AD-Ai27 415 MODELING OF DIFFUSE PHOTOMETRIC SIGNATURES OF 1/3SATELLITES FOR SPACE OBJECT-.(U) AIR FORCE INST OF TECHWRIGHT-PATTERSON RFB OH SCHOOL OF ENGI.. J D RASK

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MODCLING OF DIFFUSE PIIOTONETRIC SIGNATURES! OF SATELLITES FOR SPACE OBJECT IDENTIFICATIONt

TIESIS

John 0. RaskAFITIGSO/PH/82D-3 Capt USAF

'a,/ LUJ

LDEPARTMENT OF THE AIR FORCE

AIR UNIVERSITY (ATC)

AIR FORCE INSTITUTE OF TECHNOLOGU 04 2ELE8:TEiPater o oce Bos, o &S o,,k 2 ,81c.983

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OIDtLIt G OF DIFFUSE PIIOTOMETRIC SIGIATURES

OF SATELLITES FOR SPACE OBJECT IDENTIFICATION

TESIS

John D. RaskAFIT/GSO/PHI/82-3 Capt USAF

Approved for public release; distribution unlimited

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AFIT/GSO/PH/82D-3

MODELING OF DIFFUSE PHOTOMETRIC SIGNATURES

OF SATELLITES FOR SPACE OBJECT IDENTIFICATION

THESIS

Presented to the Faculty of the School of Engineering

of the Air Force Institute of Technology

Air University

in Partial Fulfillment of the

Requirements for the Degree of

aster of Science

rIS oIADUO TAB

mMneunaoed 0JtStltloatioa

bistribution/Avalability 0o49g

by"a 8w0rat peeial

John D. Rask, B.A.

Capt USAF

Graduate Space OperationsDecember 15182

Approved for public release; distribution unlimited

Preface

The purpose of this study was to provide the groundwork for devel-

opment of a computer program which could serve as an aid to tactical

space object identification and analysis using photometric satellite

signatures, in support of the mission of the ADC Intelligence Center

(ADIC) in the NORAD Cheyenne Mountain Complex in Colorado Springs. I

would like to thank Lt John Mertens, electro-optical space object

identification analyst at the ADIC, who provided the photometric signa-

ture data and much other information needed for completion of this

project.

I would like to thank my advisors, Naj Jim Lange and Maj Mike

Wallace of the Air Force Institute of Technology, for the excellent

guidance and encouragement th provided during the course of this

study. Special thanks go to Mr. Scott Rulong of the Aeronautical Systems

Division Computer Center, wio spent many long hours helping ma digitize

photometric signatures.

Finally, I would like to express wy gratitude to vy wife, Joanna,

whose patience and understanding meant so much during the completion of

this thesis.

John D. Riask*

r%-..-.-" .. .. . . . . - , . -.. - . '" ;; ' . '", . . ., . ......

TABLE OF CONTENTS

Page

Pre face . 0- 0 0 *t0

List of Figures ... 00000 000000000 v

List of Tabes. . . . . . . . . . . . . . . . . . . . . . . . . v

List of Symbols. . . . . . . . . . . . . . . . . . . . . . . viii

Abstract . . . . . . . . .. , a , , , , , a . , . , . . xi

I Introduction and Background . . . . . . . . ........ 1

Photometric Space Object Identification. . . . . . . . . I

Photometric Analysis Capability at the ADIC. . . . . .. 2

Operational Limitations of the Photometric Data

Analysis Module (PDA) . .. . . .... 7

PDAM Diffuse Analysis . . . . . . . . . . . . . . . . . 7

Real World SOI Requirements vs POAN Capabilities . . . . 16

Statement of the Problem . . . . . . . .... ....... 17

Scope of the Project . . .h e o *. .. .. ... . .. .. . 17

General Approach . . . . . . . . . . * . * . . * . . . . 18

Sequence of Presentation . . . . . . . . . . . . .... 19

II Theory of Satellite Photometry. . ... ..... . . . . 20

Equivalent Stellar Magnitude . . . . . . . . . . . . . . 20

Observed Irradiance . . . . . . . .. . . . . . .. . 23

Diffuse Reflected Irradiance . . . . . . .. . . .. . 24

Sun-Satelite-Sensor Geometry.... ........... 28

III Program "Satellite Identification (SATID)" Functional

Description . 0 0 0 0 0 a a .0 0 0 . . . . . % . . . . 41

The Mainline Program, SATID. .............. 41

The Subroutines . . . . . . . . . • . . . . .. . 4

)i . . ...~ .- . ...-.... -....... .... _:-' .' ."- .:_,

,,*lm - m Po # j . UL ,_ ! * . A . . ,... ],. . ' . . .

Page

IV Satellite Models and Validation Results . . . . . . . . . . 69

Model fescriptions ............. 6..... 69

Initial Model Configurations . . . . . . . . . . .. . 71

Model BIValidation .................. 71

V Results of the Satellite Identification Experiment . . . . . 93

VI Conclusions and Reconmendations. . . . . . . . . . . . . . . 117

Conclusions . . . . . . . . . . . . . . . . . . . . . . 117

Operational Recommendations.......... ..... 118

Recomnendations for Future Research. . . . . . . . . . . 119

Bibliograph~y. .. .. .. . .. . .. ... . . . . . .. . . . 120

Appendix A: Program SATID Code Listing and Supplementary

Material. .. . .. . .. .. . .. . . . . . . . . 123

Appendix B: Solar Paddle Obscuration AlgoritthuUsed by

Subroutines GEOINl, CASES, and AREAS . . . . . . . . 191

Appendix C: The Subroutine CONE Conic Irradiance

Approximation Algorithm...... . .... . . . 204

F . . . . . . .- . . ...- . U.- .. . . - . . " ..- , '.' ' '.

S a t * .* U * * '

4 , , _,. . . .. . . . . . .

LIST OF FIGURES

FigurePa

1-1 The PDAM Shape Library.. ....... .. .. ..... 8

1-2 PDA1 Diffuse Parameter Estimation . . . . . . . . . . . 11

1-3 Deep Space and Low Earth Orbits. . . . . . . . .... 13

11-1 Specular and Diffuse Reflection . . . . . . . . . . . . 25

11-2 Phase Angle and Sensor and Solar Aspect Angles. .... 30

11-3 Geocentrlc-Inertial(IJ,K), Topocentric(S,EZ), and

Body-Centered(rVCil) Coordinate Frames . . . . . . . 31

11-4 Phase Angle Effects . . . . . . . . . . . . . . . . . . 32

11-5 Ellipsoidal Earth Model . . . . . . . . . . . . .. . . 36

11-6 Line-of-Sight Obscuration . . . . . . . . . . . . . . . 40

" 111-1 SATID Logic Flow. . . . . . . . . . . . . . . . . . . . 52

111-2 ELSET Logic Flow. . . . . . . . . . . . . . . . . . . . 54

111-3 ANGLES Logc Flow .................. 56

111-4 ELIPSI and 2,Logc Flow . . . . . . . . . . . . . 57

111-5 CASES Logic Flow.... ...... . . . . . . . . . . 58

111-6 AREAS1, 2 and 3 Logic Flow... . ..... .... 60

111-7 CP123 Logic Flow. . . . . . . . . . . . . . . . . . . 61

111-8 CONE Logic Flow . . . ... . .. . . ... . . . . . . 62

111-9 SIGA1 Logic Flow. . .. . . . . . . . . . . . . . . * 63

111-10 SIGBI Logic Flow. .. . . . . . . . . . . . . . . . . . 64

111-11 SIGC Logic Flow.....a.. ........... . 65

111-12 SIGD1 Logic Flow . . . . . .* . . .* .. .0 . . . . 66

111-13 COIAR Logic Flow . . . . . . . . . . ... . . . . . . 67

IV-1 General flodel Configurations. . . . . . . . . . 70

*e v.v

-I

V

S, .. .. . ,..,,,,-o,":,.,/ ." -t4 , ," " . S s'-.._., .7 ' .' . S :' ;".:

.° .1

;'Figure PadeObcrtonGoery ::::: ::IV-2 Photometric Signature of a Stable Payload . . . . . . 77

B-1 Paddle Ob~scuratton Geomtry .. .. .. .. .. . .. 192207

;.C-1 Conic Approximation Geometry .. .. .. .. .. .. . 20

C-2 Conic Approximation Vectors . . . . . . . . . . . . . 208

vi

I .. t.. - - ,... '. , . . '''', ' ' -

. . . . . .. .

%,o'.. o . .IT Z -

LIST OF TABLES

': Table Page

1-1 Photomtric SOl Sensors . . ............ . . 3

1-2 iORAD SOI Sensors . . . . . . . . . . . . ..... . . 4

1-3 Comparison of SOI Data Information Content. . . . . . . 5

1-4 Effects of Orbit and Satellite Dynamics on the

Diffuculty of Diffuse Analysis . . . . . . . . . . . 15

11-1 Factors Influencing Photometric Signatures . . . . . . . 21

11-2 Diffuse Irradiance Equations for Simple Shapes. . . . . 29

11-3 GS-72Astrodynmtc Constants . . . . . . . . . . . . o 34

IV-1 Model B-1 Validation Results .... . . ... . . . . 76

IV-2 Signature 3883a Output.. ....... ... ..... 78

IV-3 Signature 3883b Output ...... ..... ... . 81

1V-4 Signature 3893a Output.t ........... . . 84

OilIV-5 Signature 3893b Output............ ..... .. 87

IV-6 Signature 3925 Output.., .. . . . . .. .0. *. . . . 90

V-I Results of the Satellite Identification Experiment. . . 95

V-2 Signature 3914 Output . . . . . . .. .. .. .. .. . 96

V-3 Signature 3917 Output . . ,. 0e. . . . ..... . . . 99

V-4 Signature 3898 Output. . .... a.... ..... ... 102

V-S Signature 388 5 Output . ... . . . . .......... 105

V-6 Signature 3867 Output . . .. . .... ... .... 108

V-7 Siqnature 3888 Output . ........ . ....... .112

V-8 Signature 3845 Output . . . . . . . . . . . . ..... .114

vii

.. , 4,, ,.,, ,. qr C , -.. o- .- -. .. .-. . .,.. . - ,, . . - . -.- . .... .- - .-. .

,. ... .

LIST nF SIOOLS

IPncan Letter 1 tmcls

A - Area(m2)

- 5 atelltte Lnnqitudinal Axis Vector0A Angstrom Units(1O0 cm)

a - ierutajor Axis of Ellipse

- Sedminor Axis of Ellipse

- Iormal Vector to Conic Furface

c - Constant

ODareter(m)

d- Deviation at the ith data Point

.1 - than Deviation

C Irrad anCe(U4/mZ)

E - Topocentric East Point Coord Axis

C - Eccentricity

Ti - Orbital Angular M.omentum Vector

- Height, or Y-Coord of Ellipse Center

S- Radiant Intensity(W/sr)

SGeocentric-Inertial Coord Axis to First Pointof Aries

3 - Beocentric-Inertial Coord Axis

- Geocetric-Inertial Coord Axis

k - X-Coord of Ellipse Center

L- Radimce(W/-sr). or Sensor Latitude

S- Line-of-Sight Vector

ft - Radiant Exitance(/m 2 )

- quivalent Stellar Magnitude in the Visible

t1 ) -The ith Measured Data Point

Viii

Ron Letter YTrlols

": m - Slope

1 - General lovmal Vector

n - Number of riata Points

- PIW4 Diffuse Parameter Vector

-* p - Arbitrary Parameter

PA - Paddle Axis Vector

E - Paddle Edge Vector

- Sensor Position Vector

T - Orbital Radius Vector

r - Slant Range from Sensor to Target

rl - Cylinder 1 Radius

r2 - Cylinder 2 Radius

- Topocentric South Point Chord Axis

S - Unit Vector in the Direction of the Sun

S(ti ,; ) - The ith Synthetic Data Point

SSR - Sum of the Squares of the Residuals

t - General Ltmit of Integration, or time

- Orbital Velocity Vector

V- Circular Velocity Vector

' - Solar Paddle I.lidth

x - Perpendicular Distance from the Earth'sRotational Axis to the Sensor

z Perpendicular Distance from the Earth'sEquatorial Plane to the Sensor

7Topocentric Zenith Coord Axis

ix

. "7| * ** .

-reek Lotter ,, ols

eC - Sensor Aspect Pnole

- !.nlar fispect Angle

- Conic Half Analo'

-" Angle P etween P A and 1

- Projected Solar Paddle Tilt Angle

o - Sidereal Tim , or a Function of C.K and

!'avelength

- Eastern Longitude of Sensor

- Anqle 'etween PE and 1

/f - :lean

p - Reflecti vi ty

r - Standard Deviation

I - Transmissivity of a Medium

1' - First Point of Aries

'..Pov.er(1atts)

* - Phase Angle

S- Projected Solar Paddle Rotation Angle

A - Solid Angle(Steradians)

'4

N

. .

. ..

S.X

x

AFIT/GSO/PH/82D-3

MODELING OF DIFFUSE PHOTOMETRIC SIGNATURES

OF SATELLITES FOR SPACE OBJECT IDENTIFICATION

Abstract

The diffuse reflective characteristics of four types of low earth

orbit satellites were mathematically modaled using phase functions for

ideal Lambertian surfaces. A FORTRAN computer program was developed to

generate simulated signatures and compare them point by point to real

signatures to obtain a sum of the squares of the residuals (SSR), in

order to perform pattern recognition and satellite identification.

Photometric signatures collected by the Satellite Identifica ion

and Tracking Unit (SITU), St. Nargarets, Canada were from the

ADC Intelligence Center in ,h i Cheyenne Mountain Complex in

Colorado Springs, Colorado.\ One set of signatures was used to validate

the computer model of one satellite type, and the others were used to

test the program's ability to identify the satellite. The tested model

involved line-of-sight .obcuration of some parts by others, relative

motion of body parts, and for phase shadowing.

The program was able to correctly identify the modeled satellite,

as long as the phase angle remained small, generally less than ninety

degrees. For larger phase angles, the true signatures diverged signi-

ficantly from simulated signatures. In every case, the signatures

predicted using the Lambertian assumption were dimmer than the measured

signatures at larger phase angles.

xi

7-7

"' ,Photometric pattern recognition of satellites using phase function

models appears to be feasible, but satellite models contained in an

.* operationally useful computer program must be valid for any viewing

.- geometry, and should therefore account for the non-Lambertian behavior

of illuminated surfaces where viewed at large phase angles, or away

from normal incidence.

.1

.4'

44

I. INTRODUCTION AND BACKGROUND

Photometric Space Object Identification

Space Object Identification (SOI) The secondary missions of the

North American Aerospace Defense Command (NORAD) are space track, to

maintain current orbital elements and provide reentry predictions for

all man-made space objects, and SO I, to determine the physical and

dynamic characteristics of satellites in near earth or deep space orbits

(Ref 21). SOI sensors include the majority of the NORAD space track

radars, two contractor operated wideband coherent radars, and two sat-

ellite tracking astronomical observatories which employ photoelectric

photometers to collect time vs. amplitude plots, or signatures, of the

sunlight reflected from the satellites. One facility also collects

photographic images of satellites in low earth orbit (altitude<lOOOkm).

