L'I.M N U e.7o kl L IA:, 

WHS-346 

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NRO APPROVED FO 

RELEASE 1 JULY 20 

26 May 1967 

To: Lt. Col. J. P. O'Toole 

From: R. C. Hansen 

Subject: Operational Concept for the MOL/DORIAN 

Manned/Automatic Configuration 

Reference: Letter from R. C. Hansen, same subject, dated 14 April 1967. 

The purpose of this letter is to transmit the attached study, 

MOL DORIAN OPERATIONAL CONCEPT - AVAILABILITY OF ALTERNATE TARGETS. 

The attached study completes the written action item promised in 

the referenced letter. A briefing on the study results can be given 

at your convenience anytime subsequent to 2 June 1967. 

The results of this study indicates that an operational concept 

embodying portions of the Group (Voting) and the Time-To-Go (Sequential) 

concepts provides considerable advantages over either pure strategy. 

With very little modification of the on-board logic the advantage 

of additional alternates offered by the sequential method can be had 

while at the same time permitting voting and retaining the capability 

of knowing, on the ground, what path is followed by the primary optics 

when interdicted. 

It is our recommendation that the combined concept be adopted 

immediately. With the formal adoption of the concept follow-on 

studies will be made to refine and improve on the concept. For 

example, it is generally conceded that the number of alternates available will normally exceed the system's capability to look at them all. 

If the nominal time allocated to each alternate is not used, how can 

this excess time be utilized to look at additional alternates? The 

planning and implementation of these additional alternates is an 

example of such a follow-on study. 

4w) 

.0 ffir,47.7.p. ItUri.nnmm zprt‘ ill 
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OPERATIONS ANALYSIS AND MISSION PLANNING STUDY 

MOL DDRIAN OPERATIONS CONCEPT 

AVAILABILITY OF ALTERNATE TARGETS 

26 MAY 1967 

STUDY CONDUCTED BY 

R. N. GEDDES 

CONTRIBUTORS 

M. E. SHUCAR1' 

D. R. THOMPSON 

W. L. BROGAN (Satellite Navigation Dept.) 

L. MACLEAY, Major,(SAFSL 7-C) 

• 
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WHS-346 

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26 May 1967 

ABSTRACT 

The studies presented here develop both analytical expressions 

and numerical results for the availability of alternate targets. 

Continuation of the studies performed in Reference (4) (WHS-328) 

is performed showing the conditions under which it would be advantageous 

to process alternates sequentially. 

The primary results of these studies focus their attention on 

the determination of decision times for the voting concept. In 

particular the concept of the voting has been expanded to include 

all of the desirable features of sequentially processing while maintaining the simplicity and positive control features of the voting 

strategy. Section 17 of this report presents the summary, conclusions 

and specific recommendations for alternate target selection and the 

operational concepts. 
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SECTION 1 

INTRODUCriON 

The studies presented here are a preliminary attempt to expose 

some of the salient features and tradeoffs associated with alternate 

target selection as well as decision processes. It is assumed throughout this report that the reader is familiar with the following documents: 

1. Letter, Subject: Operational Concept for the MOL/DORIAN 

Manned/Automatic Configuration, March 21, 1967 (P-30969). 

2. Letter, Subject: Comments on the Operational Concepts 

for the MOL/DORIAN Manned/Automatic Configuration, April 14, 1967. 

3. Report, Parametric Profile Studies, WFS-112, January 12, 1967. 

4. Report, Alternate Target Considerations, WHS-328, May 9, 1967. 

The scope of the studies presented here is severely limited 

because of both time constraints and the inherent complexity of the 

problem. Many simplifying assumptions have been made for the sake of 

producing closed form expressions and simple graphical results. The 

real merit of these studies is to analytically demonstrate the nature 

of the problem rather than to present detailed solutions. The mission 

planning software contractor must initially undertake definitive studies 

which will ultimately lead to definition of alternate target strategies. 

The problems approached here are not concerned with the implementation 

of decision logic on the ground vs. on-board but.rather treat the 

problem as one of a system optimization. The most general underlying 

assumption made in this analysis. is that the primary optics path has 

been preselected, based upon an independent optimization criteria. The 
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F1 - 17i 7 

optimization of score is attempted by interdicting the primary path 

in favor of alternate targets. Ideally one would like to attack the 

problem of simultaneously picking the prima)y& aLternate paths so as 

to maximize the score but the complications caused by attempting such 

an approach at this time preclude such an effort. 

The approach taken with these studies has been to provide 

the analytical theory for processing alternates and then numerically 

plot tradeoffs utilizing reasonable values for system parameters. 

The necessary and sufficient conditions have been derived for special 

cases for alternate target candidates for both the voting and sequential 

strategies. These have been compared graphically to demonstrate the 

difference in availability of alternate targets as a function of the 

relative geometry and strategies. 

SECTION 2 

TARGET TIME LINE DEFINITIONS 

A. Primary Optics Path. The primary optics path timeline 

is defined by three basic time parameters; the time that the mirror 

is slewing, the time during which the mirror is settling, and the time 

during which the mirror is tracking and photography is being performed. 

Figure (1) below represents a typical timeline for the primary optics 

path. 

Target i Ta,get j 

T

r1 T

s 

T

t T

r 

tt 

Ts r 

tr ti 

FIGURE 1 
NRO APPROVED FOR 

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In this notation, the "T's" represent the time duration of a given 

operation, while the "t's" represent the absolute time at the start 

of these operations. The specific definitions for the symbols used 

are given below. 

