operators is based on the
following considerations. Lxperimental studies using the analogdigital unit of
the autunomic navig~.ition system revealed that the accuracy of superposing navigation
stars and terrestrial landmarks in the center of the visual field of the sextant
depends little on tt~e number ot training sessions. The errors of ineasurements are
 ~;overned by the norma]. law with mathematical expectation m~~*) = 0 and standard
deviat i.on o (L1*) = 3.45' .
S.inc~: mean square c:rror 6(~*) is a gauge of accuracy of astromeasurements, by
selectin~; tile cor.relation between ratings, we can write down the standards for
accuracy i?i the fulJ.owing general form:
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5tanclard Por "ixcellent" rating: DYex  Ki~~~*~ ~
standard for "good" rating: ~Ygd = K26(p*);
standard for "satisfactory" rating: ~Ysa = K3~~~*) ~ ~
 standard for "unsatisfactory" rating: DYuns � Kaa~O*~ ~
where ~yeX, ~Y~d and pysa are maximum mean errors of astromeasurement defined by
the corresponding rating; K1, K2, K3 and K4 are coefficients characterizing the
selected proportions of standard ratings; Q(~*) is the mean square error of astro
_ navi.gation measurements using a sextant.
Errors ~y are governed by the normal law, and for this reason we can determine
the probability that error (I p~yl) does not exceed the standards for "excellent,"
"good," "satisfactory" and "unsatisfactory" on the basis of the following:
f'i lIOY~ : ~l'ex~__ q, Ki�~_?~x .
u,~;T~~~
h.~~,~ d ~ .
!':l~~Y~ ~ ~Ygd1=='U (o.G7~ )i ~
~ ti.,a1'sa'I.
~~a ~~'~Y~ ~ ~l's~`'~'Q~ (O,~i"1~~~`), ~
\
( ~ ,Y~ C ~Yun~  1 l~'s, '
where P 1, P 2 and P 3 are probabilities that absolute measurement errors will not
exceed the standards for "excellent," "good" and "satisfactory," respectively,
or the probability that the error will fall into the specified interval; Py is
the probability that the measurement error will exceed standard ~Ysa; $ is reduced
 Laplace function.
~ One can select coefficients K1i KZ and K3 by making calculations and comparisons
of different variants of standard ratings. L,et us determine for c!(p*) = 3.45'
the probability t}iat measurement errors with use of sextant will fall into each
of the confidence intervals, on the assumption that K1 = 0.8, K2 = 1.2 and K3 = 1.8.
We can then obtain:
~~,ti�~.~'~ ~1~.1,1'.t1U,~~~;
~ :i ~ . ~Ir
 1 ,~,1�'~i~ � eX (u,t;;~r~�~
~ _ ~j~ ! ,'~7 . ~U i,~s 1 ) U,7t;;
z(I 11 1'gdl.._ (u,i>7o(.~'~) ~
/~3 (i.~ ~ I � . , ;.Sa ~I ~ I ,tilia(.1"p) . (.?~(i~l)  :l),S).~;
u,~i7a~.1")
~yuns}_ 1 .O,U1.
Hence, 58% of the ratings are excellent and 7% unsatisfactory.
In order Co determine tlie pe rcentage of good and satisfactory ratings it must be
bortie in mind that 77% is referable to the sum of "good" and "excellent" ratings,
~ while 93% is refeiable to "satisfactory," "go~d" and "excellent." Hence, there
wil.l be (7758)% = 19% ~;ood and (935819)% = 16% satisfactory ratings.
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 On the basis of the foregoing, the error made by the operator when taking astro
 measurements with a sextant can be rated as follows: "excellent"up to 2.7';
"good"up to 4.2'; "satisfactory"up to 7.21' and "unsatisfactory"over 7.21'.
Witlt this variant of selected standards, the expected average grade of operator
ratings will be: 0.58�5+0.19�4+0.16�3+0.07�2 = 4.28. This is a rather good average
score and it will be aa incentive for the operator to improve measurement performance.
For space sextants with Q(~*) = 1', standard ratings with an average score of 4.28
will be: "excel.lent"0.8'; "good"1.2'; "satisfactory"1.8'; "unsatisfactory"
_ over 1.8'.