This paper is solely concerned with the analysis of visible light photo-

metric signatures of satellites and their application to the NORAD/ADCOM

SOI mission. Table 1-1 describes the two currently operating dedicated

photometric SOI sensors, and some characteristics of the soon to be

operational Ground-Based Electro-Optical Deep Space Surveillance (GEODSS)

system (Ref 10, Ref 11). Table 1-2 lists all of the SOI sensors.

The Application of Satellite Photometry to SOI No single SOI data4

type can provide an exhaustive description of all satellite character-

istics of interest, but an integrated approach, employing inputs from a

variety of sources is necessary (Ref 16:6). Some contributions of

"" "1

.

photometric signatures to the overall picture are unique.

Table 1-3 lists sowe of the information content of photometric

signatures compared to radar signatures (Ref 7, Ref 14).

Photometric Analysis Capability At the ADIC

In 1977, the General Electric Company, under SANSO contract, pub-

lished the results of a system requirements and functional description

study of a proposed SO Central Analysis System (SOICAS) (Ref 19 and

Ref 20). A reason for the SOICAS studies was recognition that, at that

time, SO analytical capabilities in general were inadequate to satisfyeither the tactical time constraints of the ADCON space defense mission

or the data analysis resolution requiremnts (Ref 20: 1-1-i). While

great strides have been made since then in the analysis and processing

of radar data, the situation has rmined essentially unchanged for

photometric analysis, despite the acquisition in 1977 of an operational

photometric analysis software package, the Photometric Data Analysis

Module (POAM), developed by the AVCO Systems Division of AVCO - Everett

Research Laboratories (Ref 7:iv).

POAN Capabilities According to the SOI analyst PDAM training course,

"PDAM is an interactive software package integrated on the HIS 6060 com-

puter in the ADIC, which has as its min purpose the analysis of photo-

metric signatures (specular and diffuse.), from which estimates of tar-

get configuration/shape, size, orientation, surface properties (and)

motion are obtained (Ref 14:18).m The software package contains three

2

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'. ~ Location Type Data Type

Ascension Is. C-Band Tracking Narrowband Radar SignatureRadar

Antigua Is. C-Band Tracking Narrowband Radar SignatureRadar

Clear, Ak. UHF Tracking Narrowband Radar SignatureRadar

Concrete, N.D. UHF Phased Narrowband Radar Signature(PAR) Array Radar

Diyarbakir, UHF Tracking Narrowband Radar SignatureTurkey Radar

Eglin AFB, UHF Phased Narrowband Radar SignatureFL Array Radar

Kwajalein Is. C-Band Coherent Wideband Radar Images(ALCOR) Tracking Radar

Millstone, Ma. X-Band Coherent Mideband Radar Images(Haystack) Tracking Radar

Shemya Is. L-Band Phased Narrowband Radar Signature(COBRA DANE) Array Radar

Maui, Hi. Telescope and Photometric Signatures, Infra-(MOTIF) Electro-Optical red Signatures, Optical Images

Sensors

St. Margaret's, Telescope and Photometric SignaturesN.B. Canada Electro-Optical(SITU) Sensor

TABLE 1-2

Norad SOI Sensors

- .h 4

": • ":-Sensor

"-~. Target Radar PhotometryInformatlon Signatures Specular Diffuse

Size Yes Yes, for.. Specular. Yes

Surface

Presence Yes, if large Yes, very Noof Small enough for radar small featuresFeatures resolution visible if

'"sufficiently.......... .. ..... reflective .. .... .

Size of Yes, if large Yes, min and Nosmall enough for radar max sizesfeatures resolution obtainable

true sizeobtainableif reflectivityis known

Rotation Yes,.if slower than Yes YesRates radar prf...

Rotation Yes Yes YesAxis

Orientation Yes, with multiple Only if orien- Canof stable signatures tation of a besat available specular esti-

feature with matedrespect to satis known''

Orientation Yes, if speculars Yes, for multipleof small appear-on.more than. identifiablefeatures one track . . . .soeculars

Surface .No -. . Yes YesR e f l e c t i v it y . . . . . . . . . . . .. .. . . . . . . . . . .

Surface No. No - YesCurvature ..... ...

TABLE 1-3 Comparison of SOI Data Information Content

* 5

p. -, ,' ,' ,* ,',,,- ,_ .. * , ,- °, * . .. .. . .. . .. . .-:% * F ;: r:( -- " * ' ""- - " ' " ..""" " "" "" " l~l

' '11lralr d" il"' .*.- .- ' ""'* J - ~ b"' l t '' ' '" '" '

;..$ operating phases for photometric signature analysis (Ref 14:40-41).

The preprocessing phase enables an analyst to retrieve any photo-

metric signature from the Intelligence Data Handling System (IDHS)

signature wraparound file, or from a disk containing permanently stored

data. The signature may be displayed in whole or in part with the

vertical (stellar magnitude) scale selected by the analyst. The ana-

lyst may edit out portions of the signal not desired for analysis (noisy

parts, stars, gaps in data) and save portions for later specular and

diffuse analysis (Ref 14:40-41). In practice, this portion of the PDAM

program has proven to be extremly valuable and easy to use.

Specular and Diffuse analysis make up the second, and most important

phase of a PDAN analysis (Ref 14:40). The specular and diffuse reflec-

tion components of a signature are analyzed separately to yield very

different kinds of information, and the two signature components are

separately stored by the analyst during preprocessing (Ref 14:33-34).

The specular signature component is used to determine the rotational

period of spinning or tumbling objects, the surface area of specularly

reflecting surfaces (flat plate or cylinder), curvature of specularly

reflecting spherical segments, the orientation of surface normals, and

* angular momentum vector direction (Ref 14:147 and Ref 15). The diffuse

components can be used to obtain an estimate of an object's size, shape,

orientation, rotational period and angular momentum vector direction

(Ref 14:25).

46

• e*6

..-. ..,. . . . .. . . . . . . . . . . . . . . . . . . . . . . .

7 ~~ ~ ~~ ~ ~ ~ i.-7 "r.-..-T--- ..- , - -

% .:.:: The third phase of a POAM analysis is the results summary, which

provides a detailed tabulation of the results of all specular and dif-

fuse analysis performed on a particular signature, including a graphics

line drawing of the satellite model obtained from the analysis (Ref 14:

40).

Operatidnal Limitations of PDN4

Operational experience with POAM has shown it to be an effective

analytical tool for specular analysis, but it rarely yields SOI informa-

tion through diffuse analysis which could not be more easily or quickly

extracted from radar signatures, at least for low earth orbit satellites.

The reason for this becomes clear when we compare the PDIAM approach to

diffuse analysis with real world SO analysis requirements.

PDAM Diffuse Analysis

The diffuse analysis module allows the analyst to select a satellite

model from a shape library containing 18 simple combinations of shapes,

each of which has well understood diffuse light scattering characteris-

tics (Ref 14:134). Figure 1-1 depicts the PDAM shape library (Ref 14:

265-282). Each library shape is characterized by a number of parameters

which specify the dimensions and reflectivities of features, and the

orientation of the body as a whole in either an inertial or a body-fixed

coordinate frame (Ref 7:81). The parameter values selected by the analyst

for a given shape constitute the parameter vector, P for the diffuse

satellite model (Ref 7:81).

"7

5: .4:s Shape Shape I of P-Vector

' Number Description Parameters Illustration

1 Sphere 1 02 Flat Plate 3

3 Cylinder 4

4 Cone 4

5 Cyl-Pit 5

6 Cone-Plt 5

7 Cone-Cyl 5

8 Cone-Plt-Cyl 6

9 Cylinder-Spher Endcaps 4

10 Sphere-Plt 4

11 Cyl-1 Frustum 6

12 Cyl-2 Frustums 6

0 13 Cyl-Rocket Nozzle 6

14 Cyl-Frust-Noz 7

15 Sphere* 2

16 Cyl-Flat Side Pit 8

17 Cyl-Edge Side Plt 8

18 Cyl-Paddle 8

*This sphere differs from shape I in that the analyst can vary theratio of specular to diffuse reflectivities. Model I includes onlydiffuse, assuming a perfect laumbertian sphere.

Figure I-1

The PDAM Shape Library

. 't.' 8

.-.. , .. . . -. -" . .. " . -" - - . .--. . .. ,. " .' ._' i _ - '_ - . . .

:'.7-

The analyst uses a three-fold approach to diffuse analysis, begin-

ning with choice of a library shape. If there is no a priori knowledge

of the satellite shape, all 18 of the library shapes should be chosen

in turn (Ref 7:80). Once the P-vector components are specified, the

program executes two iteration loops, or three, in the case of unknown

satellite orientation, and calculates the best parameter values for the

chosen shape through successive comparison of measured signature data

points to data points synthetically calculated from the satellite model

composite phase function (Ref 7:36). The program then calculates a

weighted mean squre error criterion for the chosen shape. The analyst

wishes to minimize the sum of the squares of residuals function (SSR),

given byn

n is the number of observations,

N(t1 ) is the ith data point of the measured signature,

S(t1P) is the ith synthetic data point (Ref 14:132), and

W s given by

n-

oU'

::9

.1 ,-*, - , - .,.. >. ;. - . . ' .. " "" ' , , " . . . . .. " " " - "

.i,.- The program calculates the gradient of the SSR function with respect to

each parame.er and iteratively solves for each parameter, (Ref 14:132):

.rd( f, .4rsh~

An iterative process is used instead of equating grad (SSR) to zero and

solving for p, because S(t1P) has a non-linear dependence onp(Ref 14:

132).

The new P vector is given by

The function minimization algorithm used here is the Jacobson Gradient

Method (Ref 7:81-A). Finally, an error matrix describing error associat-

ed with each of the analyst's input parameters and the total SSR, includ-

ing convergence or non-convergence of the iteration process is output in

a results summary (Ref 14:132).

The analyst repeats the above process for a single library shape,

altering the input parameters until a converging solution with minimum

SSR for that shape is obtained, or until it is determined that the chosen

shape will not allow a convergent solution.

The third step in P)AN diffuse analysis is selection of the shape

which yields the minimum SSR with respect to the real data, the P-vector

components, being the ones which produced the best data fit for the

'-S..: chosen shape (Ref 7:81). Figure 1-2 summarizes the diffuse analysis

10

,, - --. . *Q". U

-. . . . . . U -

MEASURED SYNTHETI~C

DIFVFUSEV~tl

WAVEFORM ESTIMATION

COM'PARI SON

MAC

REFIN

INU C44E W

PAATt

Figure 1-2 PDA101 Diffuse Paramieter Estimation

model parameter estimation process (Ref 18:16 and Ref 14:131).

Intrinsic Limitations of Diffuse Analysis The diffuse signature

of a satellite is dependent upon sun-target-observer geometry, target

size and shape, the reflective properties of target surface materials,

and target dynamics (Ref 14:111). Each of these factors imposes limi-

tations on the utility of diffuse data.

The combination of sun-target-observer geometry and target dynamics

has the greatest influence on a diffuse signature. The easiest case to

analyze is the rotatingsatellite in low earth orbit. From Figure 1-3

we can see that the greatest time rate of change of sensor aspect angle,

'tand phase angle,+ , occurs for the low earth orbit, spinning/tumbling

case. This greatly reduces the possibility that more than one set of

model parameters will produce a signature which closely matches the real

data (Ref 14:19). The most difficult case, on the other hand, is the

stable satellite in geosynchronous orbit. Phase angle and aspect angle

both change very slowly, and many redundant solutions are possible (Ref

14:19). In PDA4, many parameter sets may produce a converging solution

with respect to the signature of a stable object (Ref 7:105). Table

1-4 summarizes the effect of different geometries on the difficulty of

achieving a good solution (Ref 14:128).

When neither the size nor the reflectivity of a target are known,

these two parameters must be taken together as a product of reflectivity

and projected area, unless multispectral data are available to determine

reflectivity (ref 7:81).

12

-- . . .- - . - . . . . . . . . . . . . ..

.r."

,. T O S u

i4

.. / \

riue1- ep pc ad,.. ath.tt

* 5 o

.- ..T

.. - .. S ...: ..s a t s .

The diffuse analysis limitation which is most responsible for the

previously mentioned limited usefulness of PDAM in the operational

environment becomes obvious upon inspection of Figue 1-1. Many actual

satellite shapes cannot be closely approximated by any member of the

shape library. In general, the simple shape library approach is accur-".4.

ate for very simple satellites, but is useful only for obtaining esti-

mates of gross shape and orientation of more complex objects (Ref 18:78)

unless the models are more sophisticated. When the true satellite con-

figuration does not closely match a library shape, diffuse analysis

results may be meaningless. Determining the size, shape and altitude

of a satellite from the photometric time history of the brightness of

an unresolved point source is further complicated by noise in the

observations, the lack of true independence between separate observa-

tions, and the impossibility of fully describing a complex object

.42 uniquely with a few parameters (Ref 18:59).

.,.14

- .* DynmicsStable3-Axis or Tumbling or

SOrbit Earth Oriented Spin Precessing

low large d#/dt same as 3-axis large d#/dtearth small d/dt but also good large d/dt

(ALT 1O00km) large dp/dt for specular large dp/dtintermediate analysis easiest diffusedifficulty .. ........ case

deep small d#/dt same as 3-axis small d#/dtspace small dot/dt but also good large doydt

small dp/dt for specular large dp/dt(ALT 100km) long tracks analysis case of intermediate

possible difficulty. Longtoughest tracks possiblediffuse case,

is phase angle, the angle between the sun direction and line ofsight.

o( is sensor aspect angle, the angle between the satellite longi-tudinal axis of symmetry and the sensor line of sightis solar aspect angle, the angle between the satellitelongitudinal axis of symmetry and the sun direction

Table 1-4

Effects of Orbit and Satellite Dynamics on

the Difficulty of Diffuse Analysis

15

".

,I

Real World SOI Requirements vs. PDAM Capabilities

At present, there is rarely a need to use PDAN to obtain gross

.estimates of the size, shape and orientation of unknown objects because

other data sources are available which yield more definitive results.

The utility of PDA4 in this role will probably increase, however, when

the Eastern hemisphere GEODSS sensors become operational. In the mean-

time, PDA4 is not useful as an identification aid for known types of

satellites because of the generality of its shape library.

When the GEODSS system comes on line, it is likely that the

opportunities for an electro-optical sensor to detect newly launched

objects will increase, and photometric analysis software capable of

performing pattern recognition for early mission identification could

be very useful. Such software might also be useful for identification

of uncorrelated targets (Ref 23, Ref 10).

The early research in satellite photometry, which laid the ground-

work for the PDAM program, was based upon a choice between two possible

approaches to analysis of photometric satellite signatures (Ref 18:60).