T

r 

slew time 

T

s 

settle time 

T

t 

= tracking time 

It should be noted that, in general, each "T" and "t" has associated with 

it a value "i" which represents "i-th" primary with which the "T" is 

associated. 

B. Alternate Target Timelines. The alternate target timeline 

may be represented in a manner similar to the primary optics path. 

However, several distinct differences exist between the primary and 

alternate timelines. Figure (2) below represents a typical alternate 

timeline. 

T

s 

T

t 

is t

t 

t

L 

FIGURE 2 

• 

The same notation is adhered to as given above for the pimary 

path with the addition of several new terms: 

1. t

o 

is defined as that time at which the alternate target 

may first be viewed by the acquisition scope. In terms of the template 

t

a 

t

r 
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4-sTrA 4/Ik " 111 t ft;.i 

Liu t.1 

Pag 5 rt 

IYV!k 1 '7,3

e

1,11 

.1k Ft 1,1•J‘i 

work (Reference 3), this corresponds to the vehicle time at which 

intersection of the ellipse and the alternate occurs. 

2. t

L is defined as the last time at which a photograph may 

be taken of the alternate. If monoscopic photography is all that is 

required, then this time would correspond to the maximum allowable 

aft look angle. 

3. T

D is defined as the minimum allowable dwell time which 

the crew can be assured of having in order to view the target for 

activity indicators. It should be noted that, in cases where the 

target is obscured, the actual time spent for viewing the target 

may be appreciably less than TD. 

• 
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SECTION 3 

EXPLANATION OF ALTERNATE VISIBILITY TIME

, 

T

V 

The visibility time Tvis presented in Equation (4) and is 

defined as the time interval between the latest possible time for 

completing a photographic operation (tL) on a target and the earliest 

possible target acquisition time (t

a

) using the ATS. The visibility 

time essentially encompasses the time during which the ATS is tracking 

the target (dwell time), the time for the primary optics to slew and 

settle and the time for the photographic Operation. 

Tv= h I tan QS 

V cos .57 tan 47= t - L to 

( 1 ) 

where 

1 

. cos 

cos 

cos S? 

(2) 

Maximum forward look angle with ATS 

Target obliquity angle 

Photographic stereo convergence angle 

20 seconds (based upon orbit selected) 

Equation (1) assumes the latest possible time for initiating a 

photographic stereo sequence to correspond to the time of closest approach 

.(t

ca

)• This assumption can be modified by merely adding or subtracing 

a characteristic lag time to or from equation (1) to account for other 

assumptions. 

= 

= 

h _ 

v 

7" 17"5 n 711 71 
20 seconds was used to generate these curves. This h/ 

V 

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OJ r L ^-11 

WHS-346 

Page 7 . 

, v.: r 

Wc- V,iPpl 

Figures 3, 4 and 5 were generated based respectively upon stereo 

convergence angles of 15°, 20o and 25° by using equation (1) in 

conjunction with the appropriate parametric values. An h/V value of 

value is 

representative of the average value of h /V over the latitude regions 

of most interest ( h/V 

 is always within + 1.2 seconds of the 20 second 

value over the latitude range from 80°N to 10°N descending). 

• 
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NRO APPROVED FOR 

RELEASE 1 JULY 2015 

rtMitt. 

F.1 1 3 

,■ . ir 

SECTION 4 

NECESSARY AND STRITICIENT CONDITIONS FOR A TARGET TO BE AN 

ALLERMATE CANDIDATE 

The ground software must have some quantitative criteria by 

which it can determine the suitability of a target as an alternate. 

It seems reasonable for the ground software to select, initially 

alternates based upon a criteria which allows the crew to have a 

guaranteed dwell time as well as there being sufficient time for 

diverting the primary optic's path to photograph the alternate 

target in the desired photographic mode. We define the term 1K 

by Equation (3) below as. the time required to roll the primary 

optics from the primary oath, allow it to settle, and track the 

alternate target for the necessary duration in order to accomplish 

the desired photographic sequence. 

TK= T

r 

+ Ts -+ TT (3) 

It becomes obvious that the necessary and sufficient condition for 

considering a target as an alternate candidate can be expressed as 

Equation (4) below. 

V 

T

K 

 + T

— D 

An additional definition will be useful by decomposing the term TKas 

given below by Equation (5). 

T

K TC + (5) 

(10 

• 
NRO APPROVED FOR 

RELEASE 1 JULY 2015 

The term T represents the time allowed for camera operation. TCis 

the settling time and the tracking time required and this term is 

independentoftherelativegemetu atargets.TheterniT

r' 

 however, 

is specifically a function of the geometrical spacing of the targets. 

In most studies the pitch rate is double the roll rate. It is usually 

the case that the roll motion of the primary optics becomes the 

dominating conflict parameter and hence the roll history is used in 

the time line. 

The template analysis referred to in Reference 3 represents 

a two dimensional plot of the constraints specified by Equation (4). 

SECTION 5 

NECESSARY AND SUFFICIENT CONDITIONS FOR SETRCTING AN ALTERNATE 

CANDIDATE FOR THE VOTING STRATEGY. 

Figure (6) below represents a typical timeline for an alternate 

target. 

