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Accuracy of Tracking Radar System
REPORT
ON
TRACKING RADAR SYSTEM
Presented By
Nithin Nagaraj Kashyap
WAYNE STATE UNIVERSITY
Email: nithin.kashyap@wayne.edu
Cell: +1 248-525-5007

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CONTENTS
1. Objective ------------------------------------------------------------------------------------------------------- 3
2. Tracking Radar ---------------------------------------------------------------------------------------- 3
3. Monopulse Concept ------------------------------------------------------------------------- 4
 Monopulse Response Curve ---------------------------------------- 6
4. Limitation of Tracking Accuracy ----------------------------------------- 7 - 13
 Receiver Noise ---------------------------------------------------------------------------- 7
 Effects of Multipath ---------------------------------------------------------- 8
 Antenna Pattern Generation -------------------------------------- 11
5. Observations and Findings -------------------------------------------------------- 14
6. Appendix ---------------------------------------------------------------------------------------------------------- 15

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OBJECTIVE
The main aim of the study was to check the accuracy of tracking radar when it
was subjected to its limitations such as glint, receiver noise and multipath and also to
understand the concept of monopulse tracking.
TRACKING RADAR
 What is Tracking Radar?
A Tracking Radar not only recognizes the target, but it determines the target
location in range and in one or two angle co-ordinates. The Radar also provides the
target’s trajectory, or track, and predicts where it will be in the future.
 Types of Tracking Radar System:
There are 4 types of radars that can provide the tracks of targets.
Single Target Tracker – (STT).
Automatic Detection and Track – (ADT).
Phased Array Radar Tracking.
Track while Scan – (TWS).
 Methods for Tracking:
Radar can track targets in range as well as angle. Sometimes tracking of the
Doppler Frequency Shift, or the radial velocity, is also performed.
Conical Scan or Sequential Lobing Trackers: These radars use a single
time shared beam to track in two angles.
Monopulse Tracking: A monopulse tracker is defined as a one in which
information concerning the angular location of a target is obtained by
comparison of signals received in two or more simultaneous beams. A
measurement of angle can be made on the basis of a single pulse; hence,
the name monopulse.
In this paper the monopulse tracking concept is explained in detail and this
paper mainly deals with the accuracy of a tracking radar system.

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MONOPULSE CONCEPT
 Monopulse radars find their origin in tracking systems. Since the late 1970s, the
principle of monopulse has been adapted to suit PSR and SSR systems and is in
common operational use world-wide today.
 A target will be seen by radar from the moment it enters the main antenna beam
or from the moment it is illuminated by the transmitted radar antenna beam.
Search radar always makes an error in the determination of the direction of the
target because it makes the assumption that the target is situated in the direction
of the axis of the main beam of the antenna. This error is of the order of the
beam width of the main antenna beam.
 A crude way of determining angular position of a target is to move the antenna
past the target direction and note the pointing direction that gives the maximum
echo amplitude.
 Unfortunately, the estimated azimuth position will be effected by thermal noise
errors and target fluctuation errors (scintillation). The target fluctuation error is
due to the cross-section changing of the target during the time-on-target of the
antenna which gives a distortion of the envelope of the reflected pulse train.

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 Monopulse gives much better target azimuth measurements than the estimating
of the angular position shown in figure 1. It can operate at a much lower
interrogation rate to benefit others in the environment. Monopulse systems
usually contain enhanced processing to give better quality target code
information. A single pulse is sufficiently for monopulse bearing measurement
(hence the use of the term monopulse).
 The angle between the axis of the antenna (boresight axis) and the direction of
the target is also known as OBA-value (Off-Boresight Angle).
 The elevation angle is also measured at 3D radars as a third coordinate. Well,
the procedure is used twice now. Here the antenna is derived in addition in an
upper half and a lower half. The second difference channel (Δ El) is called
“Delta Elevation”.
The Monopulse antenna is divided up into four quadrants now:
The following signals are formed from the received signals of these four quadrants:
 Sum - signal Σ (I + II + III + IV).
 Difference - signal ΔAz (I + IV) - (II + III).
 Difference - signal Δ El (I + II) - (III + IV).
 If the primary radiators of the monopulse antenna consist of feed horns, then the
distribution of the received signals can be performed with a monopulse
duplexer.
There are two different types of monopulse tracking:
Amplitude - Comparison Monopulse.
Phase - Comparison Monopulse.

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 Monopulse Response Curve:
The sum pattern is employed on transmission, while both the sum and the
difference patterns are used on reception. The signal received with the
difference pattern provides the magnitude of the angle error. The direction of
the angle error is found by comparing the phase of the difference signal with the
phase of the sum signal. Signals received from the sum and difference patterns
are amplified separately and combined in a phase sensitive detector to produce
the angle error signal. This forms the monopulse response curve.
Multiple simulations were performed using Matlab to generate the angle
error signal. The results of the simulation are shown in the figure.

