Introduction to Radar
Target Tracking
Final report
By
Mohammed Soud Mohareb
120051649
Mohammed Ismail Al-faqawi
120050676
Submitted to
Dr. Mohammed Uoda
Islamic university
Gaza
January 2, 2010
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Target tracking
1. Introduction:
In this project we interested in measuring the angle and range of moving targets.
Before discuss target tracking principles we should introduce for some useful concepts.
1.1 Relation between beamwidth and accuracy:
There is a relation between the antenna beamwidth and tracking accuracy. Antennas
with wide beamwidth are less accuracy than antennas with narrow beam, so in tracking
processes radar used narrower beams.
Beamwidth vs Accuracy
Ship A
Ship B
Figure indicates the relation between beamwidth and accuracy
One type of beamwidth which used in tracking is pencil beam which a three or four
degrees wide
Figure indicates the pencil beam
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1.2 Line of Sight (LOS) axis:
The LOS is called the radar tracking axis too. It’s the line between two symmetrical
beamwidth.
Figure indicates LOS
1.3 Azimuth and Elevation Error:
Azimuth plane: In radian coordinates(r,theta,phi), it’s the plane when phi is varying and
theta equals to 90
Elevation plane: In radian coordinates(r,theta,phi), it’s the plane when phi is a contsant
and theta is varying
Figure indicates azimuth and elevation plane
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Understanding azimuth and elevation planes make azimuth and elevation errors easy to
understand.
-
Azimuth error means radar should move left or right
-
Elevation error means radar should move up or down
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2. Target tracking:
‘Tracking radar systems are used to measure the target’s relative position in range, azimuth
angle, elevation angle, and velocity. Then, by using and keeping track of these measured
parameters the radar can predict their future values’2.
Targets are divided to two types:
1- Single targets
2- Multiple targets
2.1
Single target
2.1.1 Angle tracking:
There are different ways to measure the target angle
a- Sequential lobing
b- Conical scan
c- Amplitude compression monopulse
d- Phase compression monopulse
These types of radar determine the azimuth angle, elevation angle and the range of a
single target.
Azimuth and elevation angles are determined by measuring the difference between
echo signals from two different positions.
2.1.1.1
Sequential lobing:
It is one of the first radars used in tracking processes. It is referred often as lobe
switching or sequential switching since radar move its beam from one position to other
position by closing and opening switches. So sequential lobing radar circuit is easy to
implement.
The accuracy of this type depends on the antenna beam width.
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SCR-268 sequential lobbing radar
 Concept of determining the angle by Sequential lobing:
There are two cases we can study:
1. When the target being on the LOS:
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In this case the target on LOS, that’s implies to symmetrical detection in position(A) and
position(B), which means the difference between the echo signals voltage from (A) and
(B) equal zero, also the error signal equal zero.
2. When the target being off the LOS:
From figure the target on the beam axis of position(A), so echo signal from position(A)
will attenuate more than echo signal from position(B), which means there is a difference
between echo signals voltage from (A) and (B). In this case radar will detect a target and
moves the antenna to position(A).
 Matlab Code:
Next code represents two echo signals (A and B) are detected by sequential lobing
radar.
Input:
Code input (a,b), where a is the amplitude of signal A and b is the amplitude of signal B.
Process:
Difference between echo signals A and B
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Output:
If the output of the difference process is positive that’s mean radar will move to
position(A) and angle will equal 0, else the angle will equal 180 and radar move to
position(B).
Flowchart:
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Code:
function sequantial(a,b)
%%%% input a and b which are the echo signals gains
t=0:0.1:10;
A= a*hardlim(t);
%%%%echo signal A
B= b*hardlim(t);
%%%%echo signal B
figure(1)
plot(t,A,'r')
xlabel('time')
ylabel('signal voltage A')
figure(2)
plot(t,B,'y')
xlabel('time')
ylabel('signal voltage B')
S= A-B;
%%%%difference between echo signa A and echo signal B
figure(3)
plot(t,S)
xlabel('time')
ylabel('difference between signals A & B')
S_average = mean(S)
if (S_average < 0)
theta = 180;
else
theta = 0;
end
theta
postion B
%%%%%if theta=0 thats mean the antenna must move to position A else means move to
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 Output and results:
1- When the amplitude of signal A (a=6) and the amplitude of signal B (b=5)
Echo signal A
Echo signal B
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Difference between A and B, A>=B, theta = 0
2- When the amplitude of signal A (a=5) and the amplitude of signal B (b=6)
Difference between A and B, A<B, theta = 180
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2.1.1.2
Conical scan:
It’s an extension for the sequential lobbing but in this type the feed of antenna is
rotating around the antenna axis, as shown in the below figure
Where:
ws is the beam scan frequency, in radians per second
Phi is the squint angle which the angle between the beam and tracking axes
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Simplified block diagram of conical scan radar system:
When Conical radar received the echo signal, envelope detector detects the signal
amplitude and extract it, while Automatic Gain Control (AGC) is used to reduce the echo
signal amplitude if it is strong and raises it when it is weaker. Elevation and azimuth
detector will move the servo system to minimum error.