To rate an operator's performance as a whole for the duration of a navigation
session, we need a,~eneralized criterion that takes into consideration both the
accuracy o~ readings and time ~pent on taking them. The generalized average ex
pected score For accuracy and time of performing astromeasurements with a sextant,
which would constitute 4.21 with average score of 4.28 for accuracy and 4.13 for
measurement time, could serve as such a criterion of operator proficiency.
A cr~terion selected in the form of polynomial K= A6(~) + Bc3(T*) + C, which
. includes error 6(~) in the operatorsextant system and time spent by operator
to take astromeasurements using a sextant, could be one of the possible variants
of this criterion. Coefficients A, B and C are selected on the basis of the re
sults uf stati.stical processing of astronavigational measurements by the least
squares method.
However, use of this criterion alone to evaluate the professional performance of
 cosmonautoperators in a system of autonomous astronavigation cannot presume to be
_ entirely objective. This is attributable to the fact that id~ntical errors in
_ astromeasurements could yield substantially different results with regard toerrors
in determining the piloting and navigational parameters of flight as a function
of time of the navigation session and type of orbit (normal or irregular).
6.7. Evaluation of Operator Training According to Quality of Performance of
 Ast.ronavigation Tasks
Optimization of modern systems of autnomous astronavigation is ver,y closely related
to refinement of operator training, as the chief element in this system. At the
same time, a high level of operator training, as is the case for specialists in
any other occupation, is directly related to refinement of inethocis of evaluating
' their proficiency and constant monitoring of training rESUlts.
However, development of criteria and methods for rating cosmonaut performance or,
more precisely, training level, is among the most difficult problems, and to
solve it one must make combined use of modern advances in various scientific dis
ciplines. Mathematical methods should play a prominent role here.
The known ratings and characteristics, which have been welldeveloped for technical
 equipment and closed automatic cont~ol systen~s are not suitable for quantitative
evaluation of a cosmonaut's work capacity. The reason is that an operator and,
in p3rticular, a cosmonaut is notable for an immeasurable wider variation of all
his qualities, traits and characteristics. They can change rapidly and over con
siderable ranges, depending on external working conditions of the cosmonaut, on
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his internal, psychological set, physical conditior., activities and many other
factors. For this reason, the first and main distinction of quantitative ratings
of a cosmonaut's work capacity is their stochastic nature, since the experimental
data obtained each time characterize only a certain specific condition of the
cosmonaut or system at a given point ir_ time, under given conditions, set, etc.,
but are not suitable for yielding any generalized evaluations. This problem is
the most important and, at th.e same time, the most difficult as it applies to
a research object such as a cosmonautoperator.
Many authors have tried to describe the perf~rmance (trainittg level [proficiency])
of human. operators [15, 31]. We shall describe elsewhere (see Section 7.1) one of
them, which has been developad and used extensively. At the present time, re
searchers (methodologists) must content themselves with the dynamics of critical
parameter$ of a given type o� special work, To assess operator proficiency, it
is methodologically expedient to single out two ratings: immediate [operational]
evaluation of quality of operator performance referable to a specif ic activity and,
on the other hand, comparative evaluation of operator training for performing a
task with consideration of a se.ries of training [practice] sessions within a
specific period of time. The later rating should characterize the degree o~ sta
bility of operator work in accordance with the required standards.
The methods of quantitative analysis of every such complex systems as the astro
navigation systems of a spacecraft are ained at obtaining special [partial] criteria
 of efficiency of performing different operations, which is characterized by such
parameters as accuracy (errors), time and ~nergy spent to perform a specified task.
In more complicated cases, une uses criteria such as probability of solving a
given problem within a specific time under specified conditioiis, degree of completion
of the solution, etc.
Some researchers use, if it can be thus put, unilateral generalized ratings of
, performance to describe ergatic systems. Thus, A. A. Bulat et al. use, as a
generalized criterion of level of operator tra3_ning, an integral evaluation,
which is based essentially on technical parameters, s~~h as control t1IIlP_~ energy
expenditure, accuracy of control, etc. [15].