The approach chosen for PDA was to consider a family of simple shapes

and combinations of shapes, and to ask what the dimensions and reflec-

tivity of the selected shape would have to be to produce the observed

signature, beginning with no a priori knowledge of the true satellite

shape (Ref 18:60).

16

o... . . .

The other approach is to consider a family of known target satel-

lite shapes, and to predict the photometric signature which would be

observed by a sensor if the known shape selected were an accurate model

of the satellite, and to compare the actual data to predicted signatures

for all of the known shapes, In order to select the best match (Ref 18:60).

Such an approach amounts to pattern recognition, which may be loosely

defined as "any automatic system which does tasks labeled detection, rec-

ognition, identification or classification (Ref 16:2)." Gamache and La

Rosa recognized the value and feasibility of this approach in their sig-

nature prediction study of cylindrical, solar cell covered geosynchrono

ous satellites (Ref 13:209-211).

Statement of the Problem

This thesis proposes that both of the above approaches to diffuse

analysis are necessary to fulfill the A)CON photometric data analysis

mission at the ADIC, and seeks to demonstrate that photometric patters

recognition Is possible for stable payloads which yield purely diffuse

signatures.

Scope of the Project

Tie goals of this thesis project are to:

1. Mathematically model the diffuse light scattering characteristics

of several stable foreign payloads with sufficient accuracy that the

models can be used for pattern recognition purposes.

17

5. . .. . . . . . . . . . . . . . .

.7~ -7: 77 7 .7

a

2. Validate and verify the diffuse models using open source and

intelligence Information to obtain accurate physical and dynamic

characteristics, and statistical comparisons with actVal signatures

collected by the P1ORAD photometric sensors.3. Write a FORTRAIi program which will automatically compare a real

.4

signature to a series of synthetic signatures for each satellite model

, and select the model which produces the signature most closely

* matching the original.

-The project is restricted to diffuse data on stable objects in

low earth orbit, because the stable, diffuse case is of the greatest

intelligence interest, and because more signatures and satellite

configurations are available for low earth orbit, thus making valid-

ation of the models easier.

General Approach

'1. Collect photometric signatures with their position and velocity

vectors. These were obtained with the cooperation of the photometric

analyst at the ADIC.

2. Write an orbit prediction and sensor look angles computer prog-

ram.

3. Develop diffuse satellite scattering models and incorporate them

into the computer program to generate synthetic signatures.

4. Add a statistical data comparison subroutine to the computer

program.

S-i

°.

*5- ,*. ,.. S. ,"% ". %, - " *"." / •: : ", . . . . ,. _ S .. .5'" ... . _S. .... '. . .. . -" : -

.' 5. Digitize NORAD photometric signatures and use them to validate

-satellite models.

6. Use the completed computer program to automatically identify

satellite signatures.

Sequence of Presentation

The thesis is organized as follows:

1. Introduction and Background, Chapter 1

2. Theory of Satellite Photometry, Chapter I

3. Brief Functional Description of the Computer Program,

Chapter III

4. Satellite Models and Validation Results, Chapter IV

5. Results of the Pattern Recognition Experiment, Chapter V.

6. Conclusions and Recommendations, Chapter VI.

0 7. Appendices

19

......................................... " " " 7

,%.II. THEORY OF SATELLITE PHOTOMETRY

Photometry is the measurement of the irradiance of light emitted

from a source. Applied to earth satellites it is "the measurement and

interpretation of the solar energy reflected from an orbiting body and

the time variation of the reflected energy (Ref 7:5)." Satellite

photometry employs the instrumentation and data gathering techniques

of astronomical photometry, and suffers from the same environmental and

instrumental sources of measurement error. The principal difference be-

tween the two is the nature of the objects observed.

The intensity of sunlight reflected from a satellite is dependent

*; upon sun-satellite-sensor geometry, the reflectivities of satellite

components and the satellite's motion. Measurement of this intensity

is affected by the atmosphere, optics and electronics associated with

the photometer (Ref 9:2). The high angular velocity of satellite against

the sky background is an additional complication. The astronomer need

be concerned only with slow changes in line of sight air mass, sky bright-

ness and atmospheric stability during the period of observation. A

satellite however, may cross many degrees of sky, resulting in a rapidly

changing background. Table II-1 lists the factors influencing satellite

signatures (Ref 7:19-26, Ref 9:9, Ref 3:76, 408).

Equivalent Stellar Magnitude Satellite photometry employs the

astronomical stellar magnitude scale, originated by Hipparchus over

. " 20

%V

FACTOR CHARACTERISTIC EFFECT

Size Ampl1tude

Shape Waveform

Reflectivity Ampi ttude

GEOMETRY,Orbit

Amplitude

Sun-Target-

SensorGeometry Ampl itude

Target Dynamics 11aveform Complexity, Periodicity

SKY BACKGROUIID

Sky Brightness

Airg1owArtificial Anpl itude

LightZodiacal

Light, etc.

Star Field

Mi lIky WayIlebulae Amplitude, WaveformStars, etc.

Weather

CirrusAurora AmplitudeWindsHaze

.- - TABLE II-1 Factors Influencing Photometric Signatures

21

& [~ ir ** i "-. - *. .*.* .. *..* - *... . * ". .

2000 years ago, and in common use by astronomers since the second

century A.D. (Ref 2:5). In 1856, N.R. Pogson standardized the scale

by defining a difference of 5 magnitudes as equalling a difference in

photon flux of 100 times (Ref 2:5). Therefore, a difference in intensi-

ty of one magnitude is the same as a flux ratio of 1001/ 5=10 2/5. Com-

paring the intensities of two objects of magnitudes M1 and M2, if

'2 - M1 = n magnitudes, the irradiance ratio

. El = Ooe IoMo ' \

ElEl

(Ref 2:5,25) In satellite photometry magnitude M2 becomes the exoatmos-

pheric solar magnitude (-26.78), E1 is the observed irradlance from the

satellite and E2 is the solar irradiance in the visible bandpass. The

expression for equivalent stellar magnitude of a satellite is

M = -6.7 f- 2. ~5 03,.~ Ruwhere F_ 16

reflected irradiance, and E is solar irradiance in the visible bandpass

( 616 w/in' from 3800 to 7600 A) (Ref 7:6-12). In the stellar magnitude

scale, greater brightness is represented by smaller numbers. The bright-.

est star in the sky other than the sun (sirius) has a magnitude of -1.58.

The faintest stars visible to the naked eye have a magnitude of about

+ 6.0 (Ref 7:4).

22

Observed Irradlance The total irradiance of an object seen through

the atmosphere in a bandpass , to' Iis given by (Ref 2:26),It

where t(A) is atmospheric transmission,

"[.(?k) is transmission of the optics

T4(X) is transmission of filters, and

E(A) is exoatmospheric flux.

Sometimes, all of the quantities in the integral having to do with

optics and the detector are combined into an overall detector response

function,l(h), leading to the expression (Ref 9:4),

E 'Ta (Aft (AR()E(A) CIAa..

This project deals with data which have been corrected for atmos-

pheric extinction and background radiation at the sensor, so satellite

signature predictions are for the exoatmospheric case.

The final general expression for observed Irradlance becomes (Ref

7:12),.4,

.4I

'.' 23

,"2 1. ' ' ,, ,...:. " . *. . . . . ..."... •.. ... '-'.... " .. '. ' .. + '.-.." +..* . +. ' .' .-- " ..' + "_'"." " •- ' .

, , , _, , . , r , -. .. . . . .- , - .- . . .- - . - -" : .": " " " - . -

Diffuse Reflected Irradiance This section presents the basic

principles of diffuse reflection and introduces the diffuse phase func-

tions of the simple shapec which are combined to form the satellite

models.

Diffuse reflection occurs when a surface has irregularities which

are large with respect to the wavelength of incident radiation and the

radiation is reflected in all directions, or isotropically (Ref 4:65).

Most surfaces exhibit both diffuse and specular reflection to some

degree. Figure I-1 illustrates specular and diffuse reflection prop-

erties.

Lambert defined a perfect diffuse reflector as one which has

.constant radiance, L (w/M2-sr), regardless of the angle of reflection.from the surface normal (Ref 3:95). In other words, the radiance of

0the surfdce as seen by a sensor is not dependent upon the viewing angle,if the surface fills the entire field of view (Ref 3:531). Since sat-

ellites are at great distances from earth based sensors they do not

fill the entire field of view and may be considered point souces for

photometry (Ref 3:535-537).

7 Point source irradiance is governed by the inverse square and cos-

ine laws of irradiance. If P is a point source of radiant intenstity I

and distance r from some surface element dA, and the normal to dA is an

angle 8 from the direction of P, then the radiant flux incident over

dA is

•*. ,4. ..- . . - .

GRAM

SPECULAR

SEAM

OIPPU5E

Figure 11-1 Specular and Diffuse Reflection

25

- .- -".

where dA is the solid angle subtended by dA from P (Ref 3:93). By the

"" definition of solid angle,

if the normal to dA lies along a radius r, or

&A cosOrz

if the normal is an angle 6 from the direction of P (Ref 3:94). By

definition, irradiance, E is given by (Ref 3:92).

A

so that

E IdA cosOe _ . sOSrz &A r2:,-,>

(Ref 3:94), which expresses the cosine and inverse square laws of

irradiance. The inverse square law holds for a point source (Ref 3:94).

We can now derive an expression for the reflected irradiance of a diffuse-

ly reflecting flat plate as a function of viewing and illumination angles.

The power incident upon a flat plate satellite at one astronomical

unit (A.U.), the mean distance from the earth to the sun, is

E, E Acosf

where Eo is the solar irradiance in the visible bandpass at 1 A.U.

w/ 2), A is plate area (W2), and is the angle between the plate

26

- I* .

normal and the direction of the sun (Ref 7:15). The power reflected

from the plate in the direction of the sensor is

't]rO OC where P is the diffuse reflectiv-

ity in the visible bandpass, and otis the angle between the plate

normal and the sensor line of sight (Ref 7:15). Combining these gives

the power reflected in the direction of the sensor,

The radiant exitance from the plate is (Ref 3:92),

and radiance, L is given by

ir 11'

assuming a Lambertian source. Since the satellite is a point source

(Ref 3:536), reflected irradiance, Er is

Erz 1TLO-r

where a is the radius of a circular flat plate and r is the slant range

from the sensor (Ref 3:535-536). Therefore, the point source reflected

irradiance is

E opA cogf r..SO wL ~

irr

27*. . . . . . . . . .

*. b. . *

,' -%-

The portion of the irradiance equation which contains the sun-sat-

.] ellite-sensor geometry is called the "phase function" of the flat plate,

Ft (,q). In general,

Ev £.= _pA F~O, 4i)

where + is the phase angle. For a flat plate,

ii Ff (@Lot) = ( -0 s (A$ 0'

7r r&This is the simplest of the phase functions used to determine the

integrated reflected irradiance of the shapes used to model the

diffuse reflection characteristics of satellites. Diffuse irradiance

equations for simple shapes are summarized in Table 11-2 (Ref 7).

Sun-Satellite-Sensor Geometry

I CPhase Angle, and Sensor and Solar Aspect Angles In order to use

the irradiance equations given in Table 11-2, the sensor and solar

aspect angles, oand P respectively, and the phase angle,+, must beknown. To determineac,o and + at some instant in time, we must know

the posi.tion of the satellite in its orbit, the position of the sensor,

the position of the sun and the orientation of the satellites principal

axes within a single coordinate frame. Angles m,p and + are illus-

trated in Figure 11-2, and Figure 11-3 shows the three coordinate frames

which enter into the orbit prediction problem.

To emphasize the effect that the phase angle can have on a signa-

ture, Figure 11-4 depicts two satellites in high-inclination low earth

,."

.. . . . . . . .

.. . . . .

!

SHAPE IRRADIANCE

E* PA cos oc to

Ps P~ s'n +(IT- Cos41ra L J)1

0 . d.aimeer.- :,. A$ specutar refle-tivetq

pd:dffuse reflectivLS

E opdh sin Si ) W ( -CosaI

:;.., ~ ApproIMo.4Iovi- Apperid'x C..

TABLE 11-2 Diffuse Irradiance Equations for Simple Shapes

29

o ..

7 -7 7.

.1

9%

.I• : SNOPL.Alrs

~NORMqAL

ii~iFigure 11-2 Phase Angqle and Sensor and Solar Aspect Angles

030

'.,,

ARI.

041

Figure H1-3 Geocentrlc-.Inertlal(I,J,K). Topocentric(S,E,Z)and Body-Centered(r,VCH) Coordinate Frames

31

Fiur 114'hae-ge fet

.32

orbits, visible simultaneously to a sensor, S. The sensor is in

darkness about one hour before dawn. The sensor's local horizon

intersects the plane of orbit 2 at points C and E. The arc DF marks

the intersection of the plane of orbit 2 with the cone of the earth's

shadow. Satellite I (SAT1) is sunlit for the entire time it is above

the sensor horizon, but it is illuminated from behind and + is large

so the observed diffuse irradiance is small. SAT 2 enters the earth's

shadow at point D, but while it is visible, * is small, so observed

diffuse irradiance is high, since most of the portion of the satellite

facing the sensor is illuminated.

Obtaining Phase Angle and ApectAngles This paper uses the

universal variable formulation for time of flight to solve the orbit

prediction problem (Ref 1:191-212). Radius and velocity vectors, and

epoch time were provided for each photometric signature received from

the ADIC. Since these vectors are epoched during the time of track,

and the tracks are from one to three minutes long, it was not deemed

necessary to account for orbital perturbations or to advance the sun

position from its position at start of track. Sun positions were inter-

polated from the 1982 Astronomical Almanac (Ref 17). Astrodynamic

constants are from the DOD World Geodetic System, 1972 (Ref 8). Table

11-3 lists applicable WGS-72 constants.

The vectors obtained from the orbit prediction calculation are the

radius vector, F and the velocity vector V, in the geocentric-inertial

o *33

*1 33

.*.%" ** ", ' * ', .**". " . ' . "-. "' .- .- "' ' . ." , . ". " . . ." . . -. ". '. ".. . .-" ." .", ,". . . ," . .

-. q

ASTRODYNAIC CONSTANT VALUE

One Earth Radius (Canonical distance unit): 6378.135 km

Oblateness of the Reference Ellipsoid: .0C181881066

Canonical Tie Lulit: 13.44683295 min

Earth Gravitational Parameter: 3.986008X10 5 km3

sec2

lart;i Angular Rotation Rate: 7.292115147X10"4radsec

Table 11-3 WGS-72 Astrodynamic Constants

34

coordinate system (refer to Figure 11-3). We can obtain the unit vector

in the direction of the sun through a simple spherical rectangular coor-

dinate transformation, if we know its position in right ascension (RA)

and declination (DEC). Right ascension is measured in degrees eastward

from the first point of Aries along the celestial equator, and declina-

tion is measured north or south from the celestial equator.

5 [COSe- C*S(PA)]+ [cO(OEE)&In(M)] J [I"(IDEC)]K

where I, 3 and K are the unit vectors defining the axes of the geocentric

-inertial coordinate system.