 Concept of determining the angle by Conical scan:
1. When the target being on the LOS:
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In this case radar will receive a constant amplitude level in position(A) and position(B).
As shown in the below figure
Which means zero error and radar can’t detect the target.
2. When the target being off the LOS:
In this case target exist in position(B) so there will be a difference between voltage
levels between (A) and (B). As shown in figure below
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In this case radar will detect the target and will move the antenna to target direction.
2.1.1.3
Amplitude compression monopulse:
This type is more accurate than sequential and conical scanning. It consists of a special
antenna which radiated four beams simultaneously by single pulse so it’s called
monopulse. The four beams radiated mainly by horn antenna
This figure indicates AN/FPQ-6 C-band monopulse tracking radar
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This figure indicates horn antenna generated 4 beams
This figure indicates 4 beams of monopulse radar
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 Simplified amplitude comparison monopulse radar block diagram:
When monopulse radar received the four echo signals, hybrid beam forming must used
to reduce the interference among them. Elevation and azimuth detector will move the
servo system to minimum error.
 Concept of determining the angle by monopulse radar:
1. When the target being on the LOS:
In this case voltage levels are symmetrical so the error equal zero and radar can’t detect
any target.
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2. When the target being off the LOS:
In figures above its clear the voltage levels are unbalanced so radar will detect a target
and move the antenna on its direction.
 Determining azimuth and elevation error:
Azimuth and elevation error are determined by using Microwave Comparator Circuitry
Microwave Comparator Circuitry
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1- Elevation error:
When (A+B)>(D+C) error will be positive so radar will move up or down. Let
positive means up so radar will move up. If (A+B)<(D+C) error will be negative so
radar will move down.
2- Azimuth error:
When (A+D)>(B+C) error will be positive so radar will move right or left. Let
positive means right so radar will move right. If (A+D)<B+C) error will be negative
so radar will move left.
 Error signal output
To calculate azimuth or elevation error voltage
1- Determine azimuth or elevation error by using Microwave Comparator Circuitry.
2- Calculate summation of the 4 echo signals.
3- Theta may be just (0 or 180) which means (up or down) when calculating
elevation error or it means (right or down) when calculating azimuth error.
4- When azimuth error calculated, the difference equation is (A+D)-(B+C).
5- When elevation error calculated, the difference equation is (A+B)-(D+C).
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 Matlab code:
Next code calculates elevation or azimuth error and error signal voltage.
Input:
Squint angle (phi)
Process:
Calculating elevation or azimuth error then applying error signal voltage equation
Output:
Elevation or azimuth error then applying error signal voltage equation
Flowchart:
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Code:
function mono_pulse(phi0)
eps = 0.0000001;
angle = -pi:0.01:pi;
y1 = sinc(angle + phi0); %%%echo signal represents (A+B)
y2 = sinc((angle - phi0)); %%%echo signal represents (C+D)
ysum = y1 + y2;
ydif = -y1 + y2; %%%%elevation error
figure(1)
plot(angle,y1,'k',angle,y2,'k');
grid;
xlabel('Angle - radians')
ylabel('Squinted patterns')
figure(2)
plot(angle,ysum,'k');
grid;
xlabel('Angle - radians')
ylabel('Sum pattern')
figure(3)
plot(angle,ydif,'k');
grid;
xlabel('Angle - radians')
ylabel('Difference pattern')
angle = -pi/4:0.01:pi/4;
y1 = sinc(angle + phi0);
y2 = sinc((angle - phi0));
ydif = -y1 + y2;
ysum = y1 + y2;
error_signal = ydif ./ ysum; %%%%error signal voltage
figure(4)
plot(angle,error_signal,'k');
grid;
xlabel('Angle - radians')
ylabel('voltage gain')
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 Output and results:
Two echo signals at squint angle (phi=0.4 rad)
Sum of the two signals S1,S2
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Difference between S1,S2
Elevation error signal
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Notes:
* ( +1) voltage error means radar should move up with percent of amplitude equal one
* (-1) voltage error means radar should move down with percent of amplitude equal
one
* We can use the same code to calculate azimuth error
2.1.1.4
Phased compression monopulse:
This type of tracking have the same idea as amplitude compression monopulse but here
amplitude is equal for the four beams with different phases.
Error signal is given by
Where :
phi is the squint angle
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2.1.2 Range tracking:
Target range is measured by estimating the round-trip delay of the transmitted pulses.
