PARABOLIC DISH MENSURATION TECHNIQUE

• Document Type: CREST
• Collection: NGA Records (Formerly NIMA)
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78B04560A007400010021-1
• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 12
• Document Creation Date: December 28, 2016
• Document Release Date: May 11, 2012
• Sequence Number: 21
• Publication Date: March 1, 1974
• Content Type: REPORT

Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
TECHNICAL
PUBLICATION
NATIONAL PHOTOGRAPHIC
INTERPRETATION CENTER
PARABOLIC DISH
MENSURATION TECHNIQUE
NPIC/R-1 1/74
MARCH 1974
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
OFFICIAL USE ONLY INYIL/x-li/ /'
PARABOLIC DISH
MENSURATION TECHNIQUE
NATIONAL PHOTOGRAPHIC INTERPRETATION CENTER
OFFICIAL USE ONLY
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78B04560A007400010021-1
l ul UUL UIM L 1 NPIC/R-11/74
TABLE OF CONTENTS
Introduction
Page
Technical Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
1
Mathematical Description . . . . . . . . . . . . . .
FORTRAN Program Implementation . . . . . . . . . .
Program Input Data . . . . . . . . . . . . . . . . . . . . . . . . .
4
Example of Program Output . . . . . . . . . . . . . . . . . . . . .
4
Program Validation . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Comments on Practical Application . . . . . . . . . . . . . . . . . . .
8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
LIST OF FIGURES
Rotation Parameters and Coordinates . . . . . . . . . . . . . . . . . Figure 1
Example of output . . . . . . . . . . . . . . . . . . . . . . . . Figure 2
Example of Plot ..........................Figure 3
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78B04560A007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78B04560A007400010021-1
UrrILIML U3r UIVLT NYLU/K-11/74
Communications systems and the ability to monitor them are of continuing interest to the
intelligence community. The analyst needs to know the accurate diameter of an antenna so that
it can be correctly classified by function and type. Further information can be determined when
both the azimuth and inclination of the antenna arc also known.
Equally important to the actual values for these antenna parameters of azimuth,
inclination, and diameter are the confidence limits associated with these parameters. The analyst
desires the most accurate determination that can be attained: the uncertainty associated with
the measurement should be as small as possible. Thus the reported results should include both
the parameters and the certainty with which they are known.
Most photogrammetric reductions are general purpose. They provide distances and
azimuths between two identifiable points as well as cartesian or geodetic coordinates of
individual points.
The basic problem is to determine inclination, azimuth, and diameter of a circle which lies
on an inclinedplane. To determine the inclination and azimuth, one must be able to identify
certain critical points on the circle. This type of solution is subject to large errors because the
critical points can be difficult to identify.
A solution has been derived for finding the inclination, azimuth, and diameter without
having to measure the critical points directly. The solution is also independent of the
photographic system. By using the method of least squares, the "best" estimates of the
parameters and their associated accuracies are provided.
A technical discussion of the problem solution, program checkout, and comments about
program operation are included in this report. The technical discussion involves a mathematical
description, features of the program implementation, and an example of its application. The
discussion on program checkout includes simulation as well as operational checks. Comments
from practical experience conclude the report.
Technical Discussion
The mathematical description and the discussion of the computer program implementation
are presented as separate topics in this section. The intent is to provide a basic outline rather
than complete documentation.
Mathematical Description
The solution to the problem of determining dish antenna information begins by assuming
the points of interest lie in a plane and fit a circle in three-dimensional space. Mathematically,
OFFICIAL USE ONLY
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78B04560A007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
OFFICIAL USE ONLY NPIC/R-11/74
these two conditions can be described by two equations. Let (Xi,Yi,Zi) represent the
coordinates of point i measured in an arbitrarily positioned and oriented cartesian coordinate
system. Let (X'i,Y'i,Z'i) represent the coordinates of the same point referenced to a new
(primed) cartesian coordinate system in which the X',Y' plane is in the plane of the circle and
the Z' axis passes through the center of the circle. Then (X'i,Y'i,Z'i) are related to(Xi,Yi,Zi)
by three translations (X:0,Y'0,Z'0) and a rotational matrix (M).
