TEMS RADAR ERROR MODEL REGRESS ION ANALYS IS RESULTS …

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4

NASA TECHNICAL MEMORANDUM

T E M S R A D A R E R R O R M O D E L R E G R E S S I O N A N A L Y S IS R E S U L T S F R O M T H E S A T U R N A S - 2 0 1 , A S - 2 0 2 , A N D S A - 2 0 3 F L I G H T T E S T S By Bobby G. Junkin

Computation Laboratory

NASA

N.4S4 TM X-53585

March 3, 1967

George C. Marshall $puce Flight Center, Han t s vi1 le, A lu bdmd

TECHNICAL MEMORANDUM X- 53585 I .

1

.

TEMS RADAR ERROR MODEL REGRESS ION ANALYS IS RESULTS FROM THE SATURN AS-201, AS-202,

AND SA-203 FLIGHT TESTS

Bobby G. Junkin

George C. Marshall Space Flight Center Huntsville, Alabama

ABSTRACT

The TEMS method for evaluating systematic e r r o r s in radar tracking system measurements is illustrated with data from the 201 and 202 Apollo- Saturn tests and the 203 Saturn test. On the basis of results from these three tests, it appears that e r r o r model coefficient values a re not repeatable from test to test. It is also noted that the standard deviations for several of the coefficients do not vary significantly from radar to. radar on the three flights, The average random e r r o r s remaining in the residuals for the three flights a r e .0053 degrees and .0080 degrees in azimuth and elevation, respectively, and 3 . 5 5 meters in range. The occurrence of the various terms on each test and fo r each radar indicates that no less than five and no more than nine terms are required in the truncated e r ro r models.

NASA - G E O R G E C . M A R S H A L L S P A C E F L I G H T C E N T E R

N A S A - G E O R G E C . M A R S H A L L S P A C E F L I G H T C E N T E R

-

TECHNICAL MEMORANDUM X-53585

TEMS RADAR ERROR MODEL REGRESS ION ANALYS I S RESULTS FROM THE SATURN AS-201, AS-202,


Bobby G. Junkin

COMPUTATION LABORATORY RESEARCH AND DEVELOPMENT OPERATIONS

TABLE O F CONTENTS

Page

SUMMARY. ................................ 1

............................ SECTION 1. IN'I'RODUCTJ.ON. 2

A. The Bas ic R a d a r Tracking Sys tem E r r o r Models . . 3 B. TEMS/Radar Computer P r o g r a m . . . . . . . . . . . . . . 4

SECTION III. RESULTS FROM SATURN 203 VEHICLE FLIGHT T E S T . . 5

A. Genera l In fo rma t ion . ...................... 5 B. R a d a r Multiple Regres s ion Resu l t s . . . . . . . . . . . . . 6 C. S u m m a r y . . ............................ 9

SECTION IV. CONCLUSIONS. ............................. 10 . APPENDIXES

A. R e s u l t s f r o m Apollo-Saturn 201 Vehicle Flight T e s t . . 11 B. R e s u l t s f r o m Apollo-Saturn 202 Vehicle Flight T e s t . . 23 C. R e s u l t s f r o m Saturn 203 Vehicle F l igh t T e s t . . . . . . . 35

REFERENCES .............................. 47

iii

LIST OF ILLUSTRATIONS

Figure Title Page

1 TEMSBadar Least Squares Adjustment P rogramFlow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

i

2 Geometrical Relation Between SA-203 Flight Path and the Tracking Sites . . . . . . . . . . . . . . . . . . . . . . 5

3 TEMS SA-203 Radar Tracking Data Utilization . . . . . . . . . . . 8

A1-A10 Results From AS-201 Multiple Regression Analysis. . . . . . . . 13-22

B1-B10 Results From AS-202 Multiple Regression Analysis. . . . . . . . 25-34

C1-C10 Results From SA-203 Multiple Regression Analysis. . . . . . . . 37-46

LISTOF TABLES

Table Title Page

1 Location of Launch Site and Tracking Radars Used in TEMS SA-203 Reduction ........................ 7

2 Truncated Radar Er ro r Model Multiple Regression Results on AS-201, AS-202, and SA-203 Vehicle Flight Tests ................................ 7

3 Coefficient Standard Deviations For Truncated Radar Er ro r Models on AS-201, AS-202, and SA-203 Vehicle Flight Tests. .......................... 8

A1 Coefficient Correlations for the Truncated AS-201 Radar E r r o r Models.. ......................... 12 .