Another approach to the problem of evaluating the quality of operator training
involves the recording of various physiological parameters. Auth~srs assess, on
the basis of dynami~s thereof, the psychophysiological tension of the operator and,
~ from these parameters, stability of skill [14, 56, 57, 64, 75].
In some cases, one can assess the quality of cosmonaut trai~iing in astronavigation
operations by comparing current characteristics of special [partial~ performance
parameters to the maximum values thereof, with which the entire problem can still
be solved. Thus, in one of the series of experiments conducted in the pressurized
 cabin of a spacecraft, the subjects used an algorithm for solving a navigation
problem. The first part of the problem consisted of mathematical operations using
a Vega keyboard computer and tables. The second part consisted of determining
input data for subsequent calcul.ations by means of graphs. Work time and accuracy
of solution were recorded at each stage of calculation.
Figure 85 illustrates the values of time spent on running the algorithm by two
 subjects, as well as mean values before and during the experiment. This figure
shows the maximum time, exceeding which could cause failure in solving the problem.
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As can be seen from the submitted dat~,
performance of both the first and second
t,s tmax subject did not exceed this range, even
'f~' during the most difficult, adaptational
t before experiment
m }1 stage of the experiment. Consequently,
t afte~ ex eriment
t k m. P with regard to this special criterion
~.'Z `Ztm before experim.}2 it can be noted that the operators were
..:x~,,..~l.,~fr;.
~ adequately trained to solve navigational
' problems and were able to perform the
~ o e io days task under certain "stressful" experi
Figure 85. mental conditions.
Time characteristics of subjects 1 and 2
in the problem solving process as a func At one time we noted that development of
tion of number of training sessions n skill in controlling systems based on
[tm mean time] the tracking operation depends largely
on the operator's professional training for work with other systems [38]. Thus, the
characteristics of tracking reaction of A. G. Nikolayev were somewhat higher than
those of the copilot of the Soyuz9 spacecraft. Apparently, this is attributable
to the fact that the commander, A. G. Nikolayev, is a pilot; his training, prior
professional work were related to contro~. movements of the order of visual and motor
coordinatiou, i.e., his controlling (tracking) skill was labile and rapidly
"adjusted" to other types of similar work. ~n the o~her hand, control of tracking
creates a stable conceptual model, which is used actively when switching to other
control systems.
We submitted this thesis to experimental verification. A large group of subjects,
consisting of students from an engineering school who were unfamiliar with the
astronavigation system, achieved the results (time of taking measurements) in the
 course of training that are illustrated in Figures 86 and 87. A*~other group of
sub,jects, also with no prior knowledge about this astronavigation system, consisted
of USSR pilotcosmonauts. Their achievement is also illustrated in the figures
(solid lines). As can be seen from these data, the latter group is superior to
the student group in all parameters. The instruction period for cosmonauts
 consisted of about 40SO training sessions (7080 for the first group). At all
stages of training, their parameters for performance time were 5060% better than
for the first group. A compar~tive analysis of mistakes in astronavigational
operations also revealed that the pilotcosmonauts performed the work with consider
ably less scatter of obtained data, and accuracy was 23 times higher than that of
ordinary subjects. It should be notecl that there was manifestation of previously
established skills in the work of the professional operators. They used small
economical movements for control, holding the controls lightly, often with two
fingers, 'rather than grasping with the palm of the hand. Small wrist muscle
movements were used for control. In addition, the training process was not asso
ciated with psychopiiysiological tension.
Thus, professional skill in controlling an astronavigational measurement instrument
has a beneficial effect on speed and quality of training in the specialty of
astronavigator.
This fact is linked the most closely to the extremely important problem of re
learning and "transfer" of skill. It is also encnuntered under the name of the
problem of skill interaction in the psychological literature. Many experimental
works deal with iC. However, the problem of transfer and interaction of skills
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has not been sufficiently investigated, although the success of training qualified
operators for various control systems depends on its scientific solution.
S el. .
x.
I, ( f!