X
Y,i
Yi
X.0
Y'o
L72 ]
The plane and circle conditions can be written as
Z'i=0
(X'i - X'0)2 + (Y'i - Y'0)2 - R2 = 0
Zi
Z'o
where R is the radius of the circle. It is clear that two independent rotations suffice to angularly
relate the two coordinate systems. Since the Xi,Yi,Zi are assumed to be in a topocentric
coordinate system (Z up), the rotational matrix can be formulated as
1 0 0
M = 0 SIN I COS I
0 -COS I SIN I
where I is the inclination and - is the azimuth. See Figure 1.
COS- -SIN 0 0
SIN - COS a 0
0 0 1
In general the parameters X'0,Y'o,Z'o, I, x, and R arc unknown. With two equations per
point, three points would be necessary for determining the six parameters. Typically it is
possible to obtain more than three points with little additional work. It then becomes
convenient to use a least squares algorithm for parameter determination. The problem is
nonlinear in both the parameters and the observations. The general solution to such a problem is
given by Brown (1955').1 In special situations the radius of the circle may have been attained
previously along with its associated variance. In this case the parameter R becomes an
observation. The solution to the problem under this condition is given by Schmid and Schmid
(1965).2
One distinct advantage of the least squares algorithm is that a byproduct of the
computations is a convariance matrix for the computed parameters. Thus appropriate
confidence bounds may be formed.
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
X,Y,Z-TOPOCENTRIC COORDINATE SYSTEM
1 - INCLINATION OF ANTENNA
a -AZIMUTH OF ANTENNA
FIGURE I. ROTATION PARAMETERS AND COORDINATES
FORTRAN Program Implementation
There are a number of features of the FORTRAN program implementation that make the
program particularly useful. One feature is the use of free-form input. This concept allows the
user to punch the data cards any way he chooses as long as the data is arranged in the correct
order.
Another feature is the internal computation for the initial approximations. Because the
problem is nonlinear, an iterative solution is used. Initial approximations arc important for
minimizing computational time and arriving at the correct minimum.
A third feature is an automatic data editing scheme. The theory behind the scheme is that
it is better to reject a potentially bad observation than to include it. Thus, after a first
adjustment the contribution of each point to the sum of square of the residuals is examined to
determine the "worst" point. Since it may be known apriori that some points are worse than
others, each point is given a weight as defined by the user. Then the point contribution to the
weighted sum of the residuals squared is evaluated. The rejection criterion is based on an F test
between the largest contribution and the total sum of squares (including the bad point). The
OFFICIAL USE ONLY
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
urrii,ui- L UJt UNLY NPIC/R-11/74
user controls the level of rejection by specifying the probability of rejecting a good value (a
-level). If a point is edited, a new adjustment is computed. The process is repeated until no
points are deleted.
Finally, there are two features of the output that are worth mentioning. First, a 95%
confidence interval (C.I.) for the computed diameter is given. This C.I. is computed from the
marginal variance given by the covariance matrix of the parameters. Also a joint 95%
confidence region for the inclination and the azimuth are given. This is formed by partitioning
the covariance matrix of the parameters and using the appropriate F value. The other output
feature is a two-dimensional plot of the data points in the plane of the fitted circle. If the
adjustment fails to converge to a solution, then the initial approximations are used to generate
the plot.