The sensor position vector is found using the WGS-72 ellipsoidal

earth model. Referring to Figure 11-5 (Ref 1:95),

as t= h cosL

_ _ _ _ _ ),:'. o.e (0-e1y h smn where

a is one equatorial earth radius, e is the eccentricity of the refer-

ence ellipsoid, L is sensor lattitude and h is the sensor's altitude

above sea level (Ref 1:98). The sensor position vector, R is given by

Cos mo -V + YI,' 41, where

i 35

I..I

-. 4a

o0

-p.

a-,

36....................

= -..

ID-' ... ' is local sidereal timeG g is Greenwich sidereal time, and# E is

the eastern longitude of the sensor (Ref 1:99).

At any point in time,

e, . +(I.OOZ13190-3)(ZIT)(-D) radians,

where 90 is Greenwich sidereal time at 0h U.T. on the first of January.

D is the number of days which have elapsed since 1 January, and 1.002737-

9063 is one day of mean solar time (Ref 1:101-104).

The sensor line of sight vector may be found easily, knowing F and

-. From Figure 11-3,

L -it

The remaining vector needed to determine o and (3 is the one defin-

ing the longitudinal axis of symmetry of the satellite. Many payloads

of intelligence interest have a known nominal orientation in the body-

centered coordinate frame. A coordinate transformation from the body

frame to the geocentric-Inertial frame provides the needed vector which

we will call A= (C- ) I +(')3 *( kk.L

To obtain the sensor aspect angle e, we use

The solar aspect angle is given by

\II Al)

f'. 37

S....... . .. -. . -. . .

... . .:

phase angle,+ is given by

+ 11o- Cos-, "

Other Viewing Geometry Considerations The phase functions for

simple shapes given in Table 11-2 account for the phase shadowing of

the objects based upon solar and sensor aspect angles. When the basic

shapes are combined to form a more complex satellite model, the model

photometric signature cannot be determined, in general, by a simple

linear combination of the irradiances of components. The total Irra-

diance is complicated by the casting of shadows on some components by

others, and by line-of-sight obscuration of some parts by others.

These effects are significant in diffuse signatures when they involve

-components which have large surface areas, such as solar paddles.

Small protrusions and surface features are generally not significant

to the diffuse signature component.

This thesis models a satellite which has two large, sun-tracking

solar paddles which strongly influence the observed signature. Figure

11-6 illustrates a hypothetical series of satellite images as seen by

a sensor on a pass for which the paddles are illuminated. As sensor

38

1_.*:. _ -7

aspect angle changes, the paddle away from the sensor becomes more

and more obscured by the main body. Part of the paddle closest to the

sensor also obscures part of the cylindrical body. The effects are

significant because the surface areas involved are large.

The satellite model contained in the subroutine SIGB1, described

in Chapter III, attempts to account for the portion of the spaceward

solar paddle which is obscured by the main satellite body. The devel-

.2 opment of the algorithm for doing this is given in Appendix B.

3

..4-

;., 3

3 4

.40

III. PROGRAM "SATELLITE IDENTIFICATION (SATID)"

*, FUNCTIONAL DESCRIPTION

Program SATID is written in standard FORTRAN 77 (Ref 6). The

coded listing appears in Appendix A, along with supplementary infor-

mation.

The Mainline Program, SATID:

Inputs The following quantities are required inputs to program

SATID:

1. Greenwich sidereal time at 0h U.T. on I January of the current

year. This input is necessary only once per year, and is used

to calculate Greenwich and local sidereal times at the time of

track in order to determine the sensor position vector.

2. The alphabetic sensor code of the sensor which collected the

data being analyzed. The codes used in SATID are the ones in

current use at the ADIC. The program uses sensor code to

select the applicable sensor longitude, latitude and altitude

above sea level. Only the MOTIF and SITU codes are currently

implemented.

3. The pattern number assigned to the data being analyzed. This

number is assigned to the data at the ADIC, and permanently

identifies the data for later retrieval from permanent storage.

SATID uses the number to identify the data for the analyst in

the output.

".,

4. A geocentric-inertial radius vector in canonical units of WGS-72

earth radii.

5. A velocity vector in WGS-72 earth radii per day. The more usual

units of earth radii per universal time unit were not used because

vectors provided by the AQIC were in earth radii per day. The

program converts to the other units before performing orbit pre-

dictions.

6. The epoch time of the input vectors. Items 4,5, and 6 are used in

the orbit prediction calculations.

7. The right ascension and declination of the sun, in radians, at the

start of track. These are used to determine a unit vector in the

direction of the sun for irradiance calculations.

8. The desired time increment between observations, in canonical time

units. The program can use any time increment, but it was kept at

one observation per second for this thesis. The increment is used

to update time of flight.

9. The number of observations, or data points to be read into the

program. This determines the number of synthetic data points to

be created by the program.

10. A satellite photometric signature in digital form.

Outputs Program SATID provides the following outputs:

1. Identifying information including the sensor by name, the pattern

* number, and the start time in U.T.

42

6

i--7

2. Keplerian orbital elements and the right ascension and declination

N of the orbit normal.

3. The following items in parallel columns:

a. Seconds since start of track

b. Azimuth of the satellite with respect to the sensor

c. Elevation of the satellite with respect to the sensor.

K- d. Start range of the satellite from the sensor in kilometers.Items a through d were used for comparison with look anglesprovided by NORAD to confirm that input radius and velocityvectors were correct and that the orbit prediction algorithms

, worked.

e. Right ascension of the line of sight.

f. Declination of the line of sight. Items e and f may be usedto determine if an unusual feature on the input signature isattributable to the satellite or to something in the backgroundstar field.

43 g. Phase angle.

h. Four sets of synthetic data points corresponding to the fourcurrently implemented satellite models, SIGAI, SIGB1, SIGC1and SIGDI. Units are absolute visual magnitudes. The termabsolute refers to normalization of all magnitudes to a rangeof 1000 kilometers.

I. A listing of data points from the true signature, TRUSIG.

4. A statistical results summary in tabular form. The columns cor-

respond to the four satellite models. The rows are, beginning

with row 1:

a. The mean deviation, mu, between true and synthetic datapoints.

p.' 43

I°%

.. .. .. .- . ..... . .

b. The standard deviation, SIGMA, between true and synthetic3signatures.

c. The sum of the squares of the residuals, SSR, for eachsatellite model. The model with the minimum SSR providesthe best match to the true data.

Program Logic Figure 111-1 is a logic flow chart of the mainline

program intended to clarify this narrative description of the tasks

Fperformed by SATID.

The input satellite signature is loaded into a one-dimensional

array of 1000 points capacity, TRUSIG. The first major computational

task of the program, after reading input data and performing unit con-

versions, is the calculation of Keplerian orbital elements from the

input vectors. The mainline calls subroutine ELSET which uses the

method described in Bate, Mueller and White (Ref 1:61-67) to compute

orbital elements.

A large DO-loop contains all further computational tasks with the

*-' exception of the statistical results summary calculations. The DO-loop

control variable, N, is set to the number of observations in the input

signature, in this case, the number of seconds of track to be analyzed.

The loop counter, M, goes from 1 to N. The following calculations are

performed for each second of track (or value of M) inside the large

loop:

1. Time of flight is incremented from M-1 to M seconds. If M=1,

time of flight is zero and later computations are based on the

original input vectors. The first input data point occurs at

44

delta time zero.

2. New radius and velocity vectors are calculated using the universal

variable formulation for time of flight (Ref 1:191-212).

3. Current sensor position and line of sight vectors are calculated

as described in Chapter II.

4. Sensor look angles are calculated using simple rectangular spherical

coordinate transformations to determine azimuth and elevation. A

decision structure corrects azimuth for the appropriate quadrant.

Range is obtained from the magnitude of the line of sight vector.

Phase angle is the angle between the previously determined line of

sight and the sun vector.

5. A second DO-loop within the first contains the absolute visual

magnitude calculations for each satellite model. The loop control

variable, Q' is set to the number of satellite models currently

3. in the program. In this case, Q1 is 4. The loop counter, Q, goes

from 1 to Q'. If Q equals 1, the program calls subroutine SIGAL.SIGAl stands for "signature of model type Al," where A is an

arbitrarily assigned designator for a type of soviet satellite,

and 1 indicates it is a "first generation" object. SIGAI cal-

culates the absolute visual magnitude of the type Al satellite,

and stores the point in an array called SUNA1, for "simulated

signature of type Al." The inner loop calls each satellite

model synthetic signature generation subroutine in turn, and

45

a magnitude.is calculated by each, and .is stored in a corresponding

simulated signature array.

When each satellite signature model subroutine has calculated and

stored a magnitude, the flow returns to the large DO-loop, the loop

counter, M is incremented by 1, and the entire process described in 1

through 5 above is repeated for the next second of track.

When the large DO-loop is complete, the simulated signature arrays

are complete and the mainline program calls the subroutine COMPAR,

which compares the true signature, point by point, to each simulated

signature and outputs the statistical results swmuary table.

The Subroutines

The following are very brief subroutine descriptions and the top-

level logic flow diagrams for some of them:

Subroutine ELSET ELSET stands for "element set," and calculates

the Keplerian orbital elements and the right ascension and declination

of the orbit normal. The logic flow diagram is Figure 111-2.

Subroutine ANGLES ANGLES calculates the sensor aspect angle (ALPHA)

-..k and solar aspect angle (BETA) of an earth-center stabilized satellite,J..

and the sensor and solar aspect angles (ALPHAH and BETAH) of an horizon-

stabilized satellite. The earth-center stabilized object has its long

axis along the orbital radius vector, and the horizon-stabilized object

-. has its long axis parallel to the vector formed by the cross product of

the orbit normal and the radius vector. ANGLES is called by the simu-

lated signature generation subroutines, for irradiance calculations.

-'4 l. ...- :: "46

The logic flow diagram is Figure 111-3.

Subroutine ELIPS1 and 2 ELIPS1 calculates the Y-coordinates of

points on the ellipses formed by the projection of cylinder endplate

perimeters into the optical image plane, corresponding to the X-coor-

dinates of solar paddle corner points which lie inside the sides of

cylinder 1 defined in Figure B-1. ELIPS2 does the same for cylinder 2.

.* These coordinates are used in the plane analytic geometry calculations

of subroutine GEOM1. The logic flow is Figure 111-4.

Subroutine GEO1 6gOI41 uses the line of sight vector, sun vector,

and the orbital radius vector, along with tyoe BI satellite dimensions,

to define the geometry necessary to calculate the solar paddle area

which 1i both illuminated and visible to the sensor, even though part of

one paddle is obscured by the body of the satellite. The approach is to

establish an image plane coordinate system with the projection of the

radius vector defining the Y-axis and with the X-axis perpendicular to

the Y-axis and positive to the sensor's right. The edges of all body

parts are projected into the image plane and critical points, such as

paddle corners and ellipse centers are located. The subroutine also

/locates the points of intersection of important lines and ellipses, and

creates equations for ellipses, and point-slope form line equations.

GE11 is called by SIGBI. The GEOM1 output is used by subroutines CASES,

AREAS, AREAS1, AREAS2, and AREAS3.

Subroutine Cases CASES identifies which of five viewing geometries

47

applies'to the type BI satellite, concerning the paddle obscuration

.U calculation. Case zero refers to zero paddle corner points visible to

the sensor. Case 1 is one corner point visible, and so on to case 4,

which is all four corners visible. CASES is called by subroutine

SIGBh. Figure 111-5 shows the logic flow.

Subroutines AREAS1i 2 and 3 These short subroutines evaluate

integrals to obtain the area between two curves. Limits of integration

are defined in the logic of subroutine AREAS, which repeatedly calls

these subroutines. AREASI computes the area between two lines, AREAS 2,

between a line and an ellipse, and AREAS3 between two ellipses. Figure

111-6 shows the logic flow for all three.

Subroutine CP123 CP123 stands for "corner points one, two and

three." This subroutine performs an area computation which must often

be repeated for CASE 3, when three corner points are visible. CP123 is

called by AREAS. The flow diagram is Figure 111-7.

Subroutine AREAS AREAS calculates the partial paddle area visible

to the sensor for a type B1 satellite. The subroutine determines area

based upon the case identified by CASES, and further decision logic

which identifies subcases within each case. The output is the area of

the paddle, APAD, which is actually the product of the sensor aspect

angle to the paddle normal (ALPHAP), times the true visible paddle area.

AREAS is called by subroutine SIGB1.

Subroutine CONE CONE approximates the diffuse irradiance of a cone

4V

€- . 4

or a truncated cone. The conic is modeled by 200 flat strips which are

triangular for a pure cone and trapezoidal for a truncated cone. CONE

is called by SIGCI, and receives its inputs from the SIGC1 satellite

model parameters, including reflectivity, half-angle, cone height, slant

length, base radius, and nose radius when applicable. The output of CONE

is an approximate diffuse irradiance for a conic satellite component.

Although SIGCl is now the only subroutine to call CONE, any future sub-

routine could use CONE if the appropriate vector defining the conic axis

of symmetry is input from the calling subroutine. The irradiance algo-

rithm is described in Chapter II. Figure 111-8 shows logic flow.

Subroutines SIGAI, SIGB1, SIGCI, and SIGD1. The four satellite model

subroutines calculate individual irradiances for each component of the

satellite model using the phase functions presented in Table 11-2. The

4component irradiances are summed and the absolute visual magnitude is

* •calculated. The magnitude is then read into the simulated signature ar-

ray for the appropriate satellite model, the array element subscript

corresponding to the current value of the large DO-loop counter variable,

M, described in the paragraph on mainline program logic.

All of the satellite model subroutines call subroutine ANGLES,

except for SIGD1 which models a sphere and requires only the phase angle,

which is calculated in the mainline. SIGB1 must determine the observed

irradiance of both an unobscured solar paddle and a solar paddle which

may be partially obscured by the main body of the satellite with respect

49

...................... ... . .. . ..". .. ."." . ." . . ."".".... . """- " : Id dm ;m ~ ~ L - :' N,; J ..-

to the sensor. It calculates main body irradiance, unobscured paddle

irradiance and obscured paddle irradiance. To obtain the latter, the

exposed paddle area is determined by subroutine calls to GEOMI, CASES

and AREAS. SIGC1 contains a conic component, and must therefore call

subroutine CONE. Logic flow diagrams are given in Figures 111-9

through 111-12.

Subroutine COMPAR COMPAR performs statistical comparison of the

deviations between the simulated signatures and the input true signa-

tures. COMPAR deals with the simulated signatures sequentially,

beginning with SIMAl. The subroutine begins with a large DO-loop which

has the number of satellite models, Q', as its loop control variable,

and the model number, Q, as the loop counter. When Q=1, the program

compares the true signature to SIMAl, when Q equals 2, the comparison is

0* with SIMBi, and so on. The simulated signatures are loaded into COMPAR's

working array, SIMSIG, then each data point in the true signature array,

TRUSIG, is subtracted from its counterpart in SIMSIG.