~
1. / \
~ / ` ~
ro i \ ~ '
~ ^
~ ~
1~ ~L\~~ ~ I ~ f ~f , ~
_ s b i , ..,.~r_.~ J~.~.. ~ ~ , ~ `~~.L
~ l~ti'>=V~'_ ' t~,y`*s ~ s~~+
d x
. ._._i _ _ .i~
U S w ;~c~ 7~ 1~ J5 ~i0 ay so fs v
Figure 86. Integralquadratic criterion for rating operator performance
quality as a function of number of training sessions n
_`S~ ` i I  We have tried to demonstrate that it is
lU;' i_. J I__. suf ficient to analyze the dynamics of
~ I o perator performance qualit y in the
. a~' ~ i~ I i course of training to assess his profi
~ I ; ciency in working wirh astronavigation
t~~ i ~ ~ j ' ~ l ~ systems. This can be done. But using
, ` L' J'~ s ecial criteria does not ield the
r,,i ~ ~ i~, i ~I p Y
i ~~'``=L~ . ~ j optimum evaluation. It is necessary to
; t~ L.. ~._L _..L . . 
_.~j"'~~
~U 4t~ ht~ e'l~ iG~U >2A 140 r~ work out generalized criteria that
Figure 87. would be based on both the reliability
Astromeasurement time as a function of features of machine work and funetional
number of training sessiorG n parameters of a man included in the
system as a separate uniC.
 1) operator group Tgg ,
2) ~perator group m~'t*)
operator with professional skills
 6.8. Operator's Psychophysiological Characteristics in the Manual Mode of Navigation
Automation of control processes implies optimum distribution of functions between
tlie machine and man. Man is usually charged with the duty of "insuring" the equip
ment, iii the eve~ of partial fail.ure. For this reason, we studied here the operations
that a man must perform in the event of failure of the onboard computer. Concrete
� astronavigation problems made up by a special algorithm served as information models.
Operator work consisted af performing successive arithmetic operations. The next
stage of work was with gra~hnomograms. The time of beginning and ending each
operation wa~ entered in a special log.
Concurr~ntly with running the specified work algorithms, we examined such psycho
physiological functions as logical thinking, immediate memory, motor coordination
activity, etc.
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The obtained results were used as base data to work out forms of presenting logical
and arithmetic material, logical algorithm systems that would provide for high
_ efficiency of operators in this type of work.
 Psychophysiological Characteristics of Operator Performance in Solving
Autonomous Astronavigation Problems Using an Alphanumeric Computer
It is possible to obtain and process information in a system of autonomous astro
navigation if there is a highspeed computer with memvey units aboard the ~anned
spacecraft. Of course, the AI~C [alphanumeric computer] must be small in size
and operate reliably. If the ANC has a failure, man takes on its functions. In
this case, he has to perform many arithmttic and logic operations, and under cer
tain working conditions this could lower the overall reliability of the system.
Moreover, participation of man as an element in the autono~ic navigation system
could prolong significantly the time required to solve astronavigation problems.
Apparently, a search must be made of the optimum combination of human and machine
capabilities to assure reliability of the process of control and navigation of
space fiight. This problem can be resolved if the psychophysiological capabilities
of man are taken into consideration when designing manned spacecraft.
Numerous experimental studies and manned space flights have demonstrated convin
cingly that it is expedient to have semiautomatic control and navigation systems,
_ in which the principle of optimum use of both man and machine is applied.
Thus, American researchers compared the reliability of operation of onboard auto
mated systems with numerous backups and systems including an operator. It was
established that, at first, the work capacity of all systems was the same, but
already on the 4th day of simulated flight the work capacity of the automatic sys
tem began to decline. However, by the 14th day, the work capacity of systems with
4fold backup was rated as satisfactory, whereas the reliability of the system
that included man was found to be much greater than that of automated ones.
_ . Of course, including man in any chosen
spacecraft navigation ~ystem is pre
L,M~n ceded by comprehensive determination
~ ~ of his role in this system, his capa
s~ r_~''`~~'t�t j} I bilities with regard to pe rf~rmance
_ .1
 ~'.'1~:;,~ of concrete operations. In the case
"`w'~ in question of solving autonomous astro
~ ~~_~..~a.~~L, navigation problems using an ANC, the
J 4 S 6 19 9 lJt!!11! 14 n operators worked with a set of test
Figure 88. tables which listed the results of the
 Running time for algori.thm of autonomous preceding stage, i.e., astronomic para
astronavigation using an ANC by subjects meters measured with the sextant. In
I and II as a function of training these experiments, data about primary
sessions rt astromeasurements were given to operators
1) presentations in sealed envelopes, which contained a
~ 'L, 4) average before experiment set of charts for calculating inter
3, S) average ~ifter experiment mediate results, as well as a log with
 the algorithm for calculations. .