.* F

t

d 

FIGURE 6 

It will be noticed that there exists a new point in time td which is 

defined as the decision time. The introduction of this term gives 

rise to two additional constraints. Clearly the decision time must 

r El 
NROAPPROVED FOR 

RELEASE 1 JULY 2015 

cq-nrrY e 

Z-nm PI, C:Y LA-4 ;rtii Yafj 

be set far enough forward in time from t

o 

so as to guarantee that adequate 

dwell time can be had to view the target before the decision is made. This 

condition is expressed below as Equation (6). 

t

d - to> T

D (6) 

Additionally, the decision time must be set far enough in front of the 

time tL 

so as to insure that all necessary camera and mirror operations 

can take place before time tL is reached. This condition is given below 

by Equation (7). 

tL - td T

K ( 7) 

Strictly speaking, Equation (6) and (7) are the necessary and sufficient 

conditions for determining whether or not a target is an alternate candidate 

under the voting concept, since the addition of Equation (6) and (7) yields 

Equation (4). As a matter of practicality-, however, one would originally 

screen the alternate target using Equation (4) and then having selected 

the decision time further screen the alternate target by using Equation (6) 

and (7). 

It is easy to imagine that the screening process previously mentioned 

does not take place independently of the selection of td, When the voting 

strategy is used it is the responsibility of the ground software to 

simultaneously select td appropriately so as to optimize via some predetermined criteria which is used to optimize alternate target selection. 

At the time of this writing there is no known criteria for selecting td. 
(8) 

(9) 

NRO APPROVED FOR 

RELEASE 1 JULY 2015 .4421.1a: 

WHS -346 

Page 14 

SECTION 6 

EXAMINATION OF GEOMETRY CONSTRAINTS FOR TWO ALTERNATES UTILIZING 

THE VOTING STRATEGY 

In this analysis certain simplifying assumptions need to be 

made in order to present results in a simple manner. The model 

which is considered here is shown in Figure 7 below. 

FIGURE 7 

#1 

t

al 

1 t

Ll 

#2 

tat - t

d t1,2 

Consider two alternates each with the same roll time T 

r 

from the primary optics path. Without loss of generality it is 

further assumed that t

a2 

is greater than tal. The analysis 

proposed here considers only one ATS for viewing the alternates 

and tacitly assumes the other ATS to be committed to viewing the 

primary targets. Because of the ordering of the acquisition times 

it shall be assumed that the selection of the targets for viewing will 

be target alternate number 1 first and then alternate number 2. 

Consider first the constraints applied to target number 2. 

This target will be viewed and after a suitable viewing time the 

decision time td • will occur and a decision will be made between target 

number 1, target number 2, and the primary. Hence, from Equation (6) 

and (7) we may write the two primary constraints for alternate target 

2 below. 

t

L2 

td > T 

— K 

tat TD 

nPmfilt'Ir 
r17.74- Pi r7 7 ".; 

_4 

NRO APPROVED FOR 

RELEASE 1 JULY 2015 

In order to write the constraints for alternate target #1 

it is necessary to recognize two important exceptions to equation (6). 

After the dwell time has been spent on alternate target #1, the 

decision time must still be at least an additional amount of time in 

the future to allow for the dwell time of the number 2 alternate 

target and the slew and settle time of the ATS. The constraints for 

alternate target #1 are given below.by Equations (10) and (11). 

t

L 

t

d T

K 1 

(10) 

t

d t T, + TD 

+ T

a l - 1/ B 

where T

B 

is the slew and settle time of the ATS. 

Thus, Equations (8) through (11) define the geometric constraints 

for two targets being alternates as a function of their relative geometry. 

In particular, cops (dintsfrom these equations shall be derived as a 

function of the differential acquisition time p. to and the roll time,

r 

from the primary path to the selected alternate. Equations (8) and (11) 

may be added yielding Equation (12) below. 

t

L

2 - 

t

a

l 

+ 2 TD + TB (12) 

Similarly Equations (9) and (10) may be combined yielding 

Equation (13) below. 

t

Ll 

- t

a2 

T

D + TK (13) 
r. I 

- - 

r' ' f, . • • • 2-1 71, 47' 51 

." : •, • 

NRO APPROVED FOR 

RELEASE 1 JULY 2015 

Utilizing the definition to Tv given by Equation (1) it is 

possible to write Equations (12) and (13) in the form given below by 

equations (1)4) and (15). 

t

a2 

- to •2T + TB + TC T

r 

T

V2 

(14) 

a D 1 

t

al 

- t

a2 

T

D + TC + T

r 

-T Vi (15) 

The differential acquisition time term Atais defined below 

by Equation (16). 

t

a 

t

a2 

-.t al (16) 

Equations 8, 9, 10, and 11 may be combined to yield a third 

constraint given by equation (17) below. 

T

V1 

+T 3T T 2 T

c 

2 T

r 

D B 

V

2 

Equations (18) through (22) are the five general constraint 

equations for defining the boundaries of the zone of compatable alternates 

when a voting strategy is employed. 

ta 0 

1st Quadrant Only 

Tr 0 

Ata> 1 + T 

At 4. C2 a - T 

r 

T Z C r-3 

• 
rULJ )7L. 

