M. J. Lewis · M. J. Lewis 12 November 1976 ^toorf^10^ Approved for public release; ... APPENDIX A...
Transcript of M. J. Lewis · M. J. Lewis 12 November 1976 ^toorf^10^ Approved for public release; ... APPENDIX A...
SLL 80-392/M
Project Report
Recognition of a Target on an ARWBC RTI
Prepared for the Department of the Air Force under Electronic Systems Division Contract F19628-76-C-0002 by
Lincoln Laboratory MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LEXINGTON, MASSACHUSETTS
PA-385
M. J. Lewis
12 November 1976
^toorf^10^
Approved for public release; distribution unlimited.
•'■"■".,;;' Iff y.
BMD TECHNICAL INFORMATION CBiM BALLISTIC MISSILE DEFENSE ORGANJZATiOS
7100 DEFENSE PENTAGÖM ; ,r Jj1r WASHINGTQN O.C. 2O301.?I09
h i &
The work reported in this document was performed at Lincoln Laboratory, a center for research operated by Massachusetts Institute of Technology, with the support of the Department of the Air Force under Contract F19628-76-C-0002.
I
Accession Number: 3780
Publication Date: Nov 12,1976
Tide: Recognition Of A Target On An ARWBC RTI
Personal Author: Lewis, M.J.
Corporate Author Or Publisher: Lincoln Laboratory, M.I.T., P.O. Box 73, Lexington, MA 02173 Report Number: PA-385 Report Number Assigned by Contract Monitor: SLL 80-392/M
Comments on Document: Archive, RRI, DEW
Descriptors, Keywords: Directed Energy Weapon DEW Target ARWBC RTI
Pages: 00043
Cataloged Date: Oct 08,1992
Contract Number: F19628-76-C-0002
Document Type: HC
Number of Copies In Library: 000001
Record ID: 24928
Source of Document: DEW
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LINCOLN LABORATORY
RECOGNITION OF A TARGET ON AN ARWBC RTI
M. J. LEWIS
Group 92
PROJECT REPORT PA-385
12 NOVEMBER 1976
Approved for public release; distribution unlimited.
LEXINGTON MASSACHUSETTS
ABSTRACT
The task faced by the All-Range WideBand Channel (ARWBC) operator at
ALCOR while trying to detect the presence and location of a target of interest on the
RTI display was examined with the aid of digital RTIs produced by a computer simula-
tion. Controlled levels of three degrading factors --- background clutter, missed
target returns, and an unsteady target track — were produced in the simulation RTIs
and a subjective judgment made as to which RTIs contained detectable target tracks.
In this way, useful limits were established on tolerable levels of the three degrading
factors considered.
111
TABLE OF CONTENTS
ABSTRACT
I. Introduction
II. Description of Problem
III. Computer Model of Track Wander, Leakage, and Clutter
IV. Computer - Generated Plots
V. Conclusions
ACKNOWLEDGMENT
APPENDIX A - Derivation of o
APPENDIX B - Radar Characteristics
APPENDIX C - Simulated RTIs
111
1
1
4
8
8
15
16
18
19
IV
I. INTRODUCTION
The All-Range Wide-Band Channel (ARWBC) is a component of the ALCOR radar
designed to provide range coverage greater than that available with the conventional
ALCOR wide-band window (90 m), and to test designation techniques in real-time. One
output of the ARWBC is a digital RTI displaying those range positions in each pulse in-
terval where a target is detected. (A target detection is determined by a return satis-
fying a preselected set of thresholds on amplitude, length, etc.)
An important question in the operation of the ARWBC is the ability of an oper-
ator to view the digital RTI and detect the existence and location of a target. Several
possible factors hamper this detection, the most important being:
The amount of background clutter.
The proportion of returns missing from the target trace.
The extent to which the target return, when present, wanders about on the face of the RTL
The detection problem faced by the operator—basically a psychological one—
is investigated in this report through the use of simulated RTIs which contain the de-
grading factors to controlled levels. Although the decision as to whether a particular
RTI would thwart or permit detection is a subjective one, it is believed that the ground
rules developed in this report establish useful limits on the levels of the degrading
factors. The ground rules apply equally well to RTI displays other than that of the
ARWBC.
II. DESCRIPTION OF PROBLEM
An RTI can allow an observer to follow the track of a target provided that the
tracking gate is being accurately designated along the trajectory of the target. Figure
1 shows a computer simulation of such an RTI, where time in seconds runs along the
vertical axis (increasing upwards) and range in meters relative to the tracking gate
is displayed along the horizontal axis. After an initial range displacement at time 0,
PA-385 (1)
50
40
30
B
20
10
T T r
I J ..J L..-J-. J-.U J——I- -500 -400 -300 -200 -100 0 100 200 300
Relative Range (meters)
400
j 500
Fig. 1. RTI without degrading factors.
the tracking gate is accurately designated on the target trajectory and the line of
asterisks continues up the center of the RTL The straightness of the line is an indi-
cation of the precision of the designation source. Because there are no other targets
in the environment, the rest of the screen is clear. Because all of the target returns
passed the thresholds of the RTI system, the line is continuous.* Under such conditions,
it is an easy matter for an observer to follow the target path.
But the situation is not always so simple. Several factors can complicate the
task of detection for the observer. First, depending on the thresholds built into the
ARWBC algorithms, some of the returns from the target of interest may not pass the
algorithms, and gaps may appear in the line. These will be called "missed returns. "
More important, an environment filled with penetration aids or clutter may cause addi-
tional returns in each range sweep which can obscure the path of the target of interest.
In a typical situation, the clutter might consist of several kilometers of chaff, and the
target of interest might be an RV. In this report we will occasionally refer to the pro-
blem of detecting an RV imbedded in chaff, keeping in mind that the conclusions to be
drawn apply to any general detection problem.
In addition to clutter and missed returns, a third factor working against the
observer is track wander. Depending on the source of designation information being
provided to the ARWBC, the target of interest may wander within the RTI range sweep.