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LIMITATIONS OF TRACKING ACCURACY
 GLINT: This has also been called angle noise, target noise, angle fluctuations
and angle scintillation; but glint is the term commonly used. It occurs with
complex targets that have more than one scattering center within the resolution
cell of the radar.
 RECEIVER NOISE : The theoretical accuracy of a tracking radar which is
given as the RMS Error in the angle measurement is given by the following
equation :
k = constant, θb = Half power beam width, ks = Slope of the angle error signal, B = Bandwidth, τ =
Pulse width, (S/N) = Signal to Noise ratio, fp = Pulse Repetition frequency, βn = Servo Bandwidth.
For the purpose of simulation we have considered the following values:
k = 1; θb = 2.7 degrees; ks = 1.57; Bτ = 1; fp/βn = 1, 8, 16, 32; (S/N) = 0 to 20 dB;
The Matlab Simulation for the above equation is generate and the graphs are plotted
using the below mentioned code.

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 MULTIPATH EFFECTS ON ANGLE TRACKING ACCURACY
Multipath is the propagation phenomenon that results in radio signals reaching
the receiving antenna by two or more paths. Causes of multipath include atmospheric
ducting, ionospheric reflection and refraction, and reflection from water bodies and
terrestrial objects such as mountains and buildings.
The multipath reflections returned to the antenna through the low-amplitude
sidelobes of the antenna do not limit system performance except for the case of large
targets near the region of maximum accuracy. However, when target elevation is
reduced, multipath returns become stronger, errors are less random in nature, and
tracking accuracy lessens; consequently, multipath signals in this situation can
seriously limit system performance.
Characteristics of the target, reflecting surface, tracking antenna, and radar data
processor all influence the nature and severity of multipath induced tracking errors.

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Let S and D represent the sum-pattern gain and difference-pattern gain,
respectively, of the phased array antenna upon reception in the ‘a’ direction; similarly
‘S’ will denote the transmitting antenna gain in the o direction. The subscript a will
denote either the direction of the direct ray to the target (a = t) or the ray reflected
from the ground to the target (a = g). When reflections are present, the total signal
received by the antenna will be a combination of signals which traverse four paths.
The first path is that directly to the target and back to the antenna, the second
and third are paths having one reflection from the ground surface, and the fourth
involves two reflections from the ground surface.
S = (Stt*Srt) + (grc*Y*Stt*Srg*Srt) + ((grc. ^2)*Stg*Srg*Z);
D = (Stt*Dt) + (Stt*Dg*grc*Y) + (Stg*Dg*(grc.^2)*Y);
Y = exp (-j*K*delR);
Z = exp(-j*2*K*delR);
X = 10.*log10 (D. /S);

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 FOR VARYING ANTENNA HEIGHT (HT) AND FIXED RANGE:
 FOR VARYING ANTENNA HEIGHT (HT) AND RANGE:

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 ANTENNA PATTERN GENERATION:
For the system simulation, we use a simple scheme that would give an adequate
representation of the antenna patterns to be approximated.
The patterns were generated using assumed far-field patterns of the form:
u = k2*sin (angle + offset);
g = (k1 * F * cos (u)). / (d);
θ1 = angle + offset;
To generate the sum and difference patterns, θ1 is assigned values θ and θ + θ0,
where Q is the offset angle of the bh.am. The two patterns thus created are added and
subtracted to produce sum and difference far-field patterns. In order to cause the
patterns to vary with scan angle, both θ0 and F are made to be functions of scan angle,
the specific function being determined empirically to produce the desired pattern
variation.

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By varying the values k1, k2 and F we can generate different antenna patterns.
 Case 1: k1 = 1; k2 = 1; F = 20;

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 Case 2: k1 = 1; k2 = 3; F = 50;

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OBSERVATIONS AND FINDINGS
Based on the simulation results and the study conducted we arrive at the
following conclusion.
There have been a number of methods demonstrated or proposed for reducing
the angle errors that can occur due to multipath at low elevation angles. Only few have
seemed to have had an effect on the tracking accuracy.
 Narrow Beamwidth: The surest method of reducing or eliminating tracking
errors due to multipath is to have a narrow antenna beam that does not
illuminate the surface.
 Illogical Target Trajectory: Prior knowledge of potential target behaviour can
be used to reduce the effects of low angle multipath without overly
complicating the radar.
 Off-axis or Off-Boresight, monopulse tracking: The tracking accuracy is only
slightly improved, but wide swings of the antenna and loss of track are avoided.