In these eaperime~its, we ~sed the Vega general purpose computer that is small in
size.
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The offered algorithm for solving the astronavigation problem consisted of two
parts that differed in structure of work. The first consisted of mathematical
operations (7digit numbers). The second part involved mainly determination of
base information by means of charts for subsequent calculations. 4;ork startirig gnd
finishing time was entered in the appropriate columns of the flight log.
The problem was considered solved when the cperator made no mistakes in ~he course
of the�calculations that would alter the digits in the 5th or higher positions.
Performance of arithmetic operations according to a specific algorithm with
specified accuracy, provided all operations were performed in the time reserved
for them, was the decisive factor in this methodological grocpdure. Two operators
participated in these tests, and they were trained to work with the Vega ANC 2 h
a day for 6 days.
Figure 88 illustrates the time spent on running the algorithm for autonomous navi
gation by both operators under normal experimental conditions. As can be seen
 in this figure, both curves present a tendency toward rising throughout virtually
the entire experiment. This is probably attributable not only to the influence
of the adaptation process but, to some degree, to the level of operator training.
 However, it can be noticed that the operators spent~the least time on the problem
using the specified algorithms on the 12th13th day, which virtually coincided
with the end of the experiment. For ~his reason, the improvement of performance
 in this case can also be interpreted as being the result of diminished tension
of psychophysiological processes.
The fact that average time spent on solving the algorithm decreased by 15% for
both subjects at the end of the experiment confirms that, Even in such a compli
cated activity as arithmetic operations, one observes continuation of the training
process, refinement of skill in performing the diffexent elements of the overall
experiment. In another instance, when there is a rather long interval between
perfarmance of operations for autonomous astronavigation, one may observe some
_ decrease in work skill. The presence of a training unit aboard manned spacecraft
would make it possible to maintain 3 stable skill throughout the period of the
space flight~.
The distribution of functions between the operator and computer implies, of course,
not only separation,of parts of the overall algorithm in order to program them for
the ANC. Since human characteristics are different when performing various mathe
matical operations, as well as when working with charts and nomograms, one must
determine the question of form in which the algorithm data should be submitted to
obtain optimum characteristics for the entire system. The choice of one of the
forms of graphic presentation of specific parts of the algorithm is made in order
to improve reliability of work and reduce solving time.
Thus, one can obtain the quantitative characteristics of operator performance
in such studies, with regard to solving logic and arithmetic problems inherent in
autonomous navigation of a manned spacecraft and, consequently, one can determine
whether it is possible to perform a large amount of arithmetic work, including
work under extreme conditions.
Evaluation of quality of solving the algorithm was made by means of determining
the mistakes made by the operator when solving problems with simulation of a flight
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program. Table 6.15 lists the number of errors made by operators in parts of the
algorithm that are different in type of work.
Table 6.15. Distribution of errors in different types of work
Operators Errors %
work with tables work with charts and nomo rams
No 1 82 18
No 2 73 27
As can be seen from the data listed in Table 6.15, bcth operators made most mistakes
when werking with the tables in the first part of the algorithm. In the course of
the experiment, this part of thF algorithm offered the least opportunity to improve
work skill. However, the part that was predominantly logical and required much
concentration was, strange as it seems, characterized by a tendency toward improving.
In this case, the dynamics of operator p~rformance quality throughout the experirnent
were of great interest. There was negli~ible increase in mistakes made in the
first part of the algorithm for the first few days. Most mistakes were made by the
operators on the llth experimental day, when the research program called for 15%
oxygen in the room air.
An opposite tendency was noted in running the logical part of *he al�;orithm. This
can apparently be explained as follows. Logic operations are less impervious to
interference when performed under normal conditions. In this case, normal condi
tions refer to the absence of emotional tension, exposure to deleterious environ
mental factors, etc.