B1 Coefficient Correlations for the Truncated AS-202 Radar Error Models.. ......................... 24

c1 Coefficient Correlations for the Truncated SA-203 Radar Er ro r Models. .......................... 36

iv

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DEFINITION OF SYMBOLS

Symbol Definition

AR, AA, AE functional expressions for the systematic e r r o r s in range, azimuth, and elevation, respectively

ARO, AA', AE' observed tracking e r ro r s in range, azimuth, and elevation, re spec tively

residuals in range, azimuth and elevation, respectively 'R, 'A, ' E'

acronym for Tracking System Er ro r Model Studies - - - - TEMS

co, c,, ... coefficients in range e r r o r model

Do, D l , * * * coefficients in azimuth e r r o r model

Fo, Fl ,... coefficients in elevation e r r o r model

R " , A " , E" measured tracking parameters in range, azimuth, and elevation, re spec tivel y

Rr, Ar, Er reference tracking parameters in range, azimuth, and elevation, respectively

Xe' ye, ze reference position of vehicle in an earth-fixed plumbline coordinate system with origin at the launch site

x Y , z reference position of vehicle in an earth-fixed plumbline es ' es es coordinate system with origin at the tracking site

x, y, z reference position of vehicle in an earth-fixed ephemeris coordinate system with origin at the tracking site

height of launch site and tracking site, respectively, above reference ellipsoid L' hT

h

geodetic latitude and geocentric longitude, respectively, of launch site L' AL

@

V

Symbol

T’ AT @

4

Pij

-

w - C

-a3 C

a2 , a2 ,... co ci - w

DEFINITION OF SYMBOLS (Cont’d)

Definition

geodetic latitude and geocentric longitude, respectively, of tracking site

firing azimuth of vehicle

semi-major and semi-minor axes, respectively, of reference ellipsoid

least squares residual variances in range, azimuth, and elevation, respectively

unit variance

correlation coefficient for i-th and j-th e r ro r model coefficients

parameter weight matrix

parameter approximation matrix

parameter a priori matrix

parameter correction matrix

parameter variances

observational weight matrix

variance -c ovariance matrix of the re gre s s ion parameters

c

vi

1 - TECHNICAL MEMORANDUM X- 53 58 5

I .



Bobby G. Junkin

George C. Marshall Space Flight Center Huntsville, Alabama

SUMMARY

The TEMS method for evaluating systematic e r r o r s in radar tracking system measurements is illustrated with data from the 201 and 202 Apollo- Saturn tests and the 203 Saturn test. On the basis of results from these three tests, it appears that e r ro r model coefficient values are not repeatable f rom test to test. It is also noted that the standard deviations for several of the coefficients do not vary significantly from radar to radar on the three flights. The average random e r r o r s remaining in the residuals for the three flights a r e .0053 degrees and .0080 degrees in azimuth and elevation, respectively, and 3 . 5 5 meters in range. on each test and for each radar indicates that no less than five and no more than nine terms are required in the truncated e r ro r models.

The occurrence of the various terms



SECTION 1. INTRODUCTION

The problem of evaluating systematic e r ro r s in tracking system measurements is of primary concern with regard to determining an accurate flight trajectory from the basic tracking measurements. A method for accomplishing this evaluation is provided in TEMS, an acronym for Tracking System E r r o r Model Studies. Basically, the evaluation involves establishing the tracker e r r o r s and then determining e r r o r model expressions to describe these established er rors . The detailed development of TEMS for radar tracking systems is documented in [ 11 and [ 21. Reference [ 31 contains a similar development of TEMS for the AZUSA (Glotrac Station I) tracking system. Optimal values for the coefficients of each e r r o r model can be estimated from the regression analysis presented in [ 11 . The explicit mathematical development for a rigorous least squares adjustment of radar e r r o r model parameters with constraints is presented in [ 21 . The method in [ 21 is a modification and an improvement of the procedures presented in [ 11 to include provisions for the utilization of a priori values for the e r r o r model parameters and their variances. A difficulty in- volved in the regression analysis used to evaluate the tracking system e r r o r s is the intercorrelation of various terms in the e r r o r models. The results can be misleading if two o r more correlated terms o r coordinate functions a re similar. A high random e r r o r (noise) content in the data may prevent a systematic e r r o r of comparable magnitude from being determined. e r r o r s remaining in the residuals, if significant, can be attributed to uncertain- ties in the assumed standard, unknown systematic e r r o r s not absorbed by those that a r e modeled, and/ o r geometry limitations. The presence of a significant unmodeled systematic e r r o r may prevent an adequate description of the tracking e r r o r s from being obtained.

The unmodeled Systematic

Application of the TEMS method to radar tracking systems is illustrated in [ 11 and [2] using data from the Apollo-Saturn (AS) 201 and 202 Flight Tests, respectively. A summary of the AS-201 results is included in [ 2 ] . This report presents the TEMS radar results obtained from the regression analysis on the Saturn (SA) 203 Flight Test. Included is a summary of the AS-201 and AS-202 results presented in [ i] and [ 21. On the basis of results from these three flights, it appears that e r r o r model coefficient values are not repeatable from test to test or from radar to radar. It i s also noted that the standard deviations for several of the coefficients do not vary significantly from test to test o r f rom

I

2

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4

radar to radar. The frequency of occurrence of the various terms on each of the three flights and for each radar indicates that no less than five and no more than nine terms are required in the truncated e r r o r models.

The work herein and in [ I ] , [ 21, and [ 31 has been performed under the sponsorship of Messrs. Max Horst and J. B. Haussler of the Flight Evaluation Branch in the Aero-Astrodynamics Laboratory.