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APPENDIX
 MONOPULSE RESPONSE CURVE:
function [siga,sigb, phi] = generate2pulse (squint)
phi=pi/2;
%angle = 0-phi:0.001:pi-phi;
phiDev = phi+ squint;
angle = 0-phiDev:0.001:pi-phiDev;
siga = sin(angle+phiDev);
sigb = sin(angle+ phiDev);
noOfZeros = floor(squint/0.001);
siga = [zeros(1,noOfZeros), siga];
sigb = [sigb, zeros(1,noOfZeros)];
%figure
%plot(siga);
%hold on;
%plot(sigb,'r');
%grid
%hold off
end
clear all;
close all;
sqiuntVal = 0:pi/10:pi/2;
figure
for index=1:length(sqiuntVal)
[beamA, beamB, phi] = generate2pulse(sqiuntVal(index));
diffSig = beamA - beamB;
angle = -phi-sqiuntVal(index):0.001:(-phi-sqiuntVal(index))+(length(beamA)-
1)*0.001;
plot(angle,diffSig);
hold on
end
grid;
xlabel ('Angle - radians')
ylabel('Error value');
title('Monopulse Error curve')

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 RECEIVER NOISE:
clear all;
close all;
k = 1; % constant
halfpower_beamwidth = 2.7;
ks = 1.57; % slope of the angle error signal
Btau = 1; % for monopulse
snr_db = 0:1:20; % SNR values from 0 dB to 20 dB
SNR = 10.^(0.1.*snr_db); % computing Signal to noise in dB
fpbn1 = 1; % number of pulse integrated is varied with different values
fpbn8 = 8;
fpbn16 = 16;
fpbn32 = 32;
x = (k*halfpower_beamwidth);
y1 = (ks * sqrt (Btau * SNR * fpbn1));
a1 = x./y1;
a2 = x./y2;
a3 = x./y3;
a4 = x./y4;
figure (1)
plot (snr_db,a1,snr_db,a2,snr_db,a3,snr_db,a4)
legend ('No of Pulse Integrated = 1','No of Pulse Integrated = 8','No of Pulse
Integrated = 16','No of Pulse Integrated = 32')
grid
title ('Theoretical Accuracy of a Tracking Radar')
xlabel ('SNR - dB');
ylabel ('RMS Error Signal');

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 EFFECT OF MULTIPATH ON THE ACCURACY OF A TRACKING RADAR:
clear all;
close all;
Stt_db = [25,15,5];
Stt = 10.^(0.1.*Stt_db);
Srt_db = 15.0;
Srt = 10.^(0.1.*Srt_db);
Srg_db = 13.0;
Srg = 10.^(0.1.*Srg_db);
Stg_db = 10.0;
Stg = 10.^(0.1.*Stg_db);
Dt_db = [5,15,25];
Dt = 10.^(0.1.*Dt_db);
Dg_db = 5.0;
Dg = 10.^(0.1.*Dg_db);
K = 0.86;
Ha = 500;
Ht = 1000;
j = sqrt(-1);
grc = 0.87;
Range = 10e3:20e3;
for Q = Range;
delR = (2.*Ha.*Ht)./Range;
Y = exp(-j*K*delR);
S1 = (Stt(1)*Srt)+grc*Y*Stt(1)*Srg*Srt + ((grc.^2)*Stg*Srg*Z);
D1 = (Stt(1)*Dt(1)) + (Stt(1)*Dg*grc*Y) + (Stg*Dg*(grc.^2)*Y);
X1 = 10.*log10(D1./S1);
X2 = 10.*log10(D2./S2);
X3 = 10.*log10(D3./S3);
AngleError1 = abs(K * X1);
end

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figure (1)
plot (Range,AngleError1,Range,AngleError2,Range,AngleError3)
grid
legend ('Stt = 25,Dt = 5','Stt = 15,Dt = 15','Stt = 5 ,Dt = 25')
title ('Accuracy Of Multipath')
xlabel ('Range');
ylabel ('Angle_Error')
 ACCURACY OF A TRACKING RADAR WITH RESPECT TO VARIATION IN
ANTENNA HEIGHT:
clear all;
close all;
Stt_db = 25.0;
Stt = 10.^(0.1.*Stt_db);
Srt_db = 15.0;
Srt = 10.^(0.1.*Srt_db);
Srg_db = 13.0;
Srg = 10.^(0.1.*Srg_db);
Stg_db = 10.0;
Stg = 10.^(0.1.*Stg_db);
Dt_db = 5.0;
Dt = 10.^(0.1.*Dt_db);
Dg_db = 5.0;
Dg = 10.^(0.1.*Dg_db);
K = 0.86;
Ha = 50;
j = sqrt(-1);
grc = 0.87;
Range = 15e3;
Ht = 100:1000;
for P = Ht;
b = (Ht.^2);
c = (Range.^2);
a = sqrt(b - c);
n = (Ht./a);
angle = atand (n);
delR = (2.*Ha.*Ht)./Range;
Y = exp(-j*K*delR);
S = ((Stt*Srt)+(Stt*Srg*Srt*grc*Y)) + ((grc.^2)*Stg*Srg*Z);
D = (Stt*Dt) + (Stt*Dg*grc*Y) + (Stg*Dg*(grc.^2)*Y);