However, when we could have expected the greatest number of mistakes in running
the algorithm according to the experimental conditions for the first few days of
the adaptation period, we demonstrated, on the contrary, improved work with it,
i.e., perfornance of logic operations under extreme conditions may be sufficiently
efficient and resistant to interference.
We stress the fact that the experiment was comglicated and tests limited to only
two operators and, in spite of the fact that similar results were obtained for
both subjects, they cannot be deemed statistically reliable. For this reason, the
findings of this experiment should be interpreted as illustrative, but we shall
still try to find an explanation for the demonstrated distinctions.
The first, automated part of the algorithm is rather timeconsuming, but still it
is t}ie preliminary stage of work, which yields primary data for the second part of
the algorithm. The second part of the algorithm yields the result, which should
be considered the finite [finalJ one in reaching the goal. Thus, the second stage,
being the final one, gains the significance of psychological stimulation, which
mobilizes adaprive mechanisms in the body, its psychophysiological reserves, and
thereby increases reliability of the operator's work. For this reason, concentra
tion of attention on this phase of wurk leads to inhibition of other parts of the
 cerebral cortex, and this could be the precondition for worsening of the other
activity, which is simpler in its algorithmic structure.
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~ There is another possible approach to
t,min ~ interpretation of this phenomenon, based
� 4 on the hypothesis expounded by B. M.
r6 ~ ev~
~ Teplov in 1955 [69]. According to this
, ~~'I~ i 1 i__ 4 hypothesis, the assumption was advanced
r ~
r0 4 5C i ~ ~ :~i~ that low work capacity can be interpreted
y ~,p ~ ~ as the result of high reactivity. If we
1
6~ fp ~1 ' consider the theoretical theses of I. P.
, Ut 70I ~ , i, Pavlov concerning the tyPes of nervous
z~ iof~ ;i; system, this hypothesis is valid for a
~ 1~~ wea k ne rvou s s y s t e
m. F o r t h i s r e a s o n,
Figure 89. it would hardly be correct to interpret
Characteristics of operator performance the obtained data from this point of
in manual solution of algorithm of auto view.
nomous astronavigation (anumber of
errors) The closest step in this direction was
1) base data 3) 6th day the work of V. D. Nebylitsin [80], ~in
2) lst day 4) llth day which he demonstrated an inverse corre
 lation between the functional state of
the nervous system and reliability of function of the visual analyzer. Thus, the
question remains open and it must be answered in specially conducted experiments.
In the same experiment, we also tested the possibility of solving the algorithm of
autonomous astronavigation without using a~computer. The same parts of the
algorithm, but in a somewhat abbreviated variant, were used for analysis. Three
experiments were conducted with each operator. Analysis of the results revealed
that they presented the same direction of changes and, consequently, it was possible
 to submit them in the form of averaged data for one crew (Figure 89).
In this case, of interest is the relationship between mistakes and working time at
the extreme (according to gas composition of respiratory air mixture) stage of the
experinent, namely the lltli day. Analysis of the time required to so~.ve this
algorithm revealed that it was the shortest, closest to the initial, background
data on the llth day. However, the number of mistakes increased by 27% at this
period. This tendency of change in performance characteristics (time and accuracy
of work) under extreme conditions is not unexpected, and it is preser~t iri a number
of other instances. But, for the time being, we are not able to off�er a compre
hensive psychophysiological analysis of such a trend in changes in work quality,
to demonstrate the specific mechanisms causing such differences in th~ dyuamics of
tlie par.~meters studied referaUle, it would seem, to homogPneous activity. Evi
 dently, ttie cause should be sought in the distinctive features ~f the structure
of a given activiLy and evaluation of its significanc~ to performance.
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,
CHAPTER 7. METHOD FOR OVERALL EVALUATION AND FORECASTING QUALITY OF OPERATOR
 PERFORMANCE IN SOLVING ASTRONAVIGATION PROBLEMS (ACCORDING TO
CHARACTERISTICS OF HIS PSYCHOPHYSIOLOGICAL STATE)
7.1. The Question of Generalized Evaluations in Psychophysiology of SpaceRelated
Work
; The problem of improving the quality of performance of an operator in complex con
_ trol syst~ms is one of the most important and pressing problems of engineering
psychology.