SECTION 1 1 . DISCUSS ION

A. THE BASIC RADAR TRACKING SYSTEM ERROR MODELS

The basic radar e r r o r models for describing the systematic e r r o r s in the range, azimuth, and elevation measurements are given by the following equations :

Range

AR = C t C I R t CZR t C3t t C4 ( - . 022 cosec E ) 0

Az imu th .. AA = D t D1 A t D3 A t D 0 5

tan E t D6 s e c E t D7 tan E sin A

- s in A cos A 7

s in A cos A t D8 tan E cos A +: D

( 2 . 2 ) t D l l A s e c E

Elevat ion .. AE = F t F E t F E t F5 (-sin A) t F6 cos A

0 1 3

- 10 -6 1 c o t a n E ] t F 9 ( -X tan R z E F7 [I R so,:^

t F 1 0 ( - Y t : n E ) t F l l R [ ‘Os: 1 t F l Z k c o s E ( 2 . 3 )

3

These equations a re repeated here to assist in interpreting the results. The specific physical interpretation of the various terms in each model is given in [ 11 . equations (2. i) , ( 2 . 2 ) , and ( 2 . 3 ) are given by:

Constraints in the form of functional relations between the coefficients in

Mam P r o g r a m Init ializatirn

C4 = F7

Input: (1) ID Information

(2 ) u;, u;, U'E

(3) T i m e spans and A t (4 ) ( 5 ) Plot options d e s i r e d

Total number of t e r m s in error mode l s

B. TEMS/ RADAR COMPUTER PROGRAM

Input: (1 ) *L, A C h c O T , AT, hT Coordinate Transformalions: ' Der iva t ive Evaluation:

I . . . ( 1 ) ze - Bcs - - A n KL, a, b * ( 2 ) x e s - R r (1) R . A . E

(2) Control m a t r i c e s for error (3) Xes -x .. ..

The IBM 7094 FORTRAN IV Computer Program has been developed such that any combination of terms appearing in the basic e r r o r models can be retained in a given adjustment by the use of appropriate program control matrices. The setup of these matrices is discussed in [ 11. A diagram of the flow of comp- utations through the program is summarized in Figure 1.

T r a c k i n g E r r o r s ( I ) 4 R ' = R r - R'

- ( z ) A A * = A = - A -

model selection. -

1 Del t a for ad jus tmen t Adjusted P a r a m e t e r s Summation For Dete rmine E lemen t s of' M, = ( iTW B+G)

-T-. -T- - - - . a = (P1)-'P* - e = a+e -T-- -T-- M,= (B W N - B W B C - O r )

- B W B a n d B W N t o use i n adjustment

' - ( I ) B T W E -

A R , A A , A E A R ' , A A ' . A E "

V = A I ? ' - A E -

( 2 ) A . E ( 3 ) A E ' = E = - E*

FIGURE 1. TEMS/ RADAR LEAST SQUARES ADJUSTMENT PROGRAM FLOW

4

The approach to modifying the total e r ror models has, generally, resulted in acceptable truncated e r r o r models. It is, however, time consuming and has required an average of about 10-12 runs per radar on each test.

SECTION I 1 1 . RESULTS FROM SATURN 203 VEHICLE FLIGHT TEST

A. GENERAL INFORMATION

The Saturn 203 Vehicle was launched from Cape Kennedy on July 5, 1966 at H S

9 SM 17 Eastern Standard Time. The relation between the SA-203 flight path and the various radar tracking sites i s shown in Figure 2. The postflight reference trajectory used as the standard and detailed discussions of the various data sources a re presented in 141. the S I B / S-IVB separation ( 143.44 sec. ) and S-IVB CO (433.348 sec. ) . Pre- liminary data from Radars 0.18, 19.18, 3.18, 7.18, and BDA were corrected for refraction prior to processing. The geographic coordinates and elevations

Event times that are important for the TEMS reduction a re

zoo

18O

16'

1 4 O

I2O

Longitude

FIGURE 2. GEOMETRICAL RELATION BETWEEN SA-203 FLIGHT PATH AND THE TRACKING STATIONS

5

above the Fischer Ellipsoid for Launch Pad 37B and the various tracking radar sites a re given in Table 1.

The time spans of preliminary SA-203 radar IU beacon track data used in the TEMS reduction a re shown in Figure 3. by making a first edit pass through the computer program. comparison of the reference tracking measurements and the radar tracking measurements whereby the tracking e r ro r s could be established.

These usable data were determined This provided a

B. RADAR MULTIPLE REGRESSION RESULTS

The preliminary edited-data for all the radars were processed - with the parameter weight matrix (W) and approximation matrix (C) ,equal to zero. A priori estimates of zero for the e r r o r model coefficients were also entered into the adjustment.

Fifteen e r r o r model coefficients on Radars 3.18, 7.18, and BDA, and 12 coefficients on Radars 0. 18 and 19.18 were solved for in the total e r r o r model regressions. A s on the AS-201 and AS-202 flight tests, results for the f i rs t run total e r ro r models showed extremely high correlation between certain of the coefficients. The SA-203 truncated e r r o r model results are summarized in Tables 2 and 3. Additional information is given in Appendix C and includes plots of the observed and computed deltas, and the least squares residuals.