Program Input Data
The program is set into operation by furnishing the following:
A. Parameters
1) A mode indicator that determines if the solution is to be run with R as an
observation or an unknown parameter
2) The azimuth of the +Y axis of the topocentric cartesian coordinate system
3) The alpha value that is used to control the level of the rejection of suspect
points
4) The total number of data points that are input
B. Data Points
1) An identification number
2) The apriori weight, as assigned by the user
3) The Xi,Yi,Zi topocentric coordinates of point i
Example of Program Output
Figures 2 and 3 provide an example of the output for the mensuration of a parabolic dish
antenna. The results of the functions that were performed by the program are shown in Figure
2. The following is a brief description for each element of the output.
OFFICIAL USE ONLY
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
A. The first line contains the input values for the azimuth of the +Y axis, alpha level, and
the number of points.
B. The weighting vector gives the value of the input weights for each of the data points.
C. Initial approximations are the initial values for the parameters to be used in the adjus-
tment.
D. The parameters resulting from each adjustment are shown under the heading
Adjustment Results.
E. S02 is the variance of unit weight as calculated by the adjustment.
F. The number of iterations needed for convergence is also shown. The maximum
number is 20.
G. Editing vector shows the weight of all the points and edited points (shown by weight
becoming zero).
H. The input X, Y, and Z local coordinates are listed as Data Points with the associated
corrections (VX,VY,VZ) that were applied to obtain the final adjusted values.
1. The worst point still in the solution and the alpha level necessary to reject that point
is also given.
J. The last line shows the final adjusted values for azimuth, inclination, and diameter
with the 95% confidence interval or bound for each.
Figure 3 is a plot with the adjusted position for all the data points including any deleted
points. When two points are close together, the numerical identifier for one of the points will
not be shown. The best fit circle is also plotted so that it is easier to see the relative positions of
the adjusted points.
Program Validation
The program has been tested through simulations as well as operational checks. A random
normal deviate generator was used to modify fictitious data to check the program. Different
combinations of the azimuth, inclination, diameter, and number of points were run through the
program.
In no case were any points deleted from the solution. No inclinations or azimuths differed
from the known value by more than the confidence bounds. One diameter of 17 differed from
the known value by more than the derived confidence interval.
An area having parabolic dish antennae with known parameters was used to check the
program operationally. The computed parameters plus each confidence interval always
container) flip KYl nxx,n rt,-,,-,4 .,,.1,...,,
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
UFI-IUTAL USE UNLY NFIU/K-11//4
:in
+11
+7
+17* +1R
*
_ +2f}
*
+19
I F ENO
* 3FCT FIT CTPCLE
+ ADJIJCTMENT gr,TNTc
x FDIT70 POTf,TS
FIGURE 3. EXAMPLE OF PLOT
-7 -
OFFICIAL USE ONLY
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78BO456OA007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78B04560A007400010021-1
UI I II.IML UO UIVLI 1VYll./K-11/1'+
Comments on Practical Application
The program has been in operational use for over one year. In this period the program has
been used in all cases when both azimuth and inclination were required.
The program has proven to be beneficial by --
a) making the input cards easy to prepare because of the free form concept.
b) reducing computer time and frequency of runs.
c) allowing measurement of antennae that previously could not be measured because
critical points could not be determined.
d) automatically editing points that previously had to be removed by inspection.
c) calculating a statistically significant confidence interval.
f) giving a visual record of the data points even if the adjustment does not converge.
g) determining more accurate values than any previous method available.
1. Brown, Duane C., A Matrix Treatment of the General Problem of Least Squares Con-
sidering Correlated Observations, Ballistic Research Laboratories Report No. 937, Aber-
deen Proving Ground, Maryland, May 55.
2. Schmid, E., Schmid, H. H., A Generalized Least Squares Solution For Hybrid Measur-
ing Systems, ESSA, US Coast & Geodetic Survey, Washington Science Center, Rock-
ville, Maryland, Jun 65.
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78B04560A007400010021-1
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78B04560A007400010021-1
L)1i-ICIAL USE ONLY
OFFICIAL USE ONLY
Declassified in Part - Sanitized Copy Approved for Release 2012/05/11: CIA-RDP78B04560A007400010021-1