In designing modern manmachine systems, it is imperative to take into consideration
the fact that the operator will be solving his problems under the influence of many
factors. A change in psychophysiological state of the operator is one of the main
factors.
We do not yet have a genera~ classification of objective psychophysiological ~fiat~s
of an operatcr, and on the whole this prc+blem can be viewed as formalization a=
qualitative features of his performance on the basis of recreating their statistical
dependence on a certain base system of psychophysiological and technical parameters.
This is also an important c~uestion in solving astronavigation problems by a cosmo
naut.
Tt~equestion of optimizing tlie cosmonaut instruction and training process requires
immediate work on solving problems of objective generalized evaluation of cusmonau~
pr~ficience, which could be used to formulate the principles of construction of
feedback with the training system, operatorsimulatorin~tructor system and to
create the necessary conditions for effective contrul of training.
The problem is important, theoretically warranted and necessary in practice, but it
must be noted that many authors are skeptical about the possibility of a universal
approach to the solution of this range of problems. We shall not dwell on a des
 cription of the efforts made by different authors of generalized evaluation of
 ~~erformance, but shall cite one example that characterizes the thinking of re
searchers in this direction as it applies to cosmonaut work. Let a given form of
cosmonaut work be described by parameters al, a,2, a3, an. Let the conditions
be such that these parameters must have maximum values for optimum work quality.~
_ Let us designate Ltie same parameters obtained in groundbased experiments as q,l`,
q,Z' , QI,3 ay2' , and values obtained in space as al", a2", a3", ay~~~. Then
the generalized ~valuation of operator work quality referable to this form of
cosmonaut c~ork A~eri can be expressed in the following form:
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 N'()It OMhI('IA1. lJtih: ONI,Y _
i ~t 1 u_~ u~ ttn ,
i
~~geri " C u^ }u, ~
I _ 3 n ~
a
1 ~1 'I;
oi~ , .
eri ,t ~ ui
r_~
Parameter A is measured in the range of 0 to 1. Indeed, if the value of parameters
of quality of work in space wauld be the same as under the calm conditions of a
_ laboratory, this type of work would not be subjected to the influence of space
stress factors, and the level of cosmonaut work capacity in flight could be evalu
ated on the basis of the ;results of groundbased experiment~31 studies. Oth~rwise,
as is usually the case, the values of the parameters studied (al", a2" are
found to be lower than on earth (al', a2', and then Agen is less than 1, charac
= terizing the relative decline in quality of cosmonaut work referable to this form
of activity in flight, as compared to groundbased conditions. Sometimes, it is
 more convenient to use percentages instead of fractions of 1, and for this the
value of Agen is multiplied by 100. It should be borne in mind that in making a
choice of parameters one must take only those that are functionally independent of
one another.
It is logical to assume that the significance of all parameters selected.for the
generalized evaluation in the general case will not be the same. Some may be impor
tant to evaluation of a given type of work and other.s, less important. For example,
when a cosmonaut is engaged in docking spacecraft in orbit, it is more~important
not to use too much fuel and the time spent on this operation is less important;
at another time, the reverse may be true, etc. For this reason, it is expedient to
introduce into the expression for generalized evaluation the value of the "weight"
of each parameter, which would take into consideration the importance of each of
them in the overall performance by the cosmonaut. If we consider that the sum of
"weights" is:
n .
~r~2=1
2=1
the expression for the generalized evaluation will have the following appearance:
ai~~ a2~~ a3~~
Agen � wia , + w~a ~ ? LJg~3 i + . + rarca
i 2 n~
or �
n
~ '~i .
w;~
g~n ~�J ~c~
There are some debatable questions about this solution, for example, how to define ~
the mathematical expression of the significance of the "weight" of each parameter;
there are.elemer.ts that are difficult to execute, for example, to obtain a set of
values of parameters for space conditions, but expressly this model is the first
attempt at solving the formulated problem.
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7.L. I~.v:.?.lu.i~.iun ut 1'~;y~�l~u~~liys.iol~gLcal St.i~c: ot :in U~~c~r~itor ~in~l l~`urr~