For example, the ARWBC may be designated by a beacon track. In this case, the target
skin return will generally be at a constant range relative to the beacon, with very small
range deviations due to beacon instabilities, and the operator will have little trouble
following the target through moderate chaff, even with some missed target returns. But
in a scenario more realistic from the defense point of view, ARWBC designation would
not be provided by a beacon, but perhaps by a track of the centroid of the surrounding
chaff cloud. In general, chaff trackers are characterized by substantial range residuals.
That is, at any given time, the tracking gate of a chaff tracker may be offset by a
* Unfortunately, some of the asterisks may not have passed the threshold of our re- production facilities.
substantial amount from the actual physical centroid of the cloud, which is moving
smoothly through space. These offsets will be random in nature, hopefully with zero
mean, and with some standard deviation which is a measure of the precision of the
chaff track. Since the RV is presumably fixed relative to the cloud centroid, * the RTI
tracking gate range offsets relative to the cloud centroid will be translated into range
offsets relative to the RV, causing the RV returns to wander across the face of the
RTL Thus, the standard deviation of the tracker range residuals will impact on the
task of the RTI observer. Figure 2 shows a digital RTI in which clutter fills approxi-
mately 20% of the screen,l0% of the returns from the RV imbedded in the clutter have
been deleted, and a small amount of track wander has been introduced. An observer
would require a great deal of imagination to pick out the path of the RV.
The purpose of this report is to investigate the impact of these three degrading
factors---missed returns, clutter, and target track wander---on the detection problem
faced by the RTI observer. By use of a computer program which produces simulated
digital RTIs, RTI plots containing controlled amounts of the three factors were pro-
duced, and a decision was made as to whether or not the target track was detectable.
A track was considered detectable if the observer could correctly determine
the position of the target roughly 50% of the time. It must be stressed that the detection
decision was purely subjective. Another observer might find it harder or easier to see
the target. A criterion other than 50% might be used. Despite the subjectivity involved,
it is believed that this approach can establish useful allowable limits on the three de-
grading factors investigated.
III. COMPUTER MODEL OF TRACK WANDER, LEAKAGE, AND CLUTTER
A computer program was designed to produce simulated digital RTI plots con-
taining controlled amounts of the three degrading factors. The wandering track that
"* Or at worst having a smooth velocity relative to the centroid.
PA-385 (2)
* 1 ¥¥¥¥ 1 ¥ ¥ ¥-1 ¥ ¥¥ ¥ 1 ¥ ¥ 1 ¥ 1 ¥¥¥ **l ¥ 1 ¥¥ * v ¥¥ ¥ ¥¥¥¥¥ ¥ ¥ ¥ ¥ ¥¥¥ ¥¥
* * ¥ ¥ ¥ ¥ ¥ ¥ ¥¥¥¥¥ ¥¥¥¥¥¥¥¥ ¥¥ ¥ ¥ ¥ ¥ . * ¥ ¥ ¥ -,- ¥¥¥ ¥ ¥ ¥ ¥ ¥¥ ¥ ¥ ¥
** ¥¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥¥¥ ¥ ¥ ¥ ¥¥ •
50 — ¥* ■w ¥ -Y¥ ¥¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ -'¥ ¥¥ ¥ —-i
* **♦# W ¥¥ ¥ ¥ ¥ ¥¥ ¥ ¥ ¥¥ i ¥ ¥¥¥ ¥¥ *¥¥¥•¥¥¥¥¥ ¥ ¥ ¥
¥¥ * ¥ ¥ ¥ ¥ ¥ ¥¥¥¥¥¥ ¥ ¥ ¥¥¥¥¥¥ V- ¥ ¥* ¥ ¥ ¥¥ ¥ ¥ ¥ ¥¥ ¥ ¥¥¥¥¥¥¥¥¥ ¥ ¥ ¥¥
4 * ¥¥ ¥ ¥¥ ¥ ¥¥ ¥ ¥¥ ¥ ¥ ¥¥ ■ ¥ ¥ ¥ ¥ ¥ * * ¥ ¥ ¥ ¥ ¥¥¥ ¥ * ¥¥ ¥ ¥¥ ¥ ¥ * * ¥ ¥ ¥¥¥ ¥¥¥¥¥¥ ¥ ¥ ¥
i ¥ ¥ ¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥¥ ¥ *¥ i m ¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ * ¥■ ¥ ¥ ¥ ¥ ¥¥ ¥
40 —* * ¥ ¥ ¥ ¥ ¥ ¥ ¥¥ ■■ -,' ¥ ¥ ¥ >: ¥ ¥ ¥ •¥- M,y,yyy ¥ ¥ ¥ ,«•>.' ¥ ¥ ¥ ¥ ¥ ¥',<¥ ¥¥ ¥ ¥ ¥ ¥