Page 17 

NRQ APPROVED FOR 

RELEASE 1 JULY 2015 

77N17,73,:rt, !,1 19 ' 9 

where 

C

1 2 TD + TB + T

c 

- T

V2 

=T T_ 

2 1 

Tc 

C

3 

(T + T

V2 r - 3 TB- TB- 2 Tc) 1 

(23) 

(24) 

(25) 

Equations (18) through (22) are plotted in Figure 8 to illustrate 

the effect of the constraints. 
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NRO APPROVED FOR 

RELEASE 1 JULY 2015 

WHS-346 

Page 19 

SECTION 7 

NUMERICAL EXAMPTRS OF CONFLICT ZONES FOR TWO ALTERNATES 

UTILIZING A VOTING STRATEGY 

Figures 9, 10, 11 and 12 are plots of the zonal constraints 

for selected values of T. Table 1 gives the values of C1, C2 and V 

C3 for the corresponding values of T. 

T

v 

. 20 ,T

v 

= 25 - T

V30 T

v 

= 35 

C

1 4 -1 -6 -11 

C

2 

+1 +9 +14 +19 

C

3 o 5 10 15 

Table 1 

In order to compute the above table, numerical values have been 

assumed for TB, TC and TD. 

TB= 2 seconds 

T = 10 seconds 

T

D 6 seconds 

0. 

•1 ••-• 7 7- 777'1 7 

. . . 
r' r r WHS -3/4 6 

Page 20 

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RELEASE 1 

•--, 

r r": Page 23 
NRQ APPROVED FOR 

RELEASE 1 JULY 2015 

SECTION 8 

NECESSARY AND SUFFICTENT CONDITIONS FOR SELECTING N ALTERNATE 

TARGETS AS CANDIDATES UTILIZING A VOTING STRATEGY 

Assume that there are N alternate targets which exist for 

some decision time, td, and that the alternates have been ordered 

such that the Nth target will be observed last. For the Nth target 

the constraint conditions are given below by Equations (25) and (26). 

t

d - toN D 

t, - t > T d K 

Consider now the (N-1)th target. As with the case of two alternates, 

the constraint conditions for this target are given below by Equations 

(27) and (28). 

t

d - to > T

D + TB 

+ 

N-1 

(27) 

t

L - t

d 

 > TK (28) 

N-1 

Consider the (N-2)th target. This target must accommodate in its 

constraint conditions not only its own dwell time but the dwell time 

associated with the (N-1)th alternate and the Nth alternate as well as 

the TB associated with going from (N-2) to (N-1) and in going from 

(N-1) to N. Hence, the constraint conditions for this alternate are 

given below by Equations (29) and (30). 

(25) 

(26) 

(29) 

(30) 

td - t

a 

3 TD + 2 TB N

-2 

t - t

d TK 

r 

F. ffir", •-•••-•••■ 
f,40 

,• a";"7'rm 

t.r • ■ 

WES-346 

Page 25 

NROAPPROVED FO 

RELEASE 1 JULY 201 

Repeating this process N times, the constraint conditions for the 

first target which would be selected for viewing are given below by 

Equations (31) and (32). 

t

d 

to N TD + (N-1) TB 1 

t - L t

d TK 1 

These equations may be generalized to provide the necessary 

and.sufficient conditions to tell whether or not a selected group 

of targets are capable of being alternate targets for a given decision 

time. These conditions can be expressed by Equations (33) and (34) which 

are given below. 

t

d - to (N + 1 - i) TD+ (N - i) TB (33) 

t

L. t

d T

K 

(34) 

for all i 1 4"" i L N 

SECTION 9 

MAXIMUM. NUMBER OF ALTERNATE TARGETS AVAILABLE AS A FUNCTION OF T

v 

In order to compute the maximum number of alternates available 

for a constant viewing time and decision time, we shall assume the most 

favorable geometry. This implies that the targets are arranged in such 

a manner as to provide perfect packing of the dwell times in the time 

(31) 

(32) 
NROAPPROVED FOR 

RELEASE 1 JULY 2015 

WHS-346 

Page 26 

available for dwell times. In this case we make the following 

assumptions for the values in the constraint equations given below. 

T

B = 2 

T

K 

= T

r 

11 = 12 

T

D = 6 

Combining Equations (31) and (32) we produce the general 

constraint equation given below as Equation (35). 

t

L - to = TV 

N TD 

+ (N-1) TB+ TK ( 35 ) 

Substituting the constant generated in this equation we 

develop Equation (36) which provides us with the maximum number of 

alternates available by positioning the integer part of N which is 

generated. 

T

V - 10 (36) 

8 

Table 2 below is a listing of the maximum number of alternates. 

TV 

1 18 

2 26 

3 34 

4 42 

Table 2 
NRO APPROVED FOR 

RELEASE 1 JULY 2015 

SECTION 10 

COMPARISON OF GEOMETRICAL CONSTRAINTS BETWEEN THE VOTING STRATEGY 

AND SEQUENTIAL STRATEGY 

The equation which determines geometrical constraints for two 

alternates utilizing sequential method of processing is derived by 

referring to Figure 13 below. 

#1 T

D 

T

B 

t tL 

• \ 

t 

a

2 al + TD TB 

FIGURE 13 

We begin by assum ing that either alternates given above are 

acceptable by the general necessary and sufficient conditions for 

alternates as given by equation 4. It is further assumed that ta 

2 

is greater than to and that alternate 1 is selected for viewing al 

before alternate 2. 