It was determined that the tracking e r ro r s in the range measurements from Qadar 0.18 could be sufficiently described by the bias (C ) , scale factor (C )

0 1 and refraction (C ) er rors . Regression runs were made with and without the

correlated terms C and C It was found that both of these terms were re -

quired. Various runs also indicated retaining only D and D in azimuth and F

and F in elevation.

4

1 4'

0 0 3

3

The same terms used to describe the tracking e r r o r s on Radar 0.18 were obtained in the truncated e r r o r models for Radar 19.18. It was found that both of the correlated t e rms 'C and C were required to describe the range variation. I 4 The noise content in the 19.18 data appears to be below the input estimates of 5 meters in R and .006 degrees in A and E.

Three highly correlated terms were retained in the truncated range e r r o r

i

.

model on Radar 3.18 - the bias (C ) , scale factor (C ) , and timing ( C ) terms. 0 1 2

6

TABLE 1. LOCATION OF LAUNCH SITE AND TRACKING RADARS USED I N TEMS SA-203 REDUCTION

Latitude, deg.

Height:: , m.

Longitude, deg.

80.564953

80.599293

80.664404

78.267708

71.132114

64.653801

I

Site

Launch Pad 37B

Patrick Radar (0. 18)

Merritt Island Radar (19. 18)

Grand Bahama Radar (3. 18)

Grand Turk Radar (7.18)

Bermuda Radar (BDA)

28.531857

28.226553

28.424862

26.636350

2 1.462890

32.348103

57. 00:: >:

15.51

12.02

12.05

28.45

24.31

:+ :+ :;e

Elevation above the Fischer Ellipsoid Elevation of the radar antenna above the Fischer Ellipsoid

TABLE 2. TRUNCATED RADAR ERROR MODEL MULTIPLE REGRESSION RESULTS ON AS-201, AS-202, AND SA-203 VEHICLE FLIGHT TESTS

__

T e s t NO. - 201

202

203

201

202

203

201

202

203

-

-

- No. of Data Points

323

377

259

-

-

adar

-

0.18

-

19.1

-

3.1

-

7.1

-

91.1

- BDA

-

COEFFICIENT - Fs -

L.084

-.2633

co c1 C& DO 4 D6

,0197 -172.32 -.a142 - ,0139

,0055 - 18.49 -.0040 ,0094 - - -271.06 -.00067 ,5220 -

,0105 - - . O O O l O l -

- -23.29 ,0016 -1 253 -.a362

- -275.03 ,0020 4070 -

0013 - ,0143 ,0975 -

30.39

15.37 __

57.57

51.61

-.446E-4

.075 E-4

.349E-4

-. 500E-4

,0143

,3424

,1828

-1.189 ~

.0846

,0586

,0061

.0070

.0045

,0128

,0085

,0079

-

455

360

279

427

435

270

- -7.65

55.19

-72.32

-.197E-4

2.087E-4

-. 0016

0039 -77.15 -.00086 ,430

.0273 - 0027 - -.a047 -1.667 -

,3064 ,0492

201

202

203

1.049

__ -2,204

- -

7.13

1.74

2.93

7.59

1.49

-

,0060

,0040

,0055

.0050

,0070

-

,0051

.0074

,0115

536

338

168

342

73

-

- -

201

202

2 03

,0076

,0111

- ~ =I== .

201

202

203 - I

,190 - .0063

,0080 - 139 -

NA: Not available Average o

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TABLE 3. COEFFICIENT STANDARD DEVIATIONS FOR TRUNCATED RADAR ERROR MODELS ON AS-201, AS-202, AND SA-203 VEHICLE FLIGHT TESTS

- 203 .70 . 37E-5

201 - 14E-5 19.18 202 .62 . 14E-5 1 203 .36 .20E-5

201 .68 . 15E-5 .39

203 1.21 ,463-5

201 - .30E-6 .40 -

203 2.95 -

- 3.18 202

7.18 202

NA/201

. 14E-5

NO. Occurrences I i i I 9 NA: Not available

0

==?- Bermuda (BDA)

100 200 300 400 500

Time Sec.

Grand Turk Radar (7 . 18)

Grand Bahama Radar (3. 18)

Merrit t Island Radar ( 19. 18)

Patrick Radar (0.18 3 60 0

FIGURE 3. TEMS SA-203 RADAR TRACKING DATA UTILIZATION

L

The range f i t was significantly degraded with any one of the three terms left out. The azimuth model obtained is one of the few where the coefficients D and D were retained in the truncated model.

8 5

Regression runs made with and without the correlated coefficients C and

The 0

C

timing e r r o r was also retained. The results indicate a higher noise content in the elevation data than the input estimate of .006 degrees.

indicated that both were required in the range model for Radar 7.18. 4

It was determined on the Bermuda Radar that the correlated bias and scale The high angular corre- factor te rms were required in the range e r r o r model.

lation in the total e r r o r models was reduced significantly by using the coefficients D3, Fo, and F3. These were determined to be the most significant contribu-

tors in the azimuth and elevation e r r o r models. DO'

The standard deviations of the least squares residuals for the SA-203 models in Table 2 indicate close agreement with the accuracy estimates of 5 meters in R and .006 degrees in A and E. The noted exception is the elevation data from Radar 7.18.