* * ¥¥ ¥ ¥ ¥ ¥¥ V,'¥ ¥ * ¥ ¥ ¥ ¥ ¥ ¥ * ¥¥¥ ¥ ¥ ¥¥¥¥¥¥ ¥ ¥¥ ¥¥¥¥ ¥¥ ¥ ¥ ¥¥¥¥-. i-¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥>.<¥ ¥ ¥ ■ ■ * ¥
¥
¥¥ ¥
¥ ¥¥¥¥¥¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥¥¥ ¥ ¥ ¥ ¥ ¥¥¥ ¥ ¥ ¥¥ ¥ ¥ ¥¥ ¥ * * ¥ ¥ x ¥ ¥ ¥ ¥ ¥ ¥-¥¥ ¥¥ ¥ ¥ ¥ ¥ ¥ * * ¥¥¥ ¥¥ ¥■'.' ¥ ¥ ¥ ¥ ¥ ¥
30 -* * If ¥¥
¥ ¥ ¥ ¥ ¥¥ ¥ ¥¥ ¥ ¥ •'*¥¥¥¥ ¥ ¥
¥ ¥ < ','¥ ¥¥¥ ¥ ¥ ,'• ¥ ¥ ¥ ¥ ¥¥ ¥¥¥ ¥ >
<u ¥ ¥¥ ¥¥¥ ¥ ¥¥ ¥ ¥ ¥W ¥ ¥ ¥¥ ¥ ¥¥¥¥¥¥¥ ¥ •
£ ¥*¥¥ ¥ ¥ ¥ ¥ ¥¥ ¥ ¥ ¥ ¥¥ ¥
PH ¥ ¥ ¥ ¥¥ ¥ ¥¥¥¥¥¥ ¥ ¥¥¥¥ ¥
h * ¥¥ * * ¥ ¥ ¥¥¥¥¥ ¥.¥¥¥ ¥ ■ * ¥ ¥ ¥ ¥ ¥ ¥ ¥¥¥¥¥¥ ¥ ¥ ¥ •
ww * ¥ ¥ ¥¥ ¥¥ ¥¥ -.'¥ ¥ ¥ ¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥* *♦
¥
¥¥ ¥
¥ ¥ ¥¥¥¥¥¥¥¥ ¥¥¥
¥ -■.' ¥ ¥ ¥¥ ¥ ¥ ¥¥¥
20 — *¥*¥* ¥ ¥¥ ¥¥¥¥¥¥¥¥ ¥ ¥ ¥W¥ -■¥ ¥ ¥ ¥* ¥ ." ¥ ¥- ¥¥ ¥¥ ¥ > .".'- ¥ ¥ .¥■ ¥ ¥
> * ¥ * ¥
¥
':■ •-.•¥ ¥¥¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ':" ':"'.<■ ¥ ¥¥ ¥ ¥ ¥¥¥ ¥ ¥
¥ ¥ V ¥ ¥ ¥ ¥ x ¥- ¥ ¥ ¥ ¥ * ¥¥¥ ¥ ¥ ¥ '■' ¥ ¥ ■;■ ¥ ¥ ¥ Y ,",' ¥ ¥ ¥ ¥ ¥¥¥ * T 111 ii ^ ¥ ¥ ¥ ¥ ■ ■' ¥ ¥ ¥ ¥ ¥ ;
¥¥ ¥¥¥•■■ ¥ ■'»¥ ¥¥ ¥ ¥¥ ¥ ¥ ¥¥ ¥ ¥ ¥■ ¥¥ ¥ •■
* * ¥ yyw w
¥¥ '■'""■ ¥¥¥ ¥ ¥ ¥ ¥ '■■ ¥ ¥ ¥¥¥ ¥¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥¥ ¥¥ '
10 ■+ ♦ f ¥ ¥ ¥>■•> 1 ¥ ¥ ¥ ¥ ¥ -" v ¥ ¥ ¥¥¥ ¥ ¥ -*• ¥ * ¥ ¥¥ ¥ ¥¥¥ ¥ ¥¥ -<¥¥¥¥¥¥¥¥ ¥-
* ¥¥ ¥ ¥ >:- ¥¥ ¥ ¥ ¥ *¥ ¥ ¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ■ * ¥ ¥¥ ¥¥ ¥ •'.'- ¥ ¥ ¥ ¥¥¥¥ ¥ ¥ v¥ ¥
i ¥¥ ¥ ¥ ¥ ¥ >:■- ' ¥ ¥¥ ¥¥ ¥¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥¥ ¥ ¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥¥¥¥¥¥
¥ ¥ * ¥ * * ¥ ¥ ¥ ¥¥ ..¥¥¥¥¥ ¥ *¥ ¥ ¥ ¥ ¥ ¥¥ ¥ ¥¥¥ ¥¥¥¥¥¥¥ ¥ ¥¥ ¥ ¥ ¥ ¥
* * ¥ ¥¥ ¥ ¥ ¥.'.'¥ ¥¥¥¥¥¥¥¥¥¥ ¥ ¥¥¥
0 * * | | ¥ ¥ |¥ ¥V| j_ ¥ ¥ *-: - |¥ ¥ |¥ |
-5( )0 -400 -300 - 200 -100 0 100 200 300 400 50 0
Relative Range (meters)
Fig. 2. RTI with unsteady track, missed returns and clutter.
would be produced by a designation source less steady than a beacon was modeled as a
second-order autoregressive discrete time process with zero mean and Gaussian white
noise. That is, at time k A, where A is the interpulse period and k = 0, 2,..., 55, *
the range offset, X , from the center of the RTI is given by
X = a X +cc X, „ + N, Ak 1 k-1 2 k-2 k
where a and oi are constants and N, is a Gaussian random variable with zero mean 1 2 &
and standard deviation a Each point in the series depends explicity on the two pre-
vious points. Points were plotted as integer values, but rational values of Xfc were
retained for calculation of Xfe+1 and Xk+2. In order for the process to be stationary,
a and a must satisfy the following conditions:
a +a < 1 1 2
a -a > -1 1 2
-1<« <1
If the sequence X is stationary, its mean will remain zero and its standard deviation,
which is a measure of the wander of the track about the mean, is given by
a Z /T ** a
2 3 2 2 N 1 - a ■- a + a - a, a -a 1 2 2 2 12 1
In order to manufacture assorted values of a to provide simulations of progres-
sively unsteady tracks, one can manipulate al, a ^ or a^. The relevant quantity
is o . It is a measure of the wander of the RV track across the RTI, since roughly x
~- The upper limit^oT55 is governed by the physical height of the RTI presentation on each page.
** See Appendix A for derivation.
95% of the RV returns should lie within 2 o units of the origin. Because the dependence
of o on cr is more straightforward than that on a or <x , cr was varied by manipu-
lating o while holding 01 and a constant. Values of (a , a ) = (0.8, -0.2) were
found to be convenient, reducing the constant of proportionality in the last equation to
1.37.
At this point, it is instructive to consider what values of o might be of interest. A.
Previous chaff tracking performance of the KREMS radars* was explored. The TRADEX
L-chirp waveform typically produces range residuals on the order of 30 meters.