The constraining equation which comes from this geometry 

arises from being able to get to Target 2 in time to dwell and operate 

the primary optics before L The time at which the ATS begins to 

2 

track the second alternate is equal to t

al 

+ TD T

B

. Hence, 
NRO 'APPROVED FOR 

RELEASE 1 JULY 2015 

17 WHS-34b 

Page 28 

F.11 gal 2i 

the constraint equation can be written as given below by Equation (37). 

- (t

al + TB + TD 

) T

K + TD ( 37) 

By utilizing the definition of Tvand further assuming that 

T = T

V2 

Equations (37) can be rewritten as Equation (38) and (39) V

1 

below. 

to Ch+ T — 4 r 

CL

4 = T

B 

 + TC - 

+ 2 T

D 

_ T V 

Compare these equations with Equations (20) and (23). We notice 

that the two are identical. Hence it becomes a straightforward manner 

to re-interpret Figure 8 as a constraint for sequential targets by 

neglecting the constraint imposed by Equations (21) and (22). This 

is given below in Figure 14. 

(38) 

(39) 
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NRO APPROVED FOR 

RELEASE 1 JULY 2015 

WHS-346 

Page 30 

SECTION 11 

COMPARISON OF THREE ALTERNATES VILVED SEQUENTIALLY VS TWO 

ALIERNAIES VOTED UPON 

As can be seen from the previous analysis, geometry conditions 

may exist where targets can be processed sequentially but could not 

become available simultaneously for a given decision time. When 

this is the case, it may be best to process them sequentially even 

though the sequential processing does not take place in order of 

descending weights. As was demonstrated previously in Reference 4, 

failure to process targets sequentially in order of descending 

weights will produce an average score less than by the voting method. 

The analysis here, however, concerns itself with the processing of 

three targets sequentially (in a non-optimal manner) as opposed to 

two targets using a voting strategy. 

Expected Score for the Voting Strategy. The average score 

W- for two targets in a voting strategy can be derived as given in 

Reference 4. In so doing it is assumed that two targets have equal 

apriori probabilities and the weight of Wi is greater than the weight 

W2. The false alarm rates are assumed =0 and recognition probability = 1. 

Since this analysis is carerned with differential in performance between 

the two strategies, it is not necessary to account for terms relating 

only to inactivity. Equation (40), below, gives the expected score for 

73- 
■■•-■ (IN 

lm.1 it =1 

&Iv 

NRO APPROVED FOR 

RELEASE 1 JULY 2015 

voting strategy on two targets. 

= p

2 W

1 + PQW1 + QPW2 + K (4o) 

Average Score for the Sequential Strategy 

The sequential strategy further assumes an additional third 

target which is called W3. Equation (41) below considers the expected 

score for this case. 

= 3W1 W2 w3 F PQ2 (W.1

+W2

+W3)+Qp2 Cl W2 + 

W

1 + W3 + w

2 + 1413)+ K (41) 

3 2 2 • 2 d 

The term 

W1 + W2 + W3 is the average score Obtained when 

3 

all three targets are active. The term (W1 + W2 + W

3

) represents the 

score when only one target is active in each of three cases. The 

W + W + W 

tem( 1 W2 + W1 w3 + 2 .3 represents the average score 

2 2 2 

for each of three cases when two targets are active. 

The differential score between sequential and voting strategies 

is given below.by Equation (42) 

L1W = P(-PW1 - Q (W1 + W2) + (P2

+ Q2 + QP) (W1 + W2 + W3)) 

vIAT represents the expected score of the sequential strategy minus 

the expected score of the voting strategy. After some simplification 

it is possible to write ,AW in the form of equation (43) below. 

2

2 

= P (W1 W2 W3 ) Q W3 - P W1 ) 

(42) 

(43) 
r , 

LL:iv1:1*Q.-1./6211 

WHS-346 

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7. 71 f,775 

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When 6 W 7 0 then the sequential strategy will outperform the 

voting strategy. Conversely when ®W . 0, then the voting score is 

superior. Thus, the necessary sufficient condition for 0 W > 0 

(sequential superior) is given by Equation (44) 

P

2 

(wi + w2 + w

3

) Q W3 PW, (44) 

Unfortunately Equation (44) is not easily interpreted. It can 

be shown however that there exists relatively simple sufficient conditions. 

Equation (45) is the simplest sufficient condition. 

W1 , 

- 

3 

) (45) 

A slightly better sufficient condition can be derived incorporating 

all W1 and W

3 

 terms and this is given below by Equation (46). 

wi 

w3 

3 - 1 (46) 

P (3-P) 

Equation (46) is plotted in Figure 15 to show the area for which 

W > 0 

• 
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• 

1 • f ' I ' i ,-- 
NRO APPROVED FOR 

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WHS-346 

Page 34 

SECTION 12 

CONSTRAINTS ON THE SELECTION OF THE DECISION TIME 

Consider the case of two alternates. Assume that the alternate 

targets have a Tvsuch that there is a range over which tdmay be 

chosen and specify the bands of this range by td minand td max 

Hence, the inequality is given by Equation (45) below. 

t

d td t

d min 

Figure (16) below represents the primary optics time line for 

one primary to be photographed in stereo with three possible cases 

for t d. 