&t *.r Sl.- ' where s is the ith simulated

data point, M.i is the ith measured data point, and d.i is the deviation.

-~ The deviations are stored in an array named DEVSIG. The DEYSIG array

elements are then sunmed and divided by the number of points, N, to

-' yield mean deviation, mu(.#).

At4 ist~

50

r ." ; . .. , G , . ' - - " '.- " - '. '. ' ."

"." '.' ' " '. . -'. '• . . " . " '-. " - - 2 - . - -

As mean deviations are determined for each model, they are stored

in array MEAN. The squares of the deviations in DEVSIG are then comput-

ed and summed, and standard deviation, SIGMA is calculated, and loaded

into array STDEV.

n-i

Finally, COMPAR calculates the sum of the squares of residuals for

each model, SSR, and loads them into array SMSR.

SSR-

The arrays MEAN, STDEV and SMSR are strictly for output of the

4. statistical results summary table. Figure 111-13 is the COMPAR logic

flow diagram.

51

-. START

VARIAOLE.ICL A Al IS

AND

BLOCKS

R.EADIN PUT

SIGNATUREDATA

PEIXPORM

- UmNIT

OUT PUTIDENTIFYIG

CA .LL

SUBROUTIN E

Figure III-1-1 SATII) Logic Flow

532

CCALLS SUBROUTINE,4

UFSHEINUM 11-- AI) Loqi P A QAmb V TH53

CAL

CALCULATE0IZG. ELEMENT~S

CALCULA7E ILORIGHT ASCENSIONOF ASCEN DiNG N8VE

NI CALCULATEM.A. AND D~EC- OF

OftIT U A L W,

4.UMMYo

Figure 111-2-1 ELSET Logic Flow

54

CALC.UIA7E 9

I - I030-1

LOND A EOIfO

CALC ULA71E TIWLOv

oTR6LONITUDL

OarrA L

Figure 111-2-2 LLSET Logic Flov:

55

CALLANGSLES

ICALCUALATE OILFOOL EAUY14 -Cawleft STAGILrIY

'.4* I' LALCULATM

CITE STABILUTY

CALLU LAFCIRCULAR VELOCrr

vEcraf. t I

CALCULATE 04.Ftwt MORISONI

STA tlJLITY

CALCULATE (3rOVL HOt IION>5 TA 13 !U:7v:P

1ZILI END

Figure 111-3 AflGLES Logic Flow

56

CALCULA1M Tfil

LLIft I CDRft-Ls"ODoNa TO TME

A CftwtNV. foiudi SAVWX ASE"tI PSE 2.

(sveR. ELI uSE

MND

Figure 111-4 FLIPS1 and 2 Logic Flow

57

CALLCA3S

'.4y

SCAS

58Y p

....................

:-,

C D

Figu e 1152 CSSLgcFo

ALLS£ 4 N

"~ yl

59

. .t.

* -"*. - ...-

-I

CALL

rNrE& TAT,"rfe.

A LA aETWEEA4'TWO

I END

Figure 111-6 AREPASl, 2 and 3 I.ogic Flow

6 0

CALLC.P123

FROM XCP3 7bXCP2 7MNFRO04 %CPL 76 %P2

SPARAMeEE4S-TsIAMT

lmNrmvILVL OF ZTI*

F"M ICPL TXtP31 FtAXPJ T%

CALL AREAM CALL AftASI

INTFIV4L OF: [NEOLO3 ZNTE&RA7IO' XeT seErA IN

II- efp.- I fi( IAA7~FOI i NP~ " O BR. I fm %mm 70 m3k.

~A5I ftAsLJ

CALL~~ ~ ~ APPM cfLL AR-ASEND

Figure 111-7 CP123 Logic Flow

61

CALL

AL NGE. AO

CL)14OF TRUNCATEDC

Figure!~CO El- COII LogENTo

624E

CALL

C.ALCULATE NOIft"IAL INCIOEUJC

U. P~OM~CED AR~EAS

I CA LLAT

0106 P 0IANCADINC

CALCULATEJ

SI M UATC

Figure LC L1- IATEoicFo

TOTA

-~ 63

00

CA L

CALWULAIE MOMAALINCIDEJCE PRtOO -PEC1.D' AM~A&

CA LULA

IfOA C 0 I YLIAOEI

CALCLAL

CAALL4T

CASESNCE

ICALL.-LLLLAIELULI ~.AQEASAI TO&t~AOA

Figur Ll-t LI11LgcFo

C A I, C A .A(

CALLSI&ci

C.ALC.ULAICPLATrE

l(MADIANCE

NLLYLI NNO

1f-flAOIANCES

CALL

CALCLATEq707A L

CALWULAIG " y~-1t 4irrvDC AND LoAcINwTO ARRAY svne

Figure III-11 SIGC1 Logic Flow

65

- -* - - - . -. -. - - - .

CALL

L ALLULA-r E32.flAOIAPCE OrI

[C A LrCUL9sT

Lo~~~-tn V~ANr1

It4r7 ARVAYS IMDI

Figure 111-12 SIGD1 Logic Flow

66

CALLCOM PAR

0 LO~5~VV~31 00

OUTPU STATIST-(L

FIur CAL13- RESOPAR LgO lo

Stj r m AfV T67

INTO0 N~VQ TO N

SUFH

Flqur S1-1- (ThRLoq Fvo~

68CUAI

IV. SATELLITE MODELS AND VALIDATION RESULTS

Model Descriptions

Three types of foreign satellites were modeled. These are described

in detail in the classified addendum to this thesis. To keep this thesis

unclassified, none of the actual signatures are identified by mission

class or by the object number assigned by the NORAD Space Computational

Center (SCC) in Colorado Springs. The models were given arbitrary alpha-

numeric designators having no relationship to similar designators employed

by the ADC Intelligence Center. These designators appear within the

names of the satellite model subroutines. The letter in the designator

refers to a mission class. The number refers to a variant of the mission

class.

SModel Al Model Al components are a cylinder and a flat plate. The

cylinder's longitudinal axis remains aligned with the orbital radius

vector, and the components have different reflectivities. General con-

figuration is given in Figure IV-1A.

Model B1 Model B1 components include three cylinders and five flat

plates, two of which represent sun-tracking solar paddles. Shadowing

of components by other components, and obscuration of one solar paddle

by the main body are modeled. This is the most complex of the four mod-

els, and the only model validated using actual signature data. This

model long axis also remains aligned with the orbital radius vector

(Figure IV-lB).

69

I Figure IV-1 General liodel ronfiqiirations

70

• .The purpose of model BI was to develop and test an algorithm for

computing diffuse irradiance of an object with complex geometry, causing

partial obscuration and shadowing of some parts by others.

Model C1 Model C1 components are two cylinders, one flat plate and

a cone. The body long axis is aligned with the vector formed by the

cross product of the orbital angular momentum vector and the radius

vector. If the orbit were circular, this would be the velocity vector.

Such a configuration simulates horizon stzbility in a minimum drag

configuration. Figure IV-IC gives general shape and orientation.

Model D1 This model is an arbitrary sphere which does not directly

correspond to any actual satellite. The phase function for this model

is not restricted to diffuse reflection, but includes the specular com-

ponent, which is always present for a sphere. The ratio of specular to

diffuse reflectivities for this model was chosen to be three to one.

Initial Model Configurations

Estimates of physical and dynamic characteristics of satellites

were provided by the ADC Intelligence Center. All models are simplifi-

cations of these estimates. From initial estimates, model BI was

refined by comparison with actual signatures. Other models are not

validated by data, and represent only rough approximations to actual

configurations.

Model Bi Validation

.The Data Model BI was validated using five high quality photometric

71

signatures collected by the Satellite Identification and Tracking Unit

(SITU), St. Margaret's, New Brunswick, Canada. Although data from the

Maui Optical Tracking and Identification facility (MOTIF) were collected,

the orbital radius and velocity vectors provided were invalid, and the

MOTIF signatures could not be used.

The signatures provided by the ADIC were not in digital form, but

were in the form of time versus stellar magnitude plots. Figure IV-2

shows one of the plots used to validate model BI. To make them usable

by program SATID, the signatures were digitized at the ASD computer

center, using a Gould 3054 X-Y recorder and the MODCOMP classic data

analysis computer. The signatures were digitized at one point per

second of time, or one hertz sampling rate. For near linear diffuse

data, a one to three hertz sampling rate is considered adequate (Ref 9:15). The data points were recorded on tape and then output on punch

- . cards. Each punch card contained a maximum of three data points, and

the delta time from start of track for each point. Table IV-1 is a

summary of signature data used to validate model B1.

Procedure The validation procedure was to run program SATID with

each of the five signatures, and to alter model BI input parameters be-

tween runs in order to minimize the SIGBI SSR value. The reflectivity

of the main satellite body was the parameter changed, since dimensions

* were considered to be fixed and solar paddle reflectivities are well

known (Ref 7:18).

72

77 7' .7777.-7 7

Sources of Error A nonzero SSR for a validated model is a result

of many sources of error, including:

1. Inaccurate model dimensions, configuration or orientation

2. Contributions to irradiance by unmodeled features

3. Non-uniform surface coatings of features which are modeled

4. The degree to which true surfaces depart from the Lambertian

assumption.

5. Inaccuracies in sky background corrections and sensor calibrations

6. Noise in the data

7. Unaccounted for X-Y recorder bias introduced in the digitizing

process

8. Differences among individual spacecraft of the same type, such

as alterations in surface reflectivity as the surface is exposed

to the space environment, or differences when manufactured.

The first through the fourth sources of error above could be

decreased somewhat by more elaborate modeling, but since the purpose

of the models is to enable the software to correctly identify satellites,

they need only be sufficiently accurate to allow an analyst to distin-

guish between type: with some degree of confidence.

Two categories of signatures emerged during the validation phase.

Category I signatures could be matched well by the simulated signatures

when diffuse reflectivities were in the range typical for satellite

materials. Antireflection coated silicon solar cells have a diffuse

73. . ... .,.

. * .. ..

S:reflectivity of about .06, and unpolished aluminum lies in the .2 to .3

range (Ref 7:18). The reflectivities which yielded the smallest SSR for

1.t model BI were .06 to .08 for the solar paddles and .42 to .45 for the

other main body components. Specular reflectivity for unpolished alu-

minum is about .42 (Ref 7:18), so this value for the diffuse model seems

a little high. The satellite may be painted, or it may have a slightly

glossy surface. Signatures which fall into this category are summarized

in Table IV-1. These simulated signatures exhibit the behavior expected

using diffuse phase functions, with magnitude dimming as phase angle

increases. The true signatures dimmed with increasing phase angle also,

but at a slower rate, making the synthetic signatures too dim at the

end of track. Tables IV-2 through IV-7 are actual computer output for

these signatures.

The category II signatures could not be well matched by simulated

signatures of model Bi. Reflectivities required to reduce SSR were very

high, ranging from .6 to almost 1.0 for main body components. The slope

of all simulated signatures had to follow the increasing phase angle,

dimming magnitude rule, but the true data often behaved exactly the

opposite, becoming slightly brighter as phase angle increased. These

signatures are summarized in Table IV-1. For the sake of comparison,

SSR values are given for reflectivities the same as those for category

I. Some category II tracks are actually the last half of long category

I tracks. Suffix a indicates the first half of a track, and suffix b

74

-, . rr .r r-

the last half.

Table IV-1 suggests that the critical factor in determining category

I and category II results is the phase angle. The best matches of simu-

lated and actual signatures occur for tracks with small to moderate (30

to 90 degrees) phase angles. The category II tracks all have moderate

to large (90 to 130 degrees) phase angles. A plausible explanation is

that the B1 satellite is far from being a perfect Lambertian reflector,

and that its non-Lambertian behavior becomes more obvious as sensor as-

pect angle diverges from normal incidence. The reflective properties

* of many natural surfaces are approximately Lambertian near normal in-

cidence. If the B1 satellite's surface is glossy to some degree, we

would expect the Lambertian assumption to break down at large phase

angles.

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92

V. RESULTS OF THE SATELLITE IDENTIFICATION EXPERIMENT

Table V-1 lists the signatures which program SATID was used to

identify. These signatures, or portions of signatures, were not used in

model validation. The table shows that most results are consistent with

the findings of the validation runs. Signatures with small to moderate

phase angles resulted in the smallest SSR for model B1, and the slopes

of simulated and actual signatures were compatible. Signatures with

large phase angles did not yield small SSR's for model BI, but misi-

dentified the satellite as model C1.

* The important quantity is not the value of the SSR for model BI by

itself, since this will vary with track leng th and signature quality,

but the model B1 SSR value compared to those of other models for the

' same track. Signature 3845 illustrates an important point for any

photometric analysis. Although the B1 SSR is quite low compared to

those for Al and D1, the CI SSR is lower still. Two factors have prob-

ably combined to cause the misidentification. First, the phase angles

are in the range for which the Lambertian assumption begins to break

' down significantly for the B1 satellite. Second, the viewing and illu-

mination geometry have created a coincidental situation in which the

reflectivity-area product of the diffuse Cl model, and the actual Bi

satellite are almost the same. Tracks which undergo relatively small

changes of phase angle, only about ten degrees in this case, are es-

pecially susceptible to such ambiguity. The possibility of multiple

93

.. .•

. .

* ,solutions is always present with photometric data. If SATID were a

validated, operational program, the results for signature 3845 would not

*: eliminate model BI as the possible solution. Both low SSR models would

* have to be considered possibilities, and the ambiguity would have to be

resolved by using results obtained from data collected later, other types

of sensors, or other indicators.

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116

VI. CONCLUSIONS AND RECOMMENDATIONS

Conclusions

* The results of the satellite identification experiment show that it

is feasible to perform pattern recognition of stable satellites employ-

ing diffuse reflection models of known satellite types, for geometries

* for which the Lambertian assumption is approximately true. Gamache and

LaRosa reached a similar conclusion (Ref 13).

Limitations of the Method

1. Meaningful identification of satellites is achievable only when the

satellite being observed has been modeled. It is possible for the sig-

nature of an unmodeled object could by chance exhibit a small SSR for

one of the models on a given pass. However, it is unlikely that an un-

modeled object will consistently yield a small SSR for a single model

*over several passes unless the object is in fact similar to the model.

2. The results of the satellite identification experiment show that the

one validated Lambertian model is good only for small phase angles.

Applications An operational program performing pattern recognition

from a model library could be used at sensors for early identification

and reporting to the ADIC, or at the ADIC itself by the SOI technician

on duty. The recognition process Would not depend heavily on the exper-

ience of the operator. Multiple applications of a SATID type program

include:

1. Early mission identification of newly launched payloads

* 2. Possible UCT identification

g117

*3. Monitoring resident space objects for changes in

orientation, or configuration, or surface reflec-

tivity due to aging or damage.

4. Indicating the presence of a design change in a

known mission class.

5. Determining that an object which is tentatively

identified from other sources is either not what

the other sources say it is, or that some char-

acteristic is non-nominal.