ALTAIR, using its video Track Signal Processor, has produced range residuals on the
order of 150 m. With its new Digital Track Signal Processor, the ALTAIR range re-
siduals have been reduced to fractions of one meter, which would be undetectable on
the range scale used. Thus, in order to provide a representative range of values of
2 a , six values of o from 0 to 50 meters were input to the computer program. .A. IN
Corresponding values of 2 o are shown below. It was assumed that the chaff tracking
performance of any defense radar would lie somewhere in this range.
o-.im) 2 a (m) N x
0 0
5 14
10 27
20 55
30 82
50 137
In addition to the wandering target track determined by the autoregressive
process described above, missed returns and clutter models were included in the com-
puter simulation. Missed returns were inserted by the following mechanism: before
See Appendix B for radar characteristics,
each point in the target track was plotted, a random number selected from a uniform
distribution was compared with a preset threshold called T2. For example, if T2
were set to 0.3, 30% of the target returns were randomly deleted from the plot.
Clutter was randomly scattered across the page via a similar comparison between a
preset clutter threshold and another uniformly distribution random variable at each
(range, time) coordinate on the page. For example, a clutter threshold of 0.2 resulted
in 20% of the page being filled with asterisks.
IV. COMPUTER-GENERATED PLOTS
Figures C-l to C-5 show plots generated by the simulation program with values
of a =0, 5, 10, 20, 30, and 50, respectively. There is no clutter, and all returns
were printed. Values of c^, <*2, the clutter threshold, percentage of missed returns,
a and 2a are shown at the bottom of the figures. Using these as baselines plots, pro-
gressively greater levels of clutter and missed returns were added by manipulation ot
the clutter level up to 10% and missed returns up to 50%, and judgments were made
as to when the unsteady track became undetectable to the eye. A track was considered
detectable if at least 50% of the target returns were distinguishable from clutter.
These judgments were, of course, subjective.
Table I summarizes the outcome of the examination of each plot. For each
combination of 2 a , clutter level, and missed returns shown, there is an indication
as to which RTIs contained detectable tracks (X) and which RTIs did not (O). A selec-
tion of RTIs for the reader's inspection are provided in Appendix C and indexed by
figure number in Table I. \
V. CONCLUSIONS
Figure 3 presents a summary of the results tabulated in Table I. For fixed
values of 2a , the highest tolerable level of missed returns was plotted against
clutter. For example, at 8% clutter, RTIs with 2ax = 14 meters contained detectable
TABLE I
RTI EXAMINATION RESULTS
N 2a Clutter
(%)
Missed Returns Result* Figure
0 X 10 X 20 X 30 X 40 X 50 X
0 X 10 X 20 X 30 X 40 X 50 X
0 X 10 X 20 X 30 X 40 X 50 X
0 X 10 X 20 X 30 X 40 X 50 0
0 X 10 X 20 X 30 X 40 X 50 0
C-6
C-7
C-8
C-9
C-10
X = Detectable Track; O = Undetectable Track.
a 2a Clutter Missed Returns Resu N X
(%) (%)
0 0 10 0 10 20 30 40 50
X X X X 0 0
5 14 1 0 10 20 30 40 50
X X X X X X
2 0 10 20 30 40 50
X X X X X 0
4 0 10 20 30 40 50
X X X X 0 0
6 0 10 20 30 40 50
X X X o 0 0
8 0 10 20 30
X X 0 0
Result* Figure
* X = Detectable Track; O = Undetectable Track.
C-ll
C-12
C-13
C-14
I C-15
10
<J 2CT Clutter Missed Returns Result* Figure X (%)
\
14 10 0 X 10 X 20 O 30 O
10 27 1 0 X 10 X 20 X 30 X 40 X 50 O C-16
0 X 10 X 20 X 30 X 40 O C-17 50 O
0 X 10 X 20 O 30 O 40 O
0 X C-18 10 O 20 O 30 O
0 X C-19 10 O 20 O
10 0 O 10 O
20 55 1 0 X 10 X 20 X C-20 30 O
X = Detectable Track; O = Undetectable Track.
11
a 2 a Clutter Missed Returns Result* Figure N x
'of wo.
20 55 2 0 X 10 O C-21 20 O
4 0 O 10 O
6 0 O C-22
10 O
8 0 O 10 O
10 0 O 10 O
30 82 1 0 X 10 X C-23 20 O 30 O
2 0 O C-24 10 O
3 0 O
4 0 O 10 O
50 137 1 0 O C-25 10 o
2 0 O 10 o
* X = Detectable Track; O = Undetectable Track.
12
CO
ID 00 CO
< D-
o o T—i—r
■ON
W
H D
■co
£ s-1 0)
CO 0) 5-1 f) a <D u o
(1) o
o
03 „. 4-) CO
•S a> O cd
CD
cd i—i n P Cl) CD
1—<
ca 4-> 3 o fi) ID in CO Tt
T3 <u n o
CO en CM
>> •i-4
e O
ctt m cn
S O a»
S i—i a) i—i
3 > rn Cl)
i—i "Ü ■i-> CD
CO
• en CD
XI .a
bn fan H •|H •iH o fe xi «w
X
o CO
O CN
3P
13
tracks with fraction missed of up to 10%. Missed returns over 10% rendered the
track undetectable. No curve appears for 2a = 137, as none of the tracks from that
group were detectable. Not surprisely, the highest tolerable level of missed returns
falls off with increasing clutter and increasing track wander. The rate of falloff of
maximum missed returns with clutter varies from gradual in the case of a steady
track (2a = 0) to rapid in the case of more unsteady tracks (2 a > 55). x
In summary, an observer trying to detect returns on an RTI from a target of
interest imbedded in clutter faces several obstacles. Range displacements relative to
the RTI origin may be introduced by the designation information provided by the radar
tracker. Clutter and missing returns obscure the path of the target. With a designa-
tion source which introduces range displacements of standard deviation greater than a
few tens of meters, the range of tolerable clutter and missing returns is severely
limited. Limits of tolerable track wander, clutter, and missing returns derived from
subjective criteria are displayed in Figure 3.