C. SUMMARY

An overall summary of the truncated e r r o r model results on the AS-201, AS-202, and SA-203 flight tests is included in Tables 2 and 3 . Coefficient correlations and plots of the observed deltas, computed deltas, and the least squares residuals are given in Appendixes A, B, and C for the 201, 202, and 203 tests, respectively. The firing azimuth on the AS-201 and AS-202 tests was 105" and 72" on the SA-203 test. From the results presented in Table 2, it would appear that coefficient values are not repeatable from test to test o r f rom radar to radar. The average random er rors remaining in the azimuth and elevation residuals for the three flights are .0053 degrees and .0080 degrees, respectively. estimate of ,006 degrees. A value of .006 degrees was used as the input estimate of the random e r r o r in the elevation data. The average random e r r o r in the range data of 3.55 meters is slightly less than the input estimate of 5 meters.

The average azimuth value compares favorably with the input

It is interesting to note in Table 3 that the standard deviations for several of the coefficients do not vary significantly f rom test to test o r f rom radar to radar. Another point worth noting in Table 3 is that no less than five and no more than nine terms, excluding constraints, have been retained in the truncated e r r o r models. Only in one case, Radar 19.18 on AS-202, was a nine

9

t e rm e r ro r model required.

and the bias ( D

have occurred more frequently than the other terms.

The bias (C ) and timing (C ) e r ro r s in range 0 2 F ) e r r o r s in azimuth and elevation F ) and servo lag (D

0’ 0 3’ 3

SECTION IV. CONCLUSIONS

Results from the application of the TEMS method to radar tracking data on the Saturn 203 Flight Test a re presented. A summary of the AS-201 and AS-202 results is included. On the basis of results from these three flights, it appears that e r r o r model coefficient values a re not repeatable from test to test o r from radar to radar. It i s also noted that the standard deviations for several of the coefficients do not vary significantly from test to test o r from radar to radar. The average random e r ro r s remaining in the residuals for the three flights a re .0053 degrees and .0080 degress in azimuth and elevation, respectively, and 3.55 meters in range.

The frequency of occurrence of the various terms on each of the three flights and for each radar indicates that no less than five and no more than nine terms are required in the truncated e r r o r models. be updated on each flight test and any significant changes will be noted. A current investigation is concerned with the utilization of the coefficient standard deviations as a priori inputs in the adjustment.

This information will

r

10

APPENDIX A "

RESULTS FROM APOLLO-SATURN 201 VEHICLE FLIGHT TEST

This appendix presents a summary of the results from the Apollo-Saturn 201 Vehicle Flight Test launched on February 26, 1966. The tracking e r r o r s in range, azimuth, and elevation for the various radars a re represented by dots. The description of these tracking e r ro r s a s obtained from the TEMS/ Radar Least Squares Adjustment Program i s represented by the solid computed curves. A s pointed out in [ I], goodness of fit is only one of the cri teria for determining the adequacy of a specific e r r o r model. The process of determining a valid e r r o r model to represent the tracking er rors involves a detailed examination of all coefficients that are correlated by more than .70. The goodness of f i t is often degraded in attempting to minimize correlation between coefficients.

Table A1

COEFFICIENT CORRELATIONS FOR THE TRUNCATED AS-201 RADAR ERROR MODELS

RADAR 3.18 RADAR 91.18

RADAR 7 . 1 8

c1 c2 DO D3 D8 FO F3

CZ

CO

RADAR 19.18

CI cz Do Fo F3

RADAR 0.18

.

12

.- I L

e I 8 I 0 V A L 8

0 I b

A I

e I 0 I 0 V A L 8

0 I b

e b

I I

FIGURE A i . RADAR 0.18 RESIDUALS O N AS-201

13

1. L C V L 1 I 0 I

C

I 0

a

a

0 C b

I

I m U T M

C

r

a a

a 0

0 C b

a I I

C

C a n a

n C T C

0

0

n

' AE = . 000115 - .0197 E - 172.32

T I E , K C .M

I

I

! I

,

I -.M

I I

1 TIMf I SEC

3.