Operational Recommendations

1. Retain the PDAM program for use as an aid to determining gross size

and shape of unknown satellites, but do not try to use it as a

pattern recognition tool.

2. Develop another photometric analysis program for use at the ADIC,

with basic structure similar to SATID. Improvements over SATID

should include:

a. Adding the PDAM preprocessing module

b. Incorporating a more sophisticated orbit prediction

algorithm

c. Developing diffuse models for the entire inventory of

satellites of interest, and validating them using actual

signatures. Diffuse phase functions must not assume

perfect Lambertian reflection.

118

3. Evaluate the utility of having a SATID type program available at

GEODSS sensors as well as the ADIC.

Recommendations for Future Research

1. An analysis is needed to determine a correlation between the rela-

mm tive magnitudes of the SSR's of validated models and correct iden-

" tification of satellites by program SATID. This will require collection

of many more signatures of the modeled satellites, and validation of the

other three models. Such an analysis would reveal how accurate the sat-

ellite models must be if correct identification can be counted on for

some desirable percentage (say 90%) of signatures processed, assumdng the

tracks are of modeled satellites.

The small number of signatures available to this thesis project made

such a study impossible, even for model SIGBI, but the four satellites

modeled were of such different sizes and shapes that the differences in

SSR were large in most cases for which the model was valid, and the best

fit to data could be easily selected by inspection. If research in this

area is pursued further, and many more satellites are modeled, distinct-

ions between more similar types may not be as obvious, hence the need for

establishing quantitative measures of confidence in correct identification

for each model individually.

2. Modeling of satellites without using the Lambertian reflecting sur-

face assumptions should be attempted, so that models remain valid at high

" phase angles. An operational satellite identification computer program

should retain its validity for any viewing geometry, so that minimal

detailed post analysis by the operator is necessary.

119

References

1. Bate, Roger R., et. al., Fundamentals of Astrodynamics, New York:Dover Publications, Inc., 1971.

2. Henden, Arne A. and Ronald H. Kaitchuck, Astronomical Photometry,New York: Van Nostrand Reinhold Company, inc., 1982.

3. Slater, Philip N., Remote Sensing, Optics and Optical'Systems,Reading, MA: Addison-Wesley Publishing Company, Inc., 1980.

4. Hecht, Eugene and Zajac, Alfred, Optics, Reading, MA: Addison-Wesley Publishing Company, Inc., 1974.

5. dines, William W. and Montgomery, Douglas C., Probability andStatistics in Engineering and Management Science (SecondEdition), New York: John Wiley and Sons, 1972.

6. Balfour, A. and Marwick, D.H., Programmin9 in Standard FORTRAN77, New York: North-Holland, Inc., 1979.

7. Satellite Photometry, Wilmington, MA: AVCO SystemsDivision, January 31, 1977.

8. World Geodetic System, 1972. Washington: Defense MappingAgency, U.S. Government Print g Office, 1974.

9. Sorvari, John M., "Photometry of Artificial Satellites, Applicationto the Ground Electro-Optical Deep Space Surveillance (GEODSS)Program," M.I.T. Lincoln Laboratory, Technical Note TN-1979-61,1979.

10. Beatty, J. Kelley, "The GEODSS Difference," Sky and Telescope,Vol 63: pp 469-473 (May 1982).

11. Kissel, Kenneth E., Mavko, George E., "The Canadian Forces/NORADSatellite Identification Sensor at St. Margarets," Air ForceAvionics Lab, Wright-Patterson AFB, OH, Final Technical Report

_- No., AFAL-TR-77-189, September, 1975 to August 1977.

12. Kissel, Kenneth E., "Diagnosis of Spacecraft Surface Propertiesand Dynamical Motions by Optical Photometry," Aerospace ResearchLabs, Wright-Patterson AFB, OH, Report No. ARL-69-0082, 1969.

12

;4 120

References (Cont'd.)

13. Gamache, R.G., LaRosa, D., "A Technique for Photometric SOClassification (U)," (Secret Report), AVCO Systems Division,

* Proceedings of the Ninth Annual NORAD Spacecraft Identifica-tion Conference (U), (Secret Document), July 1977.

14. Photometric Data Analysis Module SO Analyst TrainingCourse, Wilmington, MA: AVCO Systems Division, 1977.

15. Vanderburgh, Richard, Vigneron, Frank R., "Passive OpticalMeasurements of Alouette II Spin Dynamics," AerospaceResearch Labs, Wright-Patterson AFB, OH, Report No. ARL-

70-0253, 1970.

16. Vaselli, John, "Photometric Satellite Analysis (U)," (SecretReport), RADC Griffics AFB, NY, Final Report No. RADC-TR-76-57, April 1976.

17. Astronomical Almanac for the Year 1982, Washington: U.S.Naval Observatory, U.S. Government Printing Office, 1981.

18. Bentley, G., Blecher, R., LaRosa, D., Danis, N., "The Analysisand Interpretation of Photometric Data (U)," (Secret Report),AVCO Systems Division, Wilmington, MA, Final Report, May 1974.

19. "SOI Central Analysis System Requirements Trade Study,Vol I. Executive Summary (U)," (Secret Report), GeneralElectric Company, Syracuse, NY, Electronic Systems Division,Final Report, October 1977.

20. "SOT Central Analysis System Requirements Trade Study,Vol II, System Design Studies (U)," (Secret Report), GeneralElectric Company, Syracuse, NY, Electronic Systems Division,Final Report, October 1977.

21. Jensen, Allan R., "Space Object Identification Requirements inSupport of the Tactical Assessment of Satellites (U)," (SecretReport), Proceedings of the Tenth Annual NORAD SpacecraftIdentification Conference (U), (Secret Document), August 1978.

121

References (Cont'd.)

22. Posdamer, Jeffrey L., "Geometry of Orbiting Earth SatellitesGOES)," Syracuse University, NY, Final Technical Report,January, 1978-July 1979.

23. Sorvari, John M., "The Use of Photometry as an IdentificationAid During Search for Uncorrelated Targets (U)," (SecretReport), MIT Lincoln Laboratory, Lexington, MA, 15 February1979.

* 122 2

Appendix A

Program SATID Code Listing and

Supplementary Material

Ow

4'. 123

VAPIAL iIA;VE .ITS AND DEFI.ITIMIS

Th folloinj variable narle lists are arranged according to sub-

routine in alphahpetical order. If a variable occurs in more than one

subroutine, it is listed only in the first subroutine in which it Is

declared. Refer to the attached CO.MON Block man to determine which

variables are corimo to which subroutines.

The first column in the lists qives the FORTRAN variable name.

The next column gives the variable typa, Real(R), Integer(1), Character

(CH) or Complex(CX). The Definition column contains a short descrip-

tion of the variable.

124

-0..

VARIABLE NIAME DEFINITIONS

(SATID)

MNTYPE DEFINITION

ALPHA P Sensor Aspect tngle(Earth-Center Stable)

ALP11A11 P 0 (Horizon Stable)

ALT P, Sensor Altitude Above Sea Level

PZ R Sensor Line-of-Sight Azimuth

['ETA P Solar Aspect Angle(Earth-Center Stable)

PITAH' P is (Horizon Stable)

C R Series Expansion in Universal VariahieFormulation

DDD I Day Number

rFC~l~ PDeclination of the Line-of-Sight

OEC~L[I P.Declination of the Sun

['ELTAT P Time Increment Petween ('rhit Position Predictions

rThx P Time. Derivative of T WRT Universal Variable X

LL PR rensor Line-of-Sight Elevation

EP E-Cornponent of Thpocentric Radius Vector

r P Fuinction in Universal Variable Formulation

rDOT P Time Derivative of F

CR Function in Universal Variable Formulation

GKOT P Time Derivative of G

GHn I Hour Part of Greenwich Sidereal Time at Oh UT on1 January 1982

C(, 0 I Minute Part of Above

*GST R Greenwich Sidereal Time at Tire of Observation

GrT') P Greenwich sidereal Time at Oh UT on I JanuaryIMfl (Radians)

125

, i' ,. e ° ' - ' - . ' . - . . . " , . . • . . . . .. ..

NAiMF TYPE PEFINITIO4

GSO R Second Part of Above

HH I Iour Part of Track Time

I P I-Component of Input Radius Vector

ICOUNT I Loop Counter

IDOT R I-Component of Input Velocity Vector

ICOT2 R I-Component of Computed Velocity Vector

IDUPOY R I-Component of Input Velocity Vector(Earth radii.... per Day)

IS1'rz R I-Component of Sun Vector

ITER F Iteration loop Control Value

12 P I-Component of Computed Radius Vector

J P J-Comnnnent of Input Radius Vector

JDOT R J-Component of Input Velocity Vector

JPflT"' P. J-Cowponent of Computed Velocity Vector

J'IUP )Y r J-Component of Input Velocity Vector(Earth radiiper Day)

•'. P J-Component of Sun Vector

ti2 J-Corponent of Computed Radius Vector

R K-Corr'onent of Inmut Radius Vector

" MOT R K-Component of Input Velocity Vector

., ,L,.' 2 K-Cowponent of Computed Velocity Vector

.F K-Comnonent of Input Velocity Vector(Earth radiiper Day)

K-I I Z K-Component of Sun VectorU

2P -Coponent of Computed Radius Vector

LAT R Sensor Latitude

*, • Lfl P Sensor Longitude

LST R Local Sidereal Time at Time of OLservation

126

* AL TYPE DlEFIN4ITION

I Loop Counter

I *A(I P M'agnitude of !,'odel 1 Signature

*~ IAG2 R" 2

t'AG3 f 3 '

JilI Mlinute Part of Track Time

;*,PR I I Loop Control Variable

MU PMean of the Deviations

NI Loop Control Variable

P I S I0

P. Phase Angle

gil [R4( Signature Pattern 4umuber

I Loop Counter

P1P!i[ I Loop Control Variable

PP flagnitude of the Orbital Padius Vector

P.ALOS P Right Ascension of the Line-of Sight

RSA P Right Jscension of the Sun

flI'TIO P Ratio of two Vector Components

RDOTV R Dot Product of Radius and Velocity Vectors

RE PE-Coniponent of Sensor Position Vector

WI 11~O E-Cormponeent uf Line-of-Sight Vector

R11OI R I-Component of Line-of-Sight Vector

PIIOnJ J-Component of Line-of-Sight Vector

*RHIOS R S-Component of Line-of-Sight Vector

127

- r r I I - - C . - - I - ' . - ' .. .- - " ..

NAI1E TYPE DEFINITInIu

PInIZ r Z-Component of Line-of-Sight Vector

RI P I-Component of Sensor Position Vector

Rd R J-Component of Sensor Position Vector

R1, R K-Component of Sensor Position Vector

RS R S-Component of the Sensor Position Vector

* . A Z-Component of the Sensor Position Vector

I.O R Magnitude of the Input Radius Vector

S , Series Expansion in the Universal VariableForniulation

SEC R Seconds of Time

SUJSOR Cel Alphabetic Sensor Code

SIGMA R Standard Deviation

SIr.AI P Model Al Signature Array(500)

SIfI1 R Model R1 Signature Array(500)

SI:CI R Model Cl Signature Array(500)

SIDI R 'odel Dl Signature Array(500)

S' A R Semlmajor Axis of Orbit

SP4G R Slant Range

"S R Seconds Part of Track Time

!SR R Sum of the Squares of Residuals

.2 P. S-Component of Computed Radius Vector

T R Time Plus Time-of-Flight

TIME P Tire of Observation

TOF R Time-of-Flight

TRUSIG R True Signature Array(lO00)

TsU rti R Variable in Newton Iteration for UniversalVariable Determination

128

I4A11C TYPE DEFINITJO14

VO R Mlagnitude of Input V/elocity Vector

X R Universal VIariable for Time-of-Flight

* -XS fl Perpendicular Distance From! Earth's RotationalAxis to Sensor, Olate Earth Model

VY I Year

*Z R X Squared Divided by Sermimajor Axis of Orbit

ZS RPerpendicular Distance from the Earth's Equat-orial Plane to the Sensor, Oblate Earth Model

P1 Square Root of Z

Z2 1,Interwediate Value in Hyperbolic Orbit Calculation

Z 3 CX 11 U

129

VARIABLE NAMiE DEFINITIONS

(ELSET)

TYPE DEFINITION

APGLAT R AR0C1MENlT OF LFATITI'DE AT EPOCH

ARPP. R Argumnt of Perigee

DECON R Declination of the Orbit Normal

ECCE!I R Eccentricity

* -EDTR R not Product of the Eccentricity Vector and theRadius Vector

El R I-Component of the Eccentricity Vector

EJ R J-Component "H

* .EK R K-Component "

III R I-Component of the Angular Momentum Vector

4 HJi R J-Component" UU

IIr R K-Component N 11

IN~C R Orbital Inclination

I400TE R Dot Product of the Node Vector and the Eccen-tricity Vector

IIIOTR r.Dot Product of the Nlode Vector and the RadiusVector

III R I-Component of the Node Vector

Ili R J-Comnponent of the 'lode Vector (K-Camp always 0)

PER 1 no R Orbital Period

* PAArN r Right Ascension of the Ascending fiode

rZAOW Rl Right Ascension of the OrLit Normal

SjLR RSemi-Latus Rectum

130

NlAME TYPE DEFINITION

SF'AXIS P Semioiajor Axis of Orbit (kri)

TRA4OT R True A'nomnaly

TRIJL0OU R True Longitude at Epoch

'flU P I-Component of Circular Velocity Vector

VCJ P J-Coniponent

VCK1 R K-Component

131

VARIABLE NAVE DEFINITIONIS

(ANIGLES)

HNAiE TYPE BEFIIIITION

rri PI-Component of the Ritdi'ij Vector(Samp as 12in SATID. Renamed in COt-T40N/VECTR2/)

LCd P Same as Above for J2

ECI! p Same as Above for 1(2

LOSI 11I-Component of the Line-of-Sigiht Vector(Samieas RMOI in 'ATII). Renamed in CO"iI1KN/VECTR2/)

1.O~ 0 Same as Above for Rlhfl

[05KSane as fibove! for RhiOK

Plil Phase Anq1e(nape as PHASE in SATID. Renamedin COtWMt,'/VECTP2/)

R, 1-cor-ronent of the Sun Vcctor(Samw as ISDJN inSATIP. Renamed in COW4Of/VECTR2/)

N.SUf! P Same as Ab.ove for JSUII

SI~flr P. am as Above for KSUN

132

- . r

1

VARIAPLE NAME DEFINITIONS

(ELIPS1 AND ELIPc2)

.trr T"PF FINITIOJ

LIE "- Constant for Inner Edge Line Equation(Acronym)

CLE P. Lowe r

COE R " Outer N " " "

CUE R "Urper " " "