1 fore aft 

stereo s tereo 1 

1 , 1 f 1 

t

rl 

, is t

t 

t

r 2 

t

d (Case I) t

d Case II) t

d (Case III) 

FIGURE (16) 

The three cases of decision times illustrated above can be 

expressed as follows: 

• 

Case I t

d t

t 

(both photographs lost) 

Case II t

t 4: t

d t

r 

(aft photograph lost) 

Case III t

d 2N tr2 (primary photographed) 

max 

(45) 
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It should be noted that the constraint expressed by Equation (45) 

arises solely from the relative geometry of the alternates and the 

primary optics path. Two other constraints can be derived similar 

to equation (45) by considering both the effect of interdiction on 

the primary optics path with respect to loss of successive primary 

targets and the scheduling of the other ATS to view the primary target. 

Consider first the constraint imposed by successor primaries. 

Assume that the primary optics, if divered to an alternate will return 

to the primary path upon completion of the photographic sequence of 

the alternate. It is thus possible to relate the time of interdiction 

(td

) to the time of return to the primary path (t p) for a given alternate. 

Functionally we have by equation (46) for alternate (i) 

p 

f. (td

) (46) 

Having determined t it is possible to estimate the loss of 

score (primaries) caused by interdiction at a particular value of td. 

Define the term L. (td) to be the expected loss in score by - 

interdicting at td' Define the expected score of alternate (i) as 

Ei (td) when interdicted at time td. Then we have the further constraint 

that td must satisfy Equation (47) below. 
must be photographed before tL 

2 

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WHS-346 

Page 36 

A w = Ei (td) - L. (td) 0 

-- 

(47) 

Consider now the constraint imposed by viewing the primary. 

For any given alternate, there exists some maximum ATS viewing angle 

which corresponds to some time t 7 . In general it can be assumed 

that interdiction will not take place until the primary is Observed 

for activity. This constraint can be stated by Equation (48) below, 

t

d t (48) 

SECTION 13 

CONSTRAINTS FOR SEQUENTIALLY PROCESSING ALTERNATES WHICH ARE NOT TIME ORDERED 

The constraints which are derived here demonstrate the conditions 

under which two alternates can be sequentially processed in an optimum 

manner even though the lower priority alternate occurs first in time. 

Refer to Figure (17) below, 

T

D T

r 

T

c 

W1>W2 

1 TD 

FIGURE (17) 

It is possible to write the constraint equation (49) below by 

assuming that W1 is viewed first and then W2 is viewed and if found active 

t a2 

W2 

It 
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v., n rn r1\Th NHS -346 

Page 37 

t + TD4 TB+ TD+ Tr+Ta t 

a L 1 (49) 

Utilizing the definition of Tv, it is possible to write Equation (49) 

in the form of Equations 50 and 51 below. 

t L C o 5- T

r 

(50) 

where C (51) 5 = TV - 2 TD - TB - TC 

Assuming TD 6, TB2, and Tc = 10, then the minimum value 

of TV 

 is 24 seconds. Hence Equation (50) can be plotted as shown in 

Figure (17). 

TV - 24 

J 

T

v 

- 24>1 T

r —1> 

FIGURE (17) 

• 

This zone may be superimposed over Figures 10, 11, and 12 to 

show where it is possible to obtain identical results with either 

strategy. 

7 

;. 1.1,•■ 
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• 

SECTION 14 

COMPARISON OF VOTING VERSUS SEQUENTIAL STRATEGIES FOR TWO ALiERNATES 

There are four separate cases which need to be examined in order to 

compare the performance of two strategies for various geometries. These 

four cases may be represented by Table 3 below. In this Table it is 

assumed that the expected score of alternate #1 is greater than the 

expected score of alternate #2. Each case is then considered in detail. 

Case t

a 

Sequential Possible Voting Possible 

I t > t a2 a 1 

Yes No 

II t

a2

.> tal Yes Yes 

III t

a

1 > tat 

Yes (Non-optimal Yes 

IV ta> ta 

1 2 

Yes (Optimal) Yes 

TABTR 3 

Case I 

Consider the two alternates described by Figure 18 below. 

#1 tal t

d t

d I min 1 1 max 1 

t

d t

d min.21 max 2 

FIGURE (18) 

f% F12 r 

v 

#2 
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It is apparent from Figure (18) that there exists no single 

decision time for both alternates #1 and #2. The alternates can, 

however, be processed sequentially. The obvious way to recitify 

this shortcoming in voting is to allow for two decision times, 

namely tdiand td . By allowing two deciSion times, several important 

2 

concepts are raised and these are discussed below. 

a. By introducing two decision times for the two alternates 

rather than one deciSion time. the inherent mathematical advantage 

(when it exists) of voting over sequentially processing alternate 

targets disappears. The net effect of installing two decision 

times in this example is to really operate in a hybrid mode 

where alternates are processed sequentially but the actual 

interdiction of the primary optical path occurs at predetermined 

times, namely the td's. 

b. Consider the effects of implementing two tats relatively 

close to each other. Such a situation may very well arise when 

other constraints mentioned earlier further restrict the placement 

of the td's. Refer to Figure (19) which is the timeline for the 

ATS. • 
(#1)-A TB 

t 

1 ,d2 

 TD 

(#2}-7*-1 

t

d 

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WHS-346 

Page 40 

time ›- 

FIGURE (19) 

The scenario for such a timeline sequence for an ATS would 

proceed as follows: 