14
ACKNOWLEDGMENT
I wish to express my thanks to Linda Simon, who wrote the computer program
used to generate the simulation RTIs contained in this report.
15
APPENDIX A
Derivation of er x
N is a sequence of Gaussian random numbers with mean zero and standard deviation k
a N
X is a second-order auto-regressive discrete time sequence with zero mean and k
Gaussian white noise. That is,
V "l Xk-1 + "2 Xk-2 + Nk
We wish to find an expression for o- in terms of ay ay and o^.
OK E[xk2]= E[PlVl+«2xk_2+Nk)2]
= E^l2xk-l2+a22xk-22+ 2CV2Xk-lXk-2+ "i + -
2(-1xk.1+^2xk.2)Nk]'
= «* E [xtl2] + *2
2 E [xk_22] + 2^ «1 E [xk_x xk_2] + aN
2
EtXk-l2] = E[Xk-2^= E[Xk2]=ax2
Cov [xk, xk_x] = E [xk x^] = E [^ xk_x2 + ^ x^ xR_2 + x^ N^
= ^ ax2 + c2 Cov [xk, xk_x]
Solving for Cov [xk> xfc_ ^ ,
a Cov[xk, xR_1]= T-
a
L. a2
x
Thus, a 99222 1 22
"* - "l V+°2 \ +2a1°2l^T a* +^
16
Solving for o ,
1 -«.
2 3 2 2 1-a-a + a -a a -a 2 2 2 12 1
N
v (T / l-\
f 2 3 1-<V«2 +or2 -
2 a a 1 2
2 - a 1
^N
17
o co co CM
a
p co
a a,
.0 0 CL
ra
0
U
■a n c in
i3 irj 0 10 ^-< CM i~-
T 0 -1 0 ■** 0 m
r- o o C rn NO \0 N
OH
V a
3 P" i_ £« £ 5
_ OH »
U Jn x: "
c/} y "B n O O
H C/J 5 s ON
in m CM
1
OH <) O m in CM ^H T-<
W BJ H n U C3 £
u 0 s <
3 > 0 ca 1 < n <! 0- 'o
0 0
to 0
CO 1 0 m co O ^o m m
_J T« -* CM -^ ■^H
o ^o o o
4= O
§.§££ J o5 O O
■a "C
g *
(In
OH
51
c ■0"
u
OH < 9 J SQ
O Tf a HO lO O CM
§1
in 10 1/5 ^ CM co
i/> m m Q r--* i> r- m co co co -*
x: 0
M J 0
0 £ £ < ca J en O O D U
»M
s co a
0 >.
"o O P 01 >
OH ' * 03
& 0 -a S1^
0 0 c; 0 OH OH OH 0.
CO "(H ■^ CN
u 0 u u u ^ cs J -1 J j -J TH OH
CM
CO
n t- h S 0 .p OH
,5° OH CM p,-
CD in
OH 1-|
0 CM
CO
OH
a u 0 CN
OH
* in
3 «
CO h 3
as 03
fa
3
D
a u sz u
x: O
1 4->
E 3
C2
ä a
a u
O
a
0 »
_, w a W Q -a
0
U 0:5 £ OH
0' O O N
<! N < ^ CO
S". =0' U N u U H-4 - J < a -4 "* 1 1 OS OS 3 ™
^- rrl K- <
J3 0
u J
rt W 0 or! 1
a O N J <
w 0 •a OH e
CJ N J <
w CJ T) OH c
C8
C) N J < a
ill U-Jffl
Z f5
r^ in
CM Ö
& a
X! J3
u (J bo 4-1
O
J J5 1/1
n * * Ü 1.«
af" c
UHU
oi ci cd
111
<
03 -
W) O
•o c CD <U
to .ti ■3 S P. w
CN :L
CO CM n CO
.3 V
u
& xi o
p. O
! S N
^c? A1
« CA
B- i3
CO ^ O 3 B oa
a D
03 n S tä O U1
0
crt *^ 0 -A a 2
■o o
•3 1 a ' CN
CO
I o
O CM
X! M Q
18
APPENDIX C
Simulated RTIs
19
PA-385 (C-l)
50
40
30
H
20
10
-500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 0%
Missed Returns
a = 0.80
<*2 = -0.20
GN= 10
2ax= 27
Fig. C-l. Unsteady target track.
20
PA-385 (C-2)
50
40'
30
e •t-H
H
20
10
-500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 0%
Missed Returns = 0%
a = 0.80 1 °N- 5
<* =-0.20 2
2ax " 13
Fig. C-2. Unsteady target track.
21
PA-385 (C-3)
B
50
40
30
20
10
•500 -400 -300-200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter =0% ai= °'80
Missed Returns = 0% o = -0.20 2ox= 55
Fig. C-3. Unsteady target track.
22
PA-385 (C-4]
50
40
30 CD
£ H
20
10
•500 -400 -300 ■200 -100 0 100 200
Relative Range (meters)
300 400 500
Clutter = 0%
Missed Returns
a = 1
0.80 a = 30 N
012 = -0.20 2<7 ?= 82
X
Fig. C-4. Unsteady target track.
23
PA-385 (C-5)
50
40
30 0) B
•f-i
20
10
__ r
•500 -400 -300 -200-100 0 100 200 300 400
Relative Range (meters)
500
Clutter = a = 0.80 a = 50 r N Missed Returns = 0% <*2 = -0.20 2^=137
Fig. C-5. Unsteady target track,
24
50
40
30
20
10
* ¥ *
±
PA-385 (C-6)
500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 1% a= 0.80 a* 0 1 N
Missed Returns = 50% a = -0.20 2a = 0 2. X
Fig. C-6. Degraded RTI,
25
PA-385 (C-7)
50
40
30 0 &
20
* * * *
*
*
* *
* * *
10
X ■500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = a- = 0.80 a = 0 N.