-40

i t t t f i t t I t i l l 1 t i i j i + . . AR = -. 0197 R - 172.32 (-. 022 cosec E) ..a T l * C , I C C

FIGURE A2. RADAR 0 . 1 8 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-201

14

1 I 0 U A L 1

0 C 1

A t

I) c

0 C C

I

I c 1 I o U A L 1

I or 008 oor oor

. . - . . .. . -

T I Y I S C .M

.U

.a

-.U

-.M T I M f , K C

, 1 . 4 . . . llmf. 1 ¶CC

FIGURE A3. RADAR 19.18 RESIDUALS ON AS-201

15

L L C V A 1 I 0 I

C e e

e 0

D L b

A 2 I I U 7 It

I

e

e 0

D L b

e h I b c C

I) 0

e

e

C I C e

.u

.a

-.u

1 I I I UC

FIGURE A4. RADAR 1 9 . 1 8 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-201

16

t

C L

I)

1 t 0 U A L 1

e

0 C b

4 1

n L 8 I 0 U 4 L S

0 L b

n

n b

L 8 I O Y A L a

n I ? I

8

T l Y , SEC

4

-.I

-.u T t Y I SEC

FIGURE A5. RADAR 3 . 1 8 RESIDUALS ON AS-201

17

001 1 ~ 1 0 0 1 001

. m n

.e

T I Y E , K C .u

.W

.e

-.W

-.u

C L C V b 1 I 0 n

C I)

0 I)

I C b

m

A 2 I

U I w

C I) I) 0

0 I b

A I# b I

I I) I) 0 I)

C T C I)

0

TIWE , K C

rim , uc

.

I

FIGURE A6. RADAR 3.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-201

18

f L

II f 1 I 0 u A L 1

0 c 6

A I

0 c c

a

a

6

c 1 I O U A L 1

-8

-.W

-.M

.u

.W

.a

-.W

-.u TIME I IEC

4a

n

-4a

TIW , scc

FIGURE A7. RADAR 7 . 1 8 RESIDUALS ON AS-201

19

C L I

I I I 0 I

.

0 I b

A 2 I

U T n

I 1 ll b I

I I I 0 n

U I 7 C I S

.u

.U

.a

-.U

-.u TIWE , K C

FIGURE A8. RADAR 7 . 1 8 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-201

20

~

ictoor oor oor

.M

.U

.a

-.M

TIME I SEC

~- 1 -

L L

I I: 0 1 0 U A L 1

0 L c

A I

I L 1 I 0 U A L 1

0 L b

I

I c 1 I 0 U A L 1

c 1 L

1 a

FIGURE A9. RADAR 9 1 . 1 8 RESIDUALS ON AS-201

2 1

i s r o o t 00s 001

T IME , SEC

I

I

i

I

a

- sa.

- 8 8 0 .

C L C V A 1 I 0 n

C I I 0 I

D C

4 t I * U I I4

C I I 0 I

0 C

I A I(

b L

C I I 0 I

U C 1 C I

FIGURE AlO. RADAR 91.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-2Oi

22

APPENDIX B

RESULTS FROM APOLLO-SATURN 202 VEHICLE FLIGHT TEST

This appendix presents a summary of the results from the Apollo-Saturn 202 Vehicle Flight Test launched on August 25, 1966. The tracking e r ro r s in range, azimuth, and elevation for the various radars a re represented by dots. The description of these tracking errors as obtained from the TEMS/ Radar Least Squares Adjustment Program is represented by the solid computed curves. See Appendix A for comments concerning goodness of fit.

23

Table B1

Coli. C i

COEFFICIENT CORRELATIONS FOR THE TRUNCATED AS-202 RADAR ERROR MODELS

-. 0 4 . 66 0 -. 02 . 10 -. 17 -. 06 -. 14 ~ -

&I. . 64 0 -. 02 . 10 -. 16 -. 05 -. 14


c O c2 c4 D O D3 D8 F O F3 co CI c4 Do D3 D5 D7 Fo F3

C4 11. Do 0 I - . 081-. 081 . 06

(-.301-.291 . 18 D3 I I. 0 -.03 . 15 -.251-. 08 - .21 I. -. 23 - .71 -. 021 0 0

. 96 -. 59 D8 l*l

..) C4 11.

Do - . 0 4 . 01 -. 06 0 .02 1. .07 -. 30 -. 17 . 0 2


c O c2 c 4 D O D3 D8 FO F3 '0 '2 '4 D O D3 D8 F O

Coli . I - . 181. 631 . 0 2 l 0 I . O i l . 031 . O l C, 11. I. 46I-. 081. O i l - . 12I-. 051 . 01

CO

RADAR 91.18

C? CL Dn DE F n C2

24

C L

n t 1 I 0 U A L I

D C b

I 2

I b

I t I

FIGURE Bi. RADAR 0 . 1 8 RESIDUALS ON AS-202

2 5

C L C V

w o o r 0.1 o.1

.n

.Y

.a

-.m T I Y , S C

a00 l f n c I u c

A 1 I 0 I

C I I 0 I)

0 C b

A I I I U I M

I A I c C

C I) I 0 I

I c 1 c I s

FIGURE B2. RADAR 0.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-202

26

.

r I 0 U L L 1

0 C

A I

m C 1 I 0 U A L 1

0 C

n

I C 1 I 0 U A L 1

FIGURE B3. RADAR 19.18 RESIDUALS ON AS-202

27

C L I V A v I 0 M

C I I 0 I

0 C

I z I M U I I(

L I I 0 I

D L b

: : : : 1 AE = .0368 - 23.29 [<A ,R sin E - 10-0 cotan E] + . 1828 E + .0143 COS A . . , & _. .U

.m

.U

4 100 too so0

.W

..