Alternate #1 is presented to the ATS for viewing and the 

recommended dwell time TD 

displayed along with the decision time 

t

d • 

Note,however, if the crew member rejects alternate #1 

1 

after the recommended viewing time he will be viewing alternate #2 

while the "vote" is being made on alternate #1 (and possibly 

alternate #2). It is not clear how the display/implementation for 

this situation would be achieved. Alternatively the crew member 

may wish to postpone his inputs until after the recommended viewing 

time TD. He will then be looking at alternate #2 with less than 

the required viewing time. Moreover, it is not apparent how this 

condition of using excessive viewing time for alteImate #1 can be 

displayed to the crew so as to inform them of the consequences on 

alternate #2. 
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Page 41 

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c. The effects of two td's on the primary optics 

timeline needs to be examined. Refer to Figure (20). 

which shows a typical primary optics timeline with the 

two td's superimposed. 

t

d d 

1 

t2 

IT 

rl 

T

t r 

1: 1 2 

FIGURE (20) 

There are six cases to be examined concerning the relative 

placement of t

dl 

and t

d2 

on the primary optics timeline. 

These can be represented by Table 4, which enumerates the 

six possible placements of the two decision times. 

TIMELINE INTERVALS 

T

t 1 

T

r2 Sub-Case T

r + 1 Si 

. 

A 

t

d & td

1 2 • 

- 

B t 

dl 

t 

d2 

C t

d 1 

t

d 2 

D t

d 

& td 

1 2 

E t

d 1 

t

 2 d 

F t & t 

dl d2 

TABLE 3 

gi.= 734111 
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It should be clear that when a decision time falls in the 

T + T column, then interdiction at that time will cause 

r1 sl 

total loss of primary #1. When a decision time falls in the 

T

t 

column, then interdiction at that time will cause partial 

1 

loss of primary #1 (fore stereo only and possible successors. 

Finally, when a decision time falls in the T

r 

column, then 

2 

interdiction at that time will not cause a loss of primary #1 

but will cause a total loss of primary #2. 

From the above discussion it follows that even though the 

alternates may be regarded as "grouped" or in close conflict, 

they may cause conflict with different primary targets because 

of decision time constraints. 

Case II 

Consider the two alternates described by Figure (21) below. 

t

a 

t

d d. 

1

1 min„1 t MaX 1 12 

t

a2

t

d t d .min 2 max2 L

2, 

• 

FIGURE 21 

It is apparent from Figure 21 that there exists a range of 

td's which simultaneously satisfy both alternates. The only difference 

in processing these alternates sequentially versus voting lies in 
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rl t? tl I. 71 

. . , 

WHS-346 

Page 43 

in the time at which interdiction might take place and hence the 

photographic angles at which the alternate will be photographed. 

The sequential processing allows more flexibility for choosing 

preferred modes of. photography for Target #1,since the time of 

interdiction need riot be a function of target #2. 

As demonstrated in Reference (4), as long as the alternates 

are viewed in decending order of weight, then the expected score 

of the two strategies are identical. 

Case III 

Consider the two alternates described by Figure 22 below. 

#1 

#2 

FIGURE 22 

For this case, Figure 22 is drawn such that the conditions of 

Equation (50) are satisfied, i.e.,_first alternate.#1 and then' 

alternate #2 are to be viewed for activity. The expected scores 

will be identical for both voting and sequential; with the exception 
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WES-346 

Page 44 

that there will be a loss in the range of photographic angles 

with which the primary optics can photograph alternate #2. If 

this constraint lowers the expected score of the sequence, then 

it would appear to be better to vote (at least once) than to 

sequentially process the two alternates. 

Case IV 

Consider the two alternates described by Figure 22, not 

satisfying the conditions of Equation (50), i.e., the sequence 

of #1, #2 is not possible. In this instance it is clearly better 

to implement the voting strategy. 
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SECTION 15 

OPTIMIZATION OF ALTERNAIE TARGET SELECTION AND DECISION TIME 

The analysis presented so far has been concerned primarily 

with the constraints associated with alternate target and decision 

time selection. This section briefly discusses some concepts of 

how these selections may be made. It should be emphasized that 

much of the criteria for selection will be developed during the 

early phases of the mission planning software and that it is not 

the scope of the studies to attack such a problem. 

The enchancement (or degradation) of the total probable 

score when interdicting the primary in favor_of an alternate depends 

upon three factors: 

1. The expected score from the alternate. This depends on 

the priority number, the probability of activity, presence 

of activity indicators, false alarm and recognition errors, 

weather, decision time, etc. 

2. The expected loss of score from primary path if optics 

are diverted to an alternate and then returned to the primary 

after a sequence. This depends on relative geometry and td. 

3. Visibility of primary path (weather): If obscured, then 

the loss in item (2) is reduced. 

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The effect of Item (1) as a function of decision time is 

shown in Figure 23. This reflects the fact that there is some 

preferred (optimal) time to take an alternate. 

Expected gain 

from alternate 

t I d 

to t

L 

FIGURE 23 

The loss in Item (2) may grow larger the longer the 

decision time is delayed, but may experience discrete discontinuities 

also. That is, waiting for a period of time may allow completion of 

one primary sequence while causing a loss in the next primary sequence. 

The exact shape of the loss curve is unknown, but may be assumed to 

be represented by Figure 24. 