Missed Returns = 50% «2 = -0.20 2°x = 0
Fig. C-7. Degraded RTL
26
jPA-385 (C-8)
50
* * ¥ ¥ *
¥ ¥ ¥ * ¥¥
40
30
e •iH
20
10
¥ * *
* * *
¥¥¥¥¥*¥¥ * ¥ ¥ ¥ ¥ ¥ ¥¥
* ¥ ¥ ¥ ¥ * ¥
■* ** * ¥ ¥ ¥ ¥
¥ ¥ ¥ * ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ * *
* ¥ ¥¥ * * ¥ ¥¥ * ¥ *
¥ ¥ ¥ * * ¥ ¥ * * ' ¥ ¥¥ *
¥ ¥ ¥ ¥ * ¥ ¥
¥ ¥ f ¥ ¥ ¥¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥
¥¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ . — ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
|¥ Jf. ¥ ¥ ¥ * -
¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥>.' ¥ ¥ ¥ ¥
¥¥
¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥
* I • ! * I I 1*1 I I* I ± •500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = i'7o of = 0.80
Missed Returns = 50% o.^ = -0.20
o=0 N
2ax= o
Fig. C-8. Degraded RTI.
27
PA-385 (C-9)
e •1-4
50
40
30
20
10
* * i ■*■
4 14 4! * I *
* *
4 * 4* 4 4
4 4
* 4 * 4 *
44
* ♦■ I 4 4 4 4
♦ 4
* 44
* * 4 4 4
* 4 4 4 4 *»**
* 4 4 4
i If. If. if. if. If. f ,|L v
* * • 44 w 444 * * 4
* * * * * * 44 4
* *¥ 4 4
4 4 4 4 4 *
* * 4-4 4 4 4 4 4 4 4
4'4 4 * 4*4 4 4 * v
L ■ , *
* ' * * 4 * * 4 4
4 4 4
4 4 4
4 4 W 4 4
4 4 4 4
4 44 4 4 4
4 4 4
4 4 44 4 4
4 4 |44 4 4
4 4 4
— 4 4 4 4 4 4
4 4 4 4 4 f- ^ 4 4
4 4
4 4 4 4
44 4 4 4
44 44 4
4 4 4
4 4 4 4
4 4 4 4 4 *
4 4 4 4 4 4 4 4
4 4 4 4 4 4 44 4
4 4 4
4 4 4 4 4 4 4 *
4 4 4 ■ 4 ■ 4 4 4 4
4
4 4
4 44 4 4
4
4 4
4 44 4
4 4 4 44
4—1. ■500 -400 -300 -200 -100 0 100 2Q0 300 400 500
Relative Range (meters)
Clutter = 6% a = 0.80 1
CT = 0 N
Missed Returns = 40% er = -0.20 2cr = 0 ä A
Fig. C-9. Degraded RTL
28
PA-385 (C-IO;
£
50
40
30
20
10
1 ♦ * i ♦1 * . *
* 1 * i *
* 1 ¥ ¥¥' ♦ i ¥ ¥
¥ * * * * * * * * * ¥ ¥ ¥ * * ¥ ¥ ¥ ¥ ¥
¥ * * * ¥¥ ¥ ¥¥ - * * * ¥¥ ¥ *
¥ * ¥ ¥ ¥ ¥ ¥ ¥ ¥ J * * * ¥ ¥ * * * * * * * ¥ ¥¥
» ¥ * * * J ♦ * * * ¥ * ¥¥ * * ¥ ¥
* ¥ ¥ ¥¥¥ * ¥¥ ¥ ¥ . * * * ¥ ¥ * ¥
. ¥¥ * ¥ * ¥ ¥ ¥¥ J * * ¥¥ ¥ * ¥ * ¥ * ¥ ¥ ¥
¥ ¥ ¥ * ¥ ¥ ¥ ■¥-
** * ¥ ¥ * ¥ * * ¥¥ * * * * ¥ ¥ ¥ ¥ ¥ ¥¥ ¥
* * ' ¥
¥ ¥¥
¥¥ ¥¥
* ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥
* ¥ ¥ * ¥ ¥
¥ ¥¥¥ ¥¥ ¥¥ ¥ ¥ ¥
* * * * * * ¥ ¥ * ¥ * ¥ ¥ ¥ — -
¥ * ¥ ¥ ¥¥ f * * * ¥ ¥ ¥¥ ¥ * ¥ ¥ ¥ * * ¥ ¥
* * * * * ¥ ¥ ¥ ¥¥ ¥¥ ¥ ¥ > ¥ ¥ ¥
¥ * * * * ¥ * *
¥ * *
¥ * ¥ ¥
¥ * ¥ * ¥
¥ ¥ ¥ ¥
¥ ¥
¥ ¥ ¥ ¥¥ * ¥ — * * ¥¥ ¥ ¥ ¥ ¥
J
¥ ¥ ¥¥ *
* ¥
¥ ¥ * ¥ * * ¥ ¥
♦ * ¥ * * * ¥ ¥ ¥ * * ¥¥
¥¥ *
* ¥¥ * **
¥ ¥ ¥ ¥ ¥ ¥¥
: ¥ * ¥¥ * W * f ¥ ¥ ¥ ¥ ¥ * * -* * ¥¥¥ ¥ * ¥ ¥ ¥ ._.
* * * * * ¥ ¥
¥ * ¥
¥ ¥ ¥ ¥ ¥ ¥
yy yy * * * ¥ ¥¥ j ¥
* ¥
* *
* * *
* * ¥
¥ *
*
¥
¥¥ ¥
¥ ¥ ¥
¥¥
¥
¥ ¥
¥
*l * * 1 * ¥1 -4- * i ¥ * r 1 ■500 -400 -300 -200-100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 8%
Missed Returns = 50% ot
a = 0.80
■0.20 2ax= °
Fig. C-10. Degraded RTL
29
PA-385 (C-n:
50
40
30
e
20
10
*■
**
■i-
■500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 1% a = 0.80 1
Missed Returns = 50% a2 = -0.20
a = 5 N
2CT = 14
Fig. OH. Degraded RTI.