-.W

-.m

I A M C C

L n 0 I

I L f

I r


2 8

I .IO.? OOI .or

C L

I C 1 I D U L L 0

D C b

1 I

I C

0 C b

.

L L 1

T I Y , scc .u

I I

.I j I

I .m

-.I

t

I -.u T I Y I K C

n

a

-n

llm? I I C


29

I I. I 1 A 1 I 0 I

c I I 0 I

O I b

A 2 I I U I n

I I I 0 I

0 c b

I A I

c

I I

0 I

n

I I I I s

f . - * AE = .0181 + .0039 E + .0846 E - 79.15

e.4 --. I .

.W

.a

-.W

.u

..

TIME , SEC

a n . #

sa.#

. a a a a n 4w

T I U C , K C


30

IbtOOt 00) OOt

.

r L

a

s I 0 U A L I

r

0 r

A I

n C B I 0 U A L I

0 C s

I b

a r I f 0 u A L I

C r I) B

r

.M

.I

.a I

-.I

-.w

FIGURE B7. RADAR 7 .18 RESIDUALS ON AS-202

31

C

.M V I 1 I

I

C I I .. 0 1

0 .-

0 -..a

-.M

1 I 1 I U 1 M

C I I 0 I

0 C c

FIGURE B8. RADAR 7 .18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-202

32

.E4

T I W E , SEC

I I e l c C

C I I 0 I

I 1 I I S

.

11nK , I C C

1 0 r o o t oor oor

r L

I

I I 0 U A L 1

r

0

6 r

A z I r 1 I 0 U A L l

o

6 r

I

I r I I 0 U A L 0

I

1

I I

r

r

.M

.W

.a 4

-..e

-.M

I

. a -

* _ . . . * - . . . 4 . .

6 . . - l'. . : . . . . . 4

-uc . . . I . . .

4 . 4

-Ly


33

C L C W A T 1 0 N

C I I 0 I

0 C e

A I I N U 1 M

C I I 0 I

0 L c

n A N c L

C I I 0 I

M L 1 L I s

.n

.w

.a

.m e

-.W

.

TIME , s c

TIME I s c

FIGURE BlO. RADAR 91.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-202

34

APPENDIX C

RESULTS FROM SATURN 203 VEHICLE FLIGHT TEST

This appendix presents a summary of the results from the Saturn 203 Vehicle Flight Test launched on July 5, 1966. The tracking e r r o r s in range, azimuth, and elevation for the various radars a re represented by dots. The description of these tracking e r ro r s as obtained from the TENIS/ Radar Least Squares Adjustment Program is represented by the solid computed curves. See Appendix A for comments concerning goodness of f i t .

35

TABLE C i . COEFFICIENT CORRELATIONS FOR THE TRUNCATED SA-203 RADAR ERROR MODELS


RADAR 3 .18 RADAR 7 . 1 8

CO

BERMUDA RADAR

36

c

t L

I t 8 I 0 U I L a

0 t b

A ?

0 t

4 L a

i o t o o t oot oor

.U

.am

.a

-.W

-.w

.M

.W

.a

-.W

-.M T I E , K C

r

a

-48

FIGURE G I . RADAR 0.18 RESIDUALS ON SA-203

37

let001 L 001 001 L

V A

L

T I

M

C I I 0 I

AE = .0112 -. 2633 E - 271.06 0 .am

..a L

[ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i r i i i i i i 1 1 1 1 T I E I SEC

.

A 2 I

U T

I) A V I C L

L I I 0 I

I L I L I a

T I E , SEC a

a

4a

n

FIGURE C2. RADAR 0.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON SA-203

38

I L

I I a I m 0 L L a

0 I 0

L I

0 I 0

a 0

i a I D 0 L L I

108008 H 8 I08

.U

.a

4

-.a

-.U

.U

.a

.a

-.a

-.M

ba

n

8

T l l l I Y C

FIGURE C3. RADAR 19.18 RESIDUALS ON SA-203

39

I L I v A I I 0 II

I m m m 0

I b

A

I

u T

r n

n

n n n

I

0

D I b

n A

b I

I m

m n

0

I I I

0 n

40


.

L L

I) C a 1 0 U b L 0

0 L c

b 2

L

1 0 U b L 0

a

0 L 6

I) b

a (I 0 1 0 U A L 0

I I I L

B I)

.M

.U

.. -.I

-.M T l l E I xc

FIGURE C5. RADAR 3.18 RESIDUALS ON SA-203

41

L L c V A ; .as8 0 N

L I I -8 0 I

0 L

-.ow

AE = .0348 -. 0273 E t .0586 E t .0038 (-sin A)

A 2 I

0 L


.