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X = 10.*log10(D./S);
AngleError = abs(K * X);
end
figure (1)
plot (Ht,AngleError)
grid
legend ('Range = 15km')
title ('Angle Error for varying Antenna Height')
xlabel ('Height of Antenna in feet');
 ACCURACY OF A TRACKING RADAR WITH RESPECT TO VARIATION IN
ANTENNA HEIGHT AND RANGE:
clear all;
close all;
Stt_db = 25.0;
Stt = 10.^(0.1.*Stt_db);
Srt_db = 15.0;
Srt = 10.^(0.1.*Srt_db);
Srg_db = 13.0;
Srg = 10.^(0.1.*Srg_db);
Stg_db = 10.0;
Stg = 10.^(0.1.*Stg_db);
Dt_db = 5.0;
Dt = 10.^(0.1.*Dt_db);
Dg_db = 5.0;
Dg = 10.^(0.1.*Dg_db);
K = 0.86;
Ha = 50;
j = sqrt(-1);
grc = 0.87;
Range = [10e3,12e3,14e3,16e3,18e3,20e3];
Ht = 100:1000;
for P = Ht;
b = (Ht.^2);
c1 = (Range(1).^2);
c2 = (Range(2).^2);
c3 = (Range(3).^2);
c4 = (Range(4).^2);
c5 = (Range(5).^2);
c6 = (Range(6).^2);

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a1 = sqrt(b - c1);
a2 = sqrt(b - c2);
a3 = sqrt(b - c3);
a4 = sqrt(b - c4);
a5 = sqrt(b - c5);
a6 = sqrt(b - c6);
n1 = (Ht./a1);
n2 = (Ht./a2);
n3 = (Ht./a3);
n4 = (Ht./a4);
n5 = (Ht./a5);
n6 = (Ht./a6);
angle1 = atand (n1);
delR1 = (2.*Ha.*Ht). /Range (1);
Y1 = exp(-j*K*delR1);
Z1 = exp(-j*2*K*delR1);
S1 = (Stt*Srt)+(grc*Y1*Stt*Srg*Srt) + ((grc.^2)*Stg*Srg*Z1);
D1 = (Stt*Dt) + (Stt*Dg*grc*Y1) + (Stg*Dg*(grc.^2)*Y1);
X1 = 10.*log10(D1./S1);
X2 = 10.*log10(D2./S2);

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X3 = 10.*log10(D3./S3);
X4 = 10.*log10(D4./S4);
X5 = 10.*log10(D5./S5);
X6 = 10.*log10(D6./S6);
end
figure (1)
plot
(Ht,AngleError1,Ht,AngleError2,Ht,AngleError3,Ht,AngleError4,Ht,AngleError5,Ht,An
gleError6)
grid
legend ('Range = 10km','Range = 12km','Range = 14km','Range = 16km','Range =
18km','Range = 20km')
title ('Angle Error for Varying Antenna Height and Range')
xlabel ('Height of Antenna in feet');
 ANTENNA GAINS PATTERN GENERATION:
clear all
close all
k1 = 1;
k2 = 2;
F = 20;
angle = -pi:pi/100:pi;
offset1 = -pi/10;
offset2 = pi/10;
u1 = k2*sin(angle + offset1);
u2 = k2*sin(angle + offset2);
d = ones(1,length(angle));
g1 = (k1 * F * cos (u1))./(d);
g2 = (k1 * F * cos (u2))./(d);
x = abs(g1);
y = abs(g2);
figure (1)
plot (angle,20*log10(x),angle,20*log10(y))
grid
legend ('Sum Pattern','Difference Pattern')
xlabel ('Angle in Radians');
ylabel ('Gain in dB');
title ('Antenna Pattern Generation');

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hold on
sum = g1 + g2;
diff = g1 - g2;
s = abs(diff);
d = abs(sum);
figure (2)
plot (angle,sum,angle,diff)
grid
legend ('Sum Pattern','Difference Pattern')
xlabel ('Angle in Radians');
ylabel ('Gain in dB');
title ('Antenna Pattern Generation');
hold on
Reference
1. Introduction to Radar Systems, Merrill Skolnik, McGraw-Hill, 1970.
2. Introduction to Radar Analysis, Bassem R. Mahafza - 1998 - ‎Technology
& Engineering.
3. Investigation of target tracking errors in monopulse radars by G. W.
Ewell, N. T. Alexander, and E. L. Tomberlin, July 1972.
4. Simulations for Radar Systems Design, Bassem R. Mahafza, Ph.D.
Decibel Research, Inc. Huntsville, Alabama.

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