HL1 R X-Coord of Ilipse 2 Center

IL? R X-Coord of Ellipse 3 Center

ill R X-Coord of Ellipse 1 Center

KL R Y-Coord of Ellipse 2 Center

KL2 R Y-Coord of Ellipse 3 Center

Kill P Y-Coord of Ellipse 1 Center

4. LEIlCI R Length of Cylinder I

LENC2 I'. " 2

PADLiH P Paddle Length

PADSEP R Separation of Paddle and tain Body

PADV In P Paddle 1'idth

PADC1 R Radius of Cylinder I

RAI)C2 P , , 2

SLOPIO R Slope of the Inner and Outer Edge Equations(Acronym)

SLOPIUL P" " " jpper and Lower " "

*i S 4AJI Semnimjor Axis of Ellipses 1 and 2

SIt1IS R Sqitare of the Above

S1'AJ2 R Sei'imajor Axis of Ellipse 3

* SIAJ2 . R Square of the Above

133

Ul

1A'T TYPD PEFINITIOl

SII P Semiminor Axis of Ellipses 1 and 2

StI112 P " 3

. XCP q X-Coord of a Corner Point

m XCpr R X-Coord of (~rner Point 1

XCP1S R Square of the Above

XCP2 n X-Coord of Corner Point 2

cp,. P.Square of the Above

YCP3 X-Coord of Corner Point 3

.CP3' P cuare of the Above

XCP4 R X-Coord of Corner Point 4

XCP4 R Square of the Above

' :1II[E2 Q X-Intercept of the Inner Edge with Ellipse 2

TA~cronvn)

XIIEE3 P Same as Above for Ellipse 3

"IM" Same as Above for Lower Edge and Ellipse 2

XILE[3 R Same as Above for Ellipse 3

;:lOEE2 P Same as Above for Outer Edge, Ellipse 2

XInLL3 r Same as Above for Ellipse 3

XIULE2 r Same as Above for Upper Edge and Ellipse 2

XIIT13 P Same as Above for Ellipse 3

YCP1 P Y-Coord of Corner Point 1

YCP2 R 2

YCP3 P " " 3

Yr.P4 R " U4

YC2E2 P Y-Coord of Intersection of Cyl 2 with Ellipse 2

134

11MTTYPE DEFIMITIM4

Y1ICP P Y-Coord on Ellipse 1 Corresponding to the X-Coordof a Corner Point

Yf1CP1 P " ' for Corner Point I

yF1CrP.2 P 11 0 0 2

YE1CP3 P 14 It 'N 3

YEJCP4 R S N N 4

Y111C0 1 R Is 1 of 2t 1

YE2CP2 r of to 4S N N N * 2

YE2CP3 R S N U N S 3

YE2CP4 nN N U U N N U 4

Y13CP F: 55 N N U 3 ItU

YF3CP1 r 1-

ALYE3CP3 P U It N I U N t N 11U 3

Y13CP4 R 4

YIIEC1 R Y-Intercept of the Inner Edge with Eylinder 1TA~cronym)

YIIEC2 R Samie as Above for Cyl 2

YI[E2 R Sami as Above for Ellipse 2

YIIEE3 P, Same as Above for Ellipse 3

YILEC1 p r Lower Edge and Cyl 1

YILEC2 R U N N U U 5 2

Y ILIE'& P, of SI N III U'I5 Ellipse 2

YILFFE3 n5 N U S 5 I 3

YinFcl P N Outer N eCyl 1

13';

-NAME TYPE ( .FINITION

YIOEC2 R V-Intercept of the Outer Edge with Eyl 2

Y10EE2 R " U"Ellipse 2

YIOEE3 PHU Ellipse 3

YII'FC1 R I N 66 Nj~pper " £ 1

V IIJFC2 R go so 0 f o t o 2

YIIF2" P H "Ellipse 2

YII!E[3 P ' IN 3

130

VAP.IA!PLE NAME DEFINITIONS

(GEOMI)

;A'E TYPE DEFINITIOtl

CPIC1 C Corner Point 1 In Cylinder 1 (Acronym)

CP IC2 C11 . , , 2

CP1IE1 CI " "" Ellipse 1

CPIE2 r 1 2

CP1IL3 CI " " " " 3

CP21CI c: " 2 Cyiinder 1: CP21C2 CI' 2

CP2IE1 C' ' " Ellipse 1

CPI12 Cl " " 2

S •- .C P ? 1 E 3 C I' w " " 3

. % CP31C: Cl! 3 " Cylinder 1

CPIC2 C11 " N II " 2

CP31E1 rII ,, w " " Ellipse 1

CP 31I2 Q N ,, ,, U 2

PJiL3 C!: " I M " " 3

P" IC1 C " N 4 . Cylinder 1

C" IC? cI, " " o s 2

CP.IF C14 N " Ellipse 1

CP4,IE2 N1' N (A 2

CP4IE3 r1! 10 . N . w 3

:ELTAY Iteration Control Variable

ETA R Projected Solar Paddle Tilt Angle

.:4 II P I-Component of Iormal Vector 1

P J-Cw-ponent of :!orr.,al V,.ctnr I

137

. -.. -. -. . - .A . -.

i .ATYPE ' ErIIITION:'511", P K-Component of :or(tral V,,ctor 1

I-ro1..;.,ment of "orr.al Vcctrr 2

J-Conponent of ;:ofial Vcctor 2

I '.,-Component of Ilormal Vector 2

:131 r l-Conponent of Normal Vector 3

!3J PM J-Coinponent of Normal Vector 3

I :3'fK-Component of Normal Vector 3

PAl r I-Cnmponent of Paddle Axis Vector

PA.] P J-Component of Paddle Axis Vector

PAK P K-Component of Paddle Axis Vector

PEI I I-Component of Paddle Edge Vector

PU P, J-Conponent of Paddle Edge Vector

PEK P K-Component of Piddle Edge Vector

PSI P Projected Solar Paddle Rotation Angle

XI 1 Angle Get,een Paddle Edge and Line-of-Sight

XPIV X-Coord of Paddle Pivot Point

YLI;:E P Y-Coord of a Point on a Line

YPIV P Y-Coord of Paddle Pivot Point

ZETA P Angle Br:tl'een Paddle xis and Line-of-Sight

13P

6.

':

VARIALE WAt'. DEFINITIONS

(CAS.ES)

NA"E TYPEF FI IIOTI

C/SE-) CI' Case Zero, No Corner Points Visible to Sensor

CA'T CI1 Case One, One Corner Point Visible to Sensor

CASE2 CI Case Two, Two Corner Points Visible to Sensor

CAS13 C11 Case Three, Three Corner Points Visible to Sensor

CASE4 Cl! Case Four, All Corner Points Visible to Sensor

139

I,°

-------------

VARIABLE RAE DEFINITIONS

(AREASi Alin AREAS2)

IJA'E TYP r DEFINITIONS

AUEE P Area Retween Two Ellipse Curves

AFLE P Area Petween a Line and an Ellipse

ALL P Area Between Two Lines

CONST P Constant

CONSTi R Constant

C(ST2 R Constant

y. Q Y-Coord of an Fllipse Center

Kf P " " " Ellipse A Center

,- T. p " "I "I "I "

SI.(PE R Slope of a Line

o SLOPEI " "

SLOPE2 R "

.VAJA R Semimajor Axis of Ellipse A

S.'AJB P " N " p

ShItIA R Semiminor N " A

S'rNB P N N N N B".1 P Limit of Integration

X2 P " N "

i4

' ' 140

Ii

-• -...- ,, -.-- ;o - -

VARIABLE NAME DEFINITIONS

(AREAS)

1A"E TYPE PEFI'IITIONi

ALPIHAP P Sensor Aspect Angle for a Plate

''PAID P Area of Partially Otscured Paddle Visible toSensor Projected Into tlie Image Plane

ARPAD R Area of an iUnobscured Paddle Visible to Sensor

L.-4

0)1-

0.-.

i14

VARIAPLE UAII. DEFINITIOIS

(CONE)

NAIEf TYPE PEFINITION

ALPHAII P Sensor Aspect Angle to a Conic Surface Element

ARINC R Incremental Surface Element Area

VASRAD R Conic Base Radius

'VETAN R Solar Aspect Angle to a Conic Surface Element

CIl R I-Component of Conic Normal Vector

CNJ R J-Component Of Conic Normal Vector

CUK P, K-Component of Conic Normal Vector

CMN Ci Pure Cone Flag

(,OiIIT Cone Height

COuNT I Loop Counter

-6IFA'1r R Conic Half Angle

- IRCONE R Irradiance of the Cone

NOSPAD R Nose Radius of Truncated Cone

(11RCA . Angle Betueen .djacent Surface Element Normals

REFCOn R Reflectivity of the Cone

SLEPI P Slant Length of the Cone

TCOUl Cl1 Truncated Cone Flag

1

I'

F" 142

a

'JARIArLF NAME DEFINITIONS

(SI GA1)

11i'.IF TYPE N)EiNITIO1N

ARLAC r. Cylinder Projectedi Area

Al 1%E AP P Pl ate Projected Area

IRCYL p Cylinder Irradiance

IRPLT P, Plate Irradiance

LEIITHi P Cylindler Le~ngth

RADIUS RCylinder Radius

REFC R Cylinder Reflectivity

REFP pt Plate Reflectivity

TITTA R A Function of ALPHA. B3ETA and PHASE

143

"ARIABLE NAIE PFFINITIOIS

(SIGPI)

I1I11i TYPE DEFINITIONI

ARFACI P Area of Cylindr I

APLAC2 It 2

ARIAC3 " " 3

ARLAPI P. " Plate 1

ARLAP2 P. " " 2

AREAP3 P, " t t 3

BETDEG P, BETA in Degrees

IR-0flY P, Total Irradlance of Nian Satellite Body

IPCYL1 P. Cylinder 1 Irradiance

IPCYL2 R Cylinder 2 Irradiance

IPCYL3 R Cylinder 3 Irradiance

al II"PAD R Irradlance of a Paddle

IPPLTI P " Plate I

IRPLT2 P, 2

IP I.T3 P " " 3

PrF P, Reflectivity of Cylinder 1

P[FC? R"e 2

RJTC3 3

PFFPI R " Plate 1

PFFP2 P 2

PEFP3 r " 3

144

VARIABLE NJAMlE PEFINITONS

(SIGCl)

NAI TYPE r)EFIIXITION'

IRCI Irradiance of Cyllnder 1

IRC' P 2

IIIPLT r " the Plate

LEN 1 R L.ength of Cylinder 1r2 10L4f2 P " " 2

PLTLEN R Plate

PLTI'ID R Ulidth of Plate

RADIL'S P Cylinder Radius

TITrTAN r A Fuuction of ALPIIAFV, rTAII and PIl

145

6

I.IARIAFLE UNAI DEFINITIONS

(SIGfD 1)

ildA? Diamveter

Irr R iffuse Reflectivity

IPPI R Irradiance of the Sphere

~PIL F P Srecul ar IPflectivi ty

VARUL[LE NAME DEFINIITIONIS

(cn!IPAR)

MIT TY!T PErIMITIOl

~IlVI G R Array of Deviations(!5OO)

11 lorkinr' /~rray of Synthetic Signature ~Jt(500)

P Arra-/ of Mlodel 5fl's

,TrnV P Array of "odel SICIA's(25)

rtN Array of 'Model Ilean Deviations

r Sumi of the Sc:uares of Deviations

147

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Appendix B

Solar Paddle Obscuration Algorithm Used by Subroutines

GEOMI, CASES and AREAS

The satellite model SIGB includes two sun-tracking solar paddles.

Unless the satellite is observed on or near the meridian which passes

through the sensor's south point, one solar paddle will be totally vis-

ible to the sensor, but the other will be partly blocked from view by

the satellite's main body. This algorithm first determines the true

orientation of the satellite and solar paddles with respect to the

sensor, in three dimensions and then projects the points, lines and

curves which define the outline of the satellite into a plane perpen-

dicular to the line of sight vector, 7, referred to as the optical image

plane. A two-dimensional x-y coordinate system is defined in the optical

image plane with the y-axis always lying along the projection into the

plane of the orbital radius vector, F, and the x-axis orthogonal to y

and positive to the sensor's right. The origin is located at the mid-

point of the satellite's main body cylinder. Figure B-1 will be a help-

ful aid to visualization throughout the remainder of this algorithm

description.

The projected exposed area calculation is performed after the pro-

gram has determined the x-y coordinates of the paddle corners, equations

for the lines and ellipses which define the satellite body, and the angles

I;1,

|.191

* .. ~ w r PE

10CP3A

Figure B-I Paddle Obscuration Geomietry

192

between the paddle edges and the x and y-axes. The algorithm proceeds

U as follows:

Determine Key Vectors

By the time GEOMI is called, the line of sightj, the orbital

radius vector F, and the sun vector 'W are known. We must determine

the paddle axis vector A, and the paddle edge vector -:

A is orthogonal to s, since i is normal to the solar paddle, and

to 1, since F is the body longitudinal axis of symmetry. Therefore:

PA X -

su~ri f r kv

" : ( itnk- SoV%; r+ - risuwt-sovt rk) + t(risun; -sun-Lri

E is orthogonal to i and to FA, therefore:A A

I sui sun! Sunk

.o°Pk

"+ - . .

iL

=(ul A F%-.'L-(SVIMrP-Lu% +&%PA- sj*

A °,V

Determine Key Angles

Known angles at this point are sensor aspect angle, and solar

.. aspect angle,f3 We must now find the angle between the paddle axis

* . and the line of sight,t , the angle between the paddle edge vector and

the line of sight,C , the projected paddle tilt angle,1 , and the pro-

-," jected paddle rotation angle,#.

Cos-' PA + Ii P _ + lit PA1

c {14 E +i # + it PE ]

-"(zeta) andE (xi) will be used to obtain paddle dimensions pro-

jected into the optical image plane. Obtaining the angles (psi) and

(eta) is less straightforward.

"" may be viewed as the angle between two planes, both containingi.

The first plane containsJ and F, and the second plane contains and ].

Since the sensor is looking downj, it sees both planes edge-on. The

lines of intersection of these two planes with the optical image plane

are the two lines which we see as the projected paddle axis and radius

vector, depicted in Figure B-I. To obtain , the angle between these

104

two vectors in the image plane, we determine the angle between the two

planes by finding their normals and the angle between them.

:,- g,= I x- 5 i /

Note that R1 is parallel to the x-axis. In like manner,

-'-A

:-'.Therefore, is given by

V..:o N l2l j)4(N ij)(NZj) (Ni

..-i: 1 may also be viewed as the angle between two planes containing 7.~~The first plane contains 1r and PE and the second contains ][ and 1. We

find the normal to the plane containing k and PE thusly:

113 2 I (N32L)' .e.(N42) + (I43j,)V

*(MI)(t~3.b)4 N k) ~

K.. and

Iii I 31

195

Determine x-y Coordinates of Paddle Corners

First, locate the paddle pivot point depicted in Figure B-1. The

x-coordinate will be called XPIV, and the y-coordinate will be called

YPIV. Corner points will have coordinates XCP1, YCP1 through XCP4,

YCP4. These are also the FORTRAN variable names for these points.