42

r

C L

I C 1 I 0 U 1 L 1

0 C

A I

I C 1 1 0 U A L 1

0 C s

I b

I C 1 I 0 U 1 L 1

8 #root oor oor

FIGURE C7. RADAR 7.18 RESIDUALS ON SA-203 I

43

C L C V 1 T I 0 I

C I C 0 a

0 C b

1 I I m U I I4

C I I 0 I

0 C b

I A I b C

C I I 0 I

I C I C I S

I 3-". AE = . 0113 t .0073 E - 195 .46 I I - *.02? \ cotan E

11- , SLC

FIGURE C8. RADAR 7 . 1 8 RANGE, AZIMUTH, AND ELEVATION ERRORS ON SA-203

44

c

c

I L

e I 0 I

U A L 0

e

0 I b

A I

e r b I 0 U A L 0

0 I b

t

e b

e I 0 I 0 U A L 0

I l l 1 1 1 1 1 1 1 1 I I I I 1 1 1 I I 1 I I 1 l 1 1 I I l l I I I t i l I I I I l t t r rm-HI I I I I I 1 1 I I I 1 I I t l l lttttttttt I 1 1 I I

T t l l , OCC

b FIGURE C9. RADAR BDA RESIDUALS ON SA-203

45

0 I b

A I I’

0 I b

m A I

I

I I

0 m

I I 1 I

a

TIME I scc

TIME I scc

T I m I I Y C

FIGURE (310. RADAR BDA RANGE, AZIMUTH, AND ELEVATION ERRORS ON SA-203

46

* REFERENCES

i. Junkin, Bobby G. : A Tracking System Er ro r Model Regression Analysis for Systematic E r ro r Evaluation of Apollo-Saturn Radar Flight Test Data. NASA TM X-53587, July 5, 1966.

2. Junkin, Bobby G. : A Least Squares Adjustment of Constrained Parameters for Radar Tracking System Er ro r Evaluation. NASA TM X-53549, December 8, 1966.

3. Junkin, Bobby G. : A Least Squares Adjustment of Constrained Parameters for Azusa Tracking System Error Evaluation. NASA TM X-53573, February 13, 1967.

4. Haussler, J. B. : Saturn SA-203 Postflight Trajectory. NASA TM X-53472, November 4, 1966.

c

47

APPROVAL NASA TM X-53585

TEMS RADAR ERROR MODEL REGRESSION ANALYSIS

RESULTS FROM THE SATURN AS-201, AS-202, AND SA-203

FLIGHT TESTS

4

*

Bobby G. Junkin

The information in this r e p o r t has been reviewed f o r s ecu r i ty c lassi f icat ion. Review of any information concerning Depar tment of Defense o r Atomic Ene rgy Commission p r o g r a m s h a s been made by the MSFC Securi ty Class i f i - cat ion Officer. This r epor t , in its en t i re ty , h a s been de termined to be unclassif ied.

This document h a s a l s o been reviewed and approved f o r technical accu racy .

Chief, Tracking Data Section

v u J L- Roy J. Cochran Chief, Data Reduction Branch

C. P. Hubbard Chief, Engineering Computation Division

Di rec to r , Computation Lab0 r a to ry

48

DIS TRI BU TI0 N

I INTERNAL

DIR 1 D r . von Braun

DEP-T D r . E. R e e s

R-DIR M r . H. Weidner

R-C OM P-DIR D r . H. Hoelzer M r . C. L. Bradshaw M r . C a r l P r i n c e

R-COIVIP-R m M r . C. P. Hubbard

R-COMP-T M r . D. G. Aichele

1

R-COMP-RR M r . R. J. Cochran

R-COMP-RRT M r . R. H. C r a f t M r . B. G. Junkin (50) M r . N. C. Fletcher

R-COMP-RRM Mr . C. E. Houston

R-COMP-RRP . M r . P. R. H a r n e s s

R-COMP-RRV M r . J. A. J o n e s *

R-COMP-RRF M r . R. L. Neece

R-COMP-RRG Mr . P. 0. H u r s t

R-COMP-S M r . J. C . Lynn

R-AERO-DIR D r . E . G e i s s l e r

R-AERO-F M r . J. P. Lindberg

R-AERO-FF M r . C. C. Hagood M r . M. A. H o r s t

R-AERO-F M r . C. R. F u l m e r

R-AERO-FT M r . R. H . Benson

R-AERO-FFT M r . J. B. H a u s s l e r

R-ASTR-DIR D r . W. Haeusse rmann

R-RP-DIR D r . E . Stuhlinger

R-P&VE-DIR Dr . W. R . Lucas

R- LVO-DIR Dr . H. F. Gruene

R-ME-DIR M r . K u e r s

49

DISTRIBUTION (Continued)

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I - M O - 0 M r . F l e t c h e r Kurtz

R - TEST -DIR M r . K. L. Heimburg

MS-IL (8)

MS -1P

MS -H

I-RM-M

cc -P

MS-T ( 6 )

EXTERNAL

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I

L

EXTERNAL (Cont 'd)

Manned Spacecraf t Center National Aeronaut ics and Space Adminis t ra t ion Houston, Texas ATTN: M r . J. Hanaway, ED

M r . R. M. Moore, FM-12 M r . B. F. McCrea ry , FM-12 M r . E. R. S c h i e s s e r , F M - 4 M r . W . M. Boyce, F M - 4

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TEMS RADAR ERROR MODEL REGRESS ION ANALYS IS RESULTS …