30
50
30
e
20
10
"PA-385 (C-12]
40
1 * 1 1 1 1 ■
* *
¥ * * ¥
' ¥ * ¥ ¥ ¥ *
* *
* *
¥ ¥
* ¥ * ♦
¥ ¥ ¥
¥ ¥
¥
* ¥
¥ ¥
f
¥ *
¥
¥
¥
* ¥ ¥ ¥ ¥ ¥¥
¥
¥ ¥ ¥
¥ ¥ ¥
¥ ¥
¥ ¥¥
¥ ¥ ¥ ¥ ¥
¥ ¥
¥ ¥ ¥¥
¥ ¥
¥ ¥
¥ ¥
¥ ¥
4- ■500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 2% a = 0.80 a = 5 N
Missed Returns = 40% a = -0.20 2° = 14 2 X
Fig. C-12. Degraded RTL
31
^A-385 (C-T3)
50
40
4 4 4
4 4 * * 4 4
* * * 4
4 4 4 * 4 4 4 4 4 4 4 *
^ 4 44 * 44 * 4 4
* * * . * ' * if 4 4 4 * 4 44
4 4 * *
* 4 * * * *
30 0)
H
20
10
444 * ¥
4 4 * * * 4
4 *
44 4 * 4 4
4 44
4 4 *
4 4 44 4
* 4 * 4
444 4 4
* *
-¥•
4' *
4 4 4 4 4 4 4 4 4
4 4 4 4 4 4 4 4 4 4
4 4 4
4 4 4 4 4 4x4 4 4
4 * ^ ^ 4 4 4
4 44 4 4 4 4 4 4 4 4
4 4
4 4 4 4
4 4 4 4
4 44 4 4 4
X -500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 4% a = 0.80 1
a = 5 N
Missed Returns = 40% a = -0.20 2^=14
Fig. C-13. Degraded RTI.
32
fA-385 (C-14)
£
50
40
30
20
10
1 TT ¥ I ¥ *
¥ ¥ ¥ *
— ¥
* ¥ ¥
¥ ¥
; if *
* ¥ ¥
*¥ ¥ * ¥
¥
**
¥ ¥ ¥
* *
* * *
* ¥ ¥
1**1 I * *l I* * * * * ¥ ¥
* ¥ ¥ ¥
¥ * * ' * ¥¥
* ¥ * * * * * * •¥■ * ¥•
* * * * * * * ¥
¥¥ ¥ * * * * ¥ * ¥ * * ¥¥ *
¥¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ |¥ ¥ ¥ ¥
¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥¥¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥* ¥¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
|¥¥ ¥ ¥ ¥¥¥ ¥¥ ¥¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ • — ¥ ¥ ¥ ¥¥ ¥¥
¥ ¥ ¥ • ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥¥¥¥¥¥ ¥ ¥ ¥ ¥ ¥¥¥ ¥ ¥ ¥ *
* ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥¥ ¥¥ ¥ ¥ ¥ ¥ i ¥¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥¥ * ¥ ¥ ¥ ¥
* I |**| *| | * I * |¥|¥ I
¥¥ ¥ ¥ ¥
4- ■500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 6%
Missed Returns = 10% a
a = 0.80
-0.20 °N= 5
2°x " 14
Fig. C-14. Degraded RTL
33
H
50
40
30
20
10
PA-385 (C-15J
* * I 4I 4 *l * I** * * * * *
* * * * * 4 4 44 ^
I * I * 441
* * * * *
4 * • * *
¥ 4
4 4 * 4 4 44 4 44 * * * 4 * -
4 4 4 4 4 4 4 *
4 4 4 4 4 4* 44 * * * * 4 4 + 44444444 4 4
4 Jf * W * 4* * * 4 4 4 4 4*4 4
44 4 4 44 4 44 '44 444 ^ if. if. 444 44
44 44* 444 ■*• 44 4 4 4 4 4 4 4 44 44 4 444 4* 7-1'- 4
I* ¥ * 4 4 * + 4 44 4 4 444
* * * 4 4 4 4 444 44 444444 44 4
4 4 44 4 * 4 4 4 4 4 4 4
4 4444 444 * *■ Z 4 4'f
4 444444444 4 4 * 4 .4
44 444 4* * 4444 4 4444 ¥ 44 4 44 4
»4 4 4444 ¥4 4* ¥4 44444 4
¥ ¥ -.44 — 444 444 44
4 4 44 4 4 4 4> 44 4 4
44 44 4 4 4 4 4 4 4 4
* * * 44 444 4 4444 4 44 4444
44 4 44 4 4 4 44 4 4 44 444444 44 4 +44 f 4 -4 4 444 4 4 4 4 4 * -
!f \i 4 ^ 4 4 4444 4444 4 4. 4 ■
44 44 4 4 4 4 44 1 f4 4 4 4 4 4
Z * . * 4 4 44 4 4 - 4 4 4 4 4 4
4 4 4 44 44 4 4 4444 4 4
* * I * *| I 4 j * 1*1* I 4- ■500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter =8% a = 0.80
Missed Returns = 20% a = -0.20 2°X = 14
Fig. C-15. Degraded RTL
34
"fo-385 (C-16)
50
40
30
B
20
* *
10
L 4. -500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 1%
Missed Returns = 50% a
a = 0.80 a = 10 1 N
) a „ = -0.20 2CT = 27 2 X
Fig. C-16. Degraded RTL
35
PA-385(C-17)
0)
e H
50 — *
40
30
i * *i r
* *
* *i i * i *
* ** * * * * * * * * w
* ** * * * *
! * * *** * * * * * * » * ******** *
* * ***** * * * * * ** * * * -
4***** *** * * - w ** *** *** ** * * * *
* *i * i *
* * * *
* * *
*
20
* * * * * * * *
* w * ** * *
* * ** * * * *
* ** * * * *
* * * * * * * * *
* * ** * * * * *
* * * * * * ** ** * * * *
* * * * * I** * * * * * **
* * * * * * *