XPIV% sivitiVn(ri +p) where rl is the main cylinder

radius and p is the separation between the cylinder side and the inner

edge of the paddle. Note that sin (rI +p) is the length in the optical

Image plane of the line segment from the origin to the pivot point.

YPIV= -cos sin

Next, we locate the paddle corners

*xcp-- XcP Ipn+stI Sin (v/.) where W is paddle width, and sinS

. (W/2) is the length in the image plane of the line segment from the

pivot to corner point 1.

YCPL " *C/V oSv1 SIN' (W2,) and

%"P2z YILQPI-sqyksSn5() where L is paddle length,YCP2V-c f sin + L)ycft

YCe: %'ly - 1 I st (W/2)YcP4 YVPN -cos 1 sin F (wIZ)

"i XCP3 X CP4 -tsin +Si1n C (Lp)

fCr3 =YCP4 -cost Sito (L)

196

Determine the Ellipse Equations

Projections of the cylinder ends onto the image plane form ellipses.

The general equation for an ellipse is

b2 where h and k are the x and y-coordinates

of the ellipse center, a is the semi-major axis, and b Is the semi-minor

axis.

GEOMI recognizes three ellipses, formed by the top and bottom ends

of the main cylinder (ellipses 1 and 2), and by the bottom of the second

cylinder (ellipse 3). GEOM1 labels the ellipse center coordinates in

the following manner:

HUI = the x-coordinate of the center of ellipse 1

KU1 = the y-coordinate of the center of ellipse 1

HL1 = the x-coordinate of the center of ellipse 2

KL1 = the y-coordinate of the center of ellipse 2

HL2 = the x-coordinate of the center of ellipse 3

KL2 = the y-coordinate of the center of ellipse 3

From Figure B-1, It is clear that the x-coordinates of all ellipse

centers are zero. The y-coordinates are given by

KUIZ sin at (LI/Z)

KL2= -son aL ((U/Z). L2)

where Ll is the length of cylinder 1

and L2 is the length of cylinder 2.

197

The general ellipse equation for 411 values of h=O becomes:

z =-z

and solving for y gives

The positive sign gives a y-coordinate on the top half of the

ellipse, and the minus sign gives a y-coordinate on the bottom half of

the ellipse.

Determine the Paddle Perimeter Line Equations

The general equation of a line in point-slope form is y=mx+c,

where m is slope and c is a characteristic constant. The slope of the

_E vector projection in the Image plane is,

Sr e +L - (IT - 11)

GEOM1 labels rpe as "SLOPIO" for "slope of the inner and outer

edges." Similarly,

M%"tav(I+

= "SLOPUL", for "slope of the upper and lower edges."

The constants for each edge of the paddle are evaluated using the

point slope form, c=y-mx, and setting x and y equal to a known point on

the applicable line segment. Expressed in FORTRAN variable names,

19

. . .1 .8

A S C C . - -o

'C

-le zYI -L(S.PIO)CiLPIV) co~ni or i±vvera~A&.

COE c YC-P2 -(SLOPIAYCPZ, q ouer ,

CUE = ICPZ- (SLOPUL)OL LP) upper d

CL.E. y(_p4-(sLOPUL)(UCP4) p lower V

Note that if SLOPUL=O, then SLOPIO is undefined and CUE=YCP2 and CLE=

• YCP4.

Determine the Intersection Points of Paddle Edges and Cylinder Sides

The lines through each pair of corner points intersect the lines through

the cylinder sides at some points. These points are determined by using

the point-slope form of the above line equations to find y-values for x

equal to cylinder radii. This calculation is performed whether or not

the paddle edge actually crosses a cylinder side.

Determine Other Critical Points

Other points critical to later area calculations are, 1) y-values

of points on ellipses corresponding to the x-coordinates of corner points,

when their absolute value is less than that of a cylinder radius, and 2)

the intersections of paddle edge lines and ellipses under certain condi-

tions. These points are used to establish the Intervals of integration

for area calculations in subroutine AREAS.

The former set of points is found by setting x equal to the x-coor-

dinate of the corner point and solving for y in the equation for the

ellipse. For example, in Figure B-i, the y-coordinate on the lower part

of ellipse 2 for X=XCP4 is

= -- .-1 ;IY where bacosgc(r), and

199

i,.

Ta=r. Subroutines ELIPSI and ELIPS2 perform this calculation. The

y-coordinate in this case is labelled YE2CP4 for "y-coordinate on

,-... ellipse 2, for corner point 4."

The latter set of points is calculated iteratively, if it is

determined that a corner point actually lies inside one of the ellipses.

For example, if

(JCp4 )' 4.rl"Z Yc4 < , LI and YCP4.WY2cP4

then we know that corner point 4 is inside the lower

half of ellipse 2. The iteration scheme begins in GEOM1 at statement

label 75.

GEOM1 assigns a value of yes (Y) or no (N) to a set of character

variables which indicate whether or not corner points lie within cylind-

er 1, cylinder 2, or any of the three ellipses* i.e., if character

variable CP41E2='Y', "corner point 4 is inside ellipse 2." See the

variable listings in Appendix A for definition of this and similar

variable names which are designed as acronyms. These character variables

are used by subroutines CASES and AREAS to determine which of five geo-

metrical conditions (zero through 4 corner points visible to the sensor)

applies at a point in time. The case governs which area calculation

algorithm is used by subroutine AREAS.

200

Determine the Applicable Geometrical Case

Subroutine CASES contains a decision structure which assigns a

value of Yes (Y) or no (N) to character variables CASEO, CASEI, CASE2,

CASE3, and CASE 4. The number in each variable name refers to the

number of paddle corner points visible to the sensor.

CASEO means all corner points lie inside a cylinder or an ellipse

in the optical image plane, and none are visible to the sensor.

CASE has two subcases. These either indicate that corner point

two is visible and all the others are not; or that corner point three

is visible and all the others are not.

CASE2 covers three subcases. Corners 1 and 2 can be visible and

the other not, or corners 2 and 3 can be visible and the others not,

or corners 3 and 4 can be visible and the others not.

4- CASE3 has two subcases. Only corner point one can be inside a

cylinder or an ellipse and the others visible, or only corners point 4

can be insider or cylinder or an ellipse and the others visible.

CASE4 indicates that all corner points are visible.

Determine the Projected Paddle Surface and Visible to the Sensor

A sample calculation for the geometry in Figure B-I will best illus-

trate the method, Figure B-i is an example of CASE3. To determine the

exposed paddle area, it is necessary to integrate to obtain the area

enclose by exposed paddle boundaries. The area between two functions

f(x) and g(x), over an interval (tl,t 2) is given by

12.a

2nl

F-'-

Figure B-I requires integration over four intervals. Interval 1

Is from t1=r2 to t2=rl, f(x) is the equation of the line through corner

K:: points 3 and 4, and g(x) is the equation of ellipse 2. Therefore,I -°

As= r44cLE) dA f a(ctx (]

~Interval 2 is from~ tl~rl to t2=XCP1, f(x) Is the equation of the

- line through corner points 1 and 4 and g(x) is the equation of the line

- through corner points 3 and 4, so similarly, interval 3 is from tlXCPl

to~r t2XCP3 sota

Rz M e'X tL-E) i, fmiox+ CLE) cA'

Interval 3 is from tI=XCP1 to t2=XCP3, Therefore,

th cFinally, interval 4 Is from XCP3 to XCP2, giving us

:.,A 4 : Mf V - 4"(CUE)j - (!.1 id E)I

UP jI.CI m

nTotal exposed projected paddle area Is then

~- - .- - - - - - - - - - - - P3-

= E¢ ^ CE

2 0

Fialitra sfomX3t C2 iigu

I" A

Note that since this is a projected area, it would not have to be

-. multiplied by coso in the irradiance equation, and irradiance is given

S by

E ptAp eos where r is slant range

irr'

The decision structure of subroutine AREAS determines the proper

interval of integration for each case and subcase, based on the output

of subroutines GEOM1 and CASES, and calls subroutines AREASI, AREAS2,

and AREAS3 to calculate projected paddle areas. The area determined

is named APAD, and is used by subroutine SIGB1 in the calculation of

total irradiance of the satellite.

° 3

D °,

Appendix C

The Subroutine CONE Conic Irradiance Approximation Algorithm

Because of the extreme complexity of the programming decision

structure that would be necessary to evaluate the true conic phase

function (Ref 7: ), an iterative approximation is used by subroutine

CONE to obtain diffuse conic irradiance. CONE will approximate irra-

diance for a pure cone or for a truncated cone.

The conic surface is approximated by 200 flat strips as depicted in

Figure C-i. In Figure C-i, V_ is the circular velocity vector, Z-N, is

the first normal vector to a flat surface element which is calculated,

and -N. is an arbitrary ith surface element normal. The anglesoi and

are tae sensor and solar aspect angles measured from the normal to

the ith surface element. The angle 4 is the angle between adjacent sur-

face element normals. For the number of surface elements,n =200,4J=1.8

degrees. The angle I is the conic half angle. The circular velocity,

V', calculated by subroutine ANGLES, is given by

where H is the orbital angular momentum vector. The body-centered coor-A A

dinate system is defined by the unit vectors, r, vc and H. From FigureA A

C-2 we see that unit vector CN1, which lies in the r, vc plane, is

given byA VC

- O~N= ro +( c + (o)^

204

d:

AWe can express CNI in terms of the geocentric-inertial frame, since we

AAalready know and vc in that frame.

10 Ar iki (r 3 )c ") ( and

AVC (VcL) I +(Y-i) + (Vt L. Therefore,

c. COSI (4 , ')1+ SkA Wi+Vj+ 4"+i) and

A

geocentric-inertial components of CN, are given by

A

CN= cosX(r)+ sIX(YC a)n: ;cN,I =co(Atsv(c)and

CI t" cos(r) +StVI(Yck)

:" C is the only one of the flat surface element .smals V.it.h isA A A

in the. r, vc plane at an angle V' from r. To compute the components of

the other 199 normal vectors, we perform a right-handed rotation of the

body-frame about vc by the incremental angled, to establish another

vector, r , which will be an angle I from the next normal vector, CN2.

A A' A,,CN2 will lie in the r , vc plane. r is given by

A/ Ar'= cos.r- & .ioH

A

r Geocentric-inertial components of r are,

ri =cos wt ri sm wr'= rcos w i vIW (14i)

I2u5= o

Finally, CN2 is given by

2

a4" (Loc C and

CN2iL cos$ [Cos W q)+ sin w(n e] W+ s (vc)

cc COS ao() Ii)(j)4S: CNzw coStl [cosa(Vkwi ink)(Hh~ jtS'vi ~ (CI)

In subroutine CONE, the calculation of new normal vectors is done

in a DO-loop which runs from 1 to 200. Each time a normal vector isA A

determined, t is added to the previoust. and r and CN are calculated

until a normal has been determined for each flat surface element. At

each step, the sensor and solar aspect angles are calculated. If both

and Pi are less than 90 degrees, an irradiance is calculated for thesurface element and it is added to total conic irradiance. If either

or Pi is greater than 90 degrees, no irradiance is calculated forthat step in the loop. Total irradiance is given by

z : E t a'where Ei is the irradiance of the Ith surface

element and Ec is total conic irradiance, called IRCONE.

Subroutine CONE is currently configured for a conic which is axi-

Aally aligned along vc, but it could easily be made general by allowing

it to receive a different vector as input.

, .206

CN,

207

CN

Figure C-2 Conic Approximation Vectors

* 208

VITA

John D. Rask was born on 20 May 1949 in San Diego, California.

He graduated from high school in Spring Valley, California in 1967 and

attended San Diego State College from which he received the degree of

Bachelor of Arts in Astronomy in June 1971. Upon graduation, he enlisted

in the Air Force and served for four years as a Czechoslavakian linguist.

In 1975 he completed OTS and entered the Space Systems career field as a

Space Surveillance Officer with the 14th Missile Warning Squadron until

September 1978. After a remote tour with the 13th Missile Warning

Squadron at Clear, Alaska, he served as a Space Object Identification

Analyst at the ADCOM Intelligence Center, Colorado, until entering the

School of Engineering, Air Force Institute of Technology, in June 1981.

Permanent address: 5520 Hubner Rd.

San Diego, CA 92105

209

4.

"'~-' " " ""."" , ..

SECURITY CLASSIFICATION OF TIS PAGE (When Date Entered) __________________

* AF IT/GSO/PH/82D-34. TITLE (mid Subtitle) a YEo EOTaPRO Ogz

MODELING OF DIFFUSE PHOTOMETRIC SIGNATURESMSTei

OF SATELLITES FOR SPACE OBJECT IDENTIFICATION S. PERFORMING ONG. REPORT MUMMER

7. AUTHOR(@) SCONTRACT OR GRANT MUMSER(o)

John D. Rask

S. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMEtu. PROJECT, TASK

Air Force Institute of Technology (AFIT-EN)ARAAWKUNTM"S

Wright-Patterson AFB. Ohio 45433 ______________

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT OATS

December, 1982IS. MUMMER OF PAGES

1.MONITORING AGENCY NAME &AODRESS(Si different from Controlling Office) IS. SECURITY CLASS. (of Ole. 0"peu)

* UNCLASSIFIED

S.. ECL ASSI FIC ATION/ DOWN GRADING

* 16. DISTRIBUTION STATEMENT (of Ole Report)

Approved for Public Release; Distribution Unlimited

'.DIST RIOU TION STAT EMEN T (of the abstract ufoted in Blck 20. if different how. Reprt)

I$. SUPPLEMENTARY NOTES

no Aw An w~. Approved for Publ ic Release; IAW AFR 190-17

IS 110400chMd 1tPM~jg ~ i APR 1b

19. KEY WORb (Cotinue an ,ovoree side inece@owj aid identify by block nhmbher)

Photometric SignaturesSatellite PhotometryDiffuse Photometric Signatures

20. ABSTRACT (Continu, a roveroo aid* if noooeary and identily by bloak .,be)

The diffuse reflection characteristics of four types of satellites weremodeled assuming perfect Lambertian reflection. A FORTRAN program was devel-oped to generate synthetic photometric signatures of the models and statisticallpcompare them to actual data, in order to perform pattern recognition. Datawere available for the most complex model, which accounted for phase shadowing.and obscuration of some body parts by others. One set of signatures was used tovalidpte the satellite model, and others were used to test the program's

DD 1473 CDITION OF I1NOV 65 OBSOLETE9 UNCLASSIFIEDSECURITY CLASSIFICATION Of T"IS PAGE. (Ohmae WON. to,.

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ability to correctly identify satellites. The program was able tocorrectly identify the satellite as long as the phase angle remainedsmall, generally less than 90 degrees. For larger phase angles, thetrue signatures diverged significantly from synthetic signatures.Failure of the model at large phase angles was probably the resultof the Lambertlan assumption being untrue, with the difference becomingmore noticable as phase angle increased. Future research should attemptto model diffuse reflection not assuming Lambertian reflection.

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