Introduction to Radar

Target Tracking

Final report

By

Mohammed Soud Mohareb 120051649

Mohammed Ismail Al-faqawi 120050676

Submitted to

Dr. Mohammed Uoda

Islamic universityGaza

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 targets2- Multiple targets

2.1 Single target2.1.1 Angle tracking:

There are different ways to measure the target angle a- Sequential lobingb- Conical scanc- Amplitude compression monopulsed- 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 gainst=0:0.1:10;A= a*hardlim(t); %%%%echo signal AB= 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 Bfigure(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 %%%%%if theta=0 thats mean the antenna must move to position A else means move to postion B

Output and results:

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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.

2. When the target being off the LOS:17

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

1- Elevation error:

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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).

Matlab code:

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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:

Code:

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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 errorfigure(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 voltagefigure(4)plot(angle,error_signal,'k');grid;xlabel('Angle - radians')ylabel('voltage