* * * * * * * * * * *
* * * * * * * *
* * * * * *
* * *
* * ** * *
* * * *
* ** * * *
* * *
* * * *
10
* ** * * * w*
* * * *
** ** *
* * * * * *
* * * * * * *
* * * *
* * ¥ * * *
* * ** * * * * * * *
* * *> * *
* * *l | * 1 * 1*1*
* * *
* ** * *
-500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 6%
Missed Returns = 0%
a = 1
0.80 a = N
10
*2 = -0.20 2o = X
27
Fig. C-17. Degraded RTL
36
PA-385(C-18)
I441 4I44: 4 1 * i 4I4441 4I4 4 4 4 4 4 4 4
444 44444 444 4 44 4 4 4 4 4 4 4
4 4444444 44
50 4 4 4 44 44 44 444* 444 4
J
* 44 444
4 4 44 4 4 4 44 4 »■•■ 4, 4 4 4 4 44444444 4 4
4 44 4444444
" ■
4
4
4 4 4 4 4 4 4 44 4 444 4 44
4444 444 444 44
40
*
4 4 44 4 444 .4- 44 4 4 444 4 4 4 44 4 44 4 444 44 444
4 44 4 4 4 4 4 44 4 4 444,.,
4 4 4 4 4 44' 44 4 44 444444 44 4
4 4 44 4 44 4 4 4 444
30 4 4 44444 444 —
44 4 4 44 0) 4 4 444444444 4
B • ft
4 4 4 4 4 ^ 44 4444 44 4
H 4 4
4444 4 4444 4 4 4 4 4 4 4
4 4 444 44 44 4 4 444444 4
* 4 4 44
20 444 444 44 — 4 4 44 4444
J
4
44 4 4 4 4 44 4 4 4 4 4 4 44
444 44 4444 4 444 4 44 4444
44 4 444 4 44 J 4 4
4 44 4 4Y4 4444 4 444 4
10 -4 4 444 4 4 4 4 4 4 — 44 44 4 4 4.444
4 4 4 4 4 44. 4444 4444 444
J 44 4 4 44 44 4 4 4 44 44 4
4 4 4 4 4 4 4 4 * 4 4 44 4
4 4 4 4 4 4 4
w 0 . *\ ! * * 1 * *i I * 1 * |*l* |
-5C )0 -400 -300 -200 -100 0 100 200 300 400 50 0
Relative Range (meters)
Clutter = 8%
Missed Returns = 0%
a
a2 =
0.80
■0.20 N
10
2Gx = 27
Fig. C-18. Degraded RTL
37
50
40
30 0>
20
10
PA-385(C-19)
i rr
*
*
* * * 4-JU-.
•500 -400 -300 -200 -100 0 100 200 300 400 .500
Relative Range (meters)
Clutter = 1% a = 0.80 1
a = 20 N
Missed Returns = 20% a2 = "0.20 2^= 55
Fig. C-19. Degraded RTL
38
PA-385(C-20)
50
40
30
e
20
10
* * * * *
* * *
* * *
*¥•
* * *¥
* **
* *
* * * *
4- -500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = a = 0.80
Missed Returns = 20% <*2 = -0.20 2°X = 55
Fig. C-20. Degraded RTL
39
e •t-i
50
40
30
20
10
PA-385(C-21)
1 * * | | 4 4 1 4 1 * 1 4 * * 1 4 4 * * *
* * * 4 * 4 4 4
4 * 4 4 * * * * 44 4 4
* * *
4 * * 4
4
A * * 4 4 ^
* ¥ *
4 * **¥• 4 4
4 ♦ 4 * 4 4 * * *¥ * 4 4 * 4 * * * W * ;
* * * * * 1 4 4 4 *
it 4 4 *
>l * * 4 4 4 * * 4 4 * — 4 4 44 * 4 * 4 ■*-
** 4 4 4 4 * * 4
4 4 4 * 4 4 4 44 * * * 4 4 4 4
4 44 4 4 4 4 * 4 W 4 4
4 4 4 * 44
4 4
4 4 44 4 4 4
* 4 4 4 4 4 * * * 4 4 4 —
* 4 1 ¥■ * 4 f
* 4
4 4
4 4
* 4
4
4
4
4
vgtyL If.
4 * * 4
4 4 4
4
4
4 4
4
4 4
*
* 4 4 4 4 4 4 W 4 4 4 4
4 * * 4 4
4 *
* — 4 4 4 4 4 4
4 4 * * *
♦ * *
4
4 4
4 4
4
4
4
4 4 4 4
4 4 4 * .4
4 4 4
4 4
4 4
4 4
4 44
1 4 f -*-
4
4 4
4
444
4
4 4
4 4 44
4 4
4
4
4 4 4
4 4
4
4 4
4 *¥ W 4 4 4 4 4
1 W- * 4 * - 4 * 4 4 4 4
* 4
4 4 4
* 4 **
4 4
* 1 4 4 | 1 4
1 * 1 4
4 1 * * 4
•500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 6%
Missed Returns = 0%
a = 0.80 1
a = -0.20 2
a = 20 N
2°x ■ 55
Fig. C-21. Degraded RTL
40
50
40
30 CD
& ■»-I
20
10
PA-385(C-22)
* *
¥*
* *
4- ■500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 1% at = 0.80 °N' 30
Missed Returns = 10% a = -0.20 2o =82
Fig. C-22. Degraded RTL
41
50
40
30
G
20
PA-385(C-23)
10
* * *
* * * *
** * *
* *
* ¥
-500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 2%
Missed Returns = 0%
a = 0.80 1
a = -0.20 2
a = 30 N
Fig. C-23. Degraded RTL
42
;PA-385(C-24)
i r
50
40
30 o
i-
20
* * * *
*
10
* * *
I *
■500 -400 -300 -200 -100 0 100 200 300 400 500
Relative Range (meters)
Clutter = 1%
Missed Returns =0% or
a - 1
0.80 z = 50 N
-0o20 2? = 137 A
Fig. C-24. Degraded RTL
43