‘Since the range to a moving target is changing with time, the range tracker must be constantly
adjusted to keep the target locked in range. This can be accomplished using a split gate system,
where two range gates (early and late) are utilized’2
Split range gate:
It is used to predict the target movement (Is it to right or to left?). By dividing the echo
signal for two parts (Early and late gates), then by using some formulations on these two
parts, it can determines the response of these gates (Is it positive or negative?), to
decide the target direction (Is it to right or to left?). The below figure show Split range
gate operations
Split range gate
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2.2 Multiple targets:
Tracking processes to multiple targets is more complex than single target, since in this
case radar is tracking for early exited targets, scanning for new targets and deciding if
targets are new or old.
Track while scanning (TWS)
This type of radar is used for multiple targets which scan for new targets while it’s
tracking old targets. When TWS scan a new target it initiates a new track file for this
target then it measures position, velocity and acceleration of the new target, then using
it to predict the target movement.
 The below figure shows simplified TWS block diagram
Correlation unit correlates old tracked file with a new scanned measurements. If the
new measurements is correlate with old measurements that’s mean the target is
existing earlier, otherwise a new track file is initiates.
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TWS requirements
There are multiple functions carried out by TWS radar:
- Target detection
- Generation Gates
- Correlation
- Target track initiation and track file generation
- Track gate positioning
- Display and future target calculations
1- Generation Gates
The gate is a portion of the space that consists of some cells, which surrounds the
tracked target and centered to it.
The gate function knows if the target is new or old, and continuously tracks the target
information.
 Gate Types
Gates are divided to three types:
a- Acquisition gate
b- Tracking gate
c- Turning gate
a) Acquisition gate
This gate is generated at the beginning of tracking processes which scans for new
targets.
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Acquisition gate
b) Tracking gate
If the target moves from acquisition gate to the next scan, the tracking gate is
generated. Tracking gate is small for more accurate observations.
Tracking gate
c) Turning gate
It’s generated when tracking gate doesn’t give sufficient information about the target.
In this case, tracking gate stay around the target, and turning gate surrounds it to give
more details about this target. The figure below indicates this operation.
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Turning gate
2- Track file generation
As soon as acquisition gate is generated, the track file is initiated in the digital
computer's high-speed memory.
Track file for any target has all necessary information about the target as (range – angle
– position – gate data…etc), and this information is updated continuously.
If the target was previously detected (old target), the track file will deleted and the
previously track file is supported; otherwise the new track file is adopted for this new
target. This operation is determined by correlation and association.
3- Track correlation
Correlation is the process which compared observations are located in the tracking gate
with all track files that exists in radar computer memory.
Perhaps, observation is correlated with one track file, several tracks or no track, so if it is
correlated with any tracks then this target is discovered earlier, otherwise the target is
new.
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 Tracking Ambiguity Results
This problem occurs because of one or both of these two points:
1- Several targets site in the same gate.
2- Several gates overlap around a single target.
If ambiguity is occurred the observations will correlate with several track files that’s
mean no new track file.

Ambiguity solution
Solving for ambiguity problem varies according to radar type:
1- If radar allows the operator to initiate the tracks, then the solution by delete this
ambiguity tracks, and initiate new track.
2- If radar is automatic radar, the solving will be by some software rules. Some of
these rules are:
a- If several observations lie in the same gate, observation which closest to the gate
center will accepted.
b- If several gates overlap around a single target, the target will be assigned to the gate
nearest to the center.
4- Track gate smoothing and positioning
We know that if the target off the radar antenna axis, error will be appear. This error
requires from servo system to repositioning the antenna axis on the target. During
repositioning operation, the radar response will be smooth, where any moving to the
target radar will response.
Smoothing is completed by comparing predicted parameters with observed parameters.
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 TWS operation
The below flowchart indicates track while scan radar operation
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3. Conclusion:
Target tracking is important to military and civilian purposes as missile guidance and
airport traffic control so it’s very important topic to study.
In this project we tried to determine angle and range of single and multiple targets,
and introduce sufficient material about this topic.
At the beginning of our study, we faced many problems with understanding target
tracking but by studying hard and searching more we thought we succeed to
introduce a good basic concepts about our project.
Finally, we attached Matlab codes and references with CD-Rom. And thanks a lot to
Dr.Mohammed Ouda for his encouraging and helpness.
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4. References:
1- Radar Handbook
Author: MERRILL I. SKOLNIK
Book edition: Second Edition
Publisher: McGraw-Hill
2- Radar Systems Analysis and Design Using MATLAB
Author: Bassem R. Mahafza
Publisher: CHAPMAN & HALL/CRC
3-Fundamentals of Naval Weapons Systems
http://www.fas.org/man/dod-101/navy/docs/fun/part06.htm
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