Expected loss 

from primary 

to t L 

t

d 

FIGURE 24 

Item 3 will add or subtract a bias onto Figure 24. The 

overall net gain to be expected from interdiction is obtained by • 

combining the three effects, as shown in Figure 25. 
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An alternate would not be considered unless Figure 25 has a 

net positive value for some rante of tdl (Inactive low priority 

alternates loose more on primary than they could add.) 

In considering alternate strategies, the weight assigned to 

alternates should include not only a priority number based on the 

value of the target, but also the relative geometry dependent term 

accounting for the probable loss in the primary if interdiction occurs. 

That is, all considerations of Figure 25 should be accounted for. 

Most of these considerations could be pre-computed, with the crew 

supplying inputs on activity and weather. These inputs would, in effect, 

shift Figure 25 upward or downward. Thus, some targets will never be 

,feasible alternates even if there are no geometrical constraints. 

(i.e.: no part of Figure 25 positive.) Other targets will be feasible 

alternates if active, but not if inactive. Thus, they would always be 

viewed for activity. Still other targets will be feasible alternates, 

even if inactive, if the primary path is obscured by clouds. There will 

never be alternates that will always be preferred over the primary. They 

would be on the primary if they were that important. Thus, Figure 25 

will have some negative values under certain conditions for all targets. 
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SECTION 16 

REAL TIME SCHEDULING OF ALTERNATE TARGETS 

Consider a timeline for an ATS where there are three alternate 

targets to be viewed, each with a nominal recommended viewing time. 

The situation will often arise where the entire recommended viewing 

time will not be utilized to determine the state of the alternates. 

In the case of weather it will take only a fractional portion of the 

time allotted to determine status. After the crew has rejected the 

alternates originally scheduled for the ATS it would be deSirable 

to present additional alternates, if available, for viewing. The 

problem with doing this scheduling on the ground lies with the fact 

that it is not possible to predict how long it will take the crew 

to observe the alternates and hence the ground cannot preschedule 

these additional alternates. 

The probable solution to this problem will require the 

ground software to select groups of reserve alternates to be sent 

to the MOL and let the on-board computer access this pool in real 

time when the conditions permit additional viewing of alternates. 

The ability for the on-board computer to select, in real time, 

additional alternates presents some implementation problems which 

will need to be .studied in as much as no such capability exists to 

date. 
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SECTION 17 

CONCLUSIONS AND RECOMMENDATIONS 

Sections 2 through 10 of this report developed the analytical 

constraints (necessary and sufficient conditions) for the candidacy 

of alternate targets utilizing both the voting and sequential strategies. 

These results were 'presented graphically, for numerical values assumed 

for certain system parameters. While the analysis performed here was 

concerned with only two alternates at the same roll angle, and utilized 

only one ATS scope, certain extensions can be implied by these studies. 

The assumptions of having both alternates at the same roll angle may 

be interpreted as two alternates at different roll angles with the 

average roll angle being the one used in the analysis. Section 9 

demonstrated that it is highly improbable that ATS will ever be able 

to scheduled to view more than three alternates for a given decision time, 

hence the limitation of two alternates and an implied primary do not 

seem restructive when one considers the potential utilization of the 

system. Finally, the inclusion of a second ATS only strengthens arguments 

given for utilizing a hybrid voting strategy. 

Section 11 of this report is a continuation of the decision strategy 

analysis presented in the report of Reference (4). In particular it 

derived the sufficient conditions whereby it is better to examine three 

alternates sequentially in a non-optimal manner rather than to examine 

two alternats utilizing a voting strategy. 

Section 12 addresses the inverse question of selecting the decision 

time rather than selecting the alternates. In particular certain general 

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criteria are derived which constrain the placement of decision times. 

Section 15 further considers the optimization of the decision time 

within the constraints previously described. The general criteria by 

which decision times will be selected was presented and it was stated 

that the further development of this criteria will be the responsibility 

of the mission planning software contractor during early phases of 

development. 

Section 16 is included in this report to demonstrate some of 

the current shortcomings of the implementation of alternate targets 

and the need for doing more work in this area. 

Section 14 addresses the question of the actual strategy which 

will be used. In this section it is demonstrated that by judiciously 

selecting additional decision times it is possible to eliminate any 

requirement for sequentially processing. It should be emphasized, 

however, that when decision times are placed relatively close together 

then the statistical performance of the system approaches that of the 

sequential method. The primary concept, however, is that decision times 

are placed on the time line so as to guarantee availability of alternates, 

and decision times are not necessarily selected based upon geometric 

groupings of targets. 
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The implementation of utilizing decision times in this manner 

will require only minor modifications to the existing on-board computer 

software. 

Such modifications would go to simple changes in uplink message 

data card format, i.e. appropriate flags, and to the on-board computer 

logic. With respect to the logic modification, it is proposed that 

no change be made in the manner the computer operates on groups 

containing primaries. Additional logic, however, will be required 

to recognize the flag for and operate on the groups containing alternates 

alone. Because the operational program sequence involves a functional 

deletion, i.e. if there are no valid activity inputs prior to td, no 

specific commands would be given to the primary optics at td' the 

necessary logic modifications appear to be small. 

It is strongly recommended that these minor modifications be 

incorporated into the on-board computer software at the earliest 

possible date. Upon selection of the mission planning softwarecontractor he should be directed to spend a major portion of his 

effort to further define and consider implementation of the overall 

problem of alternate target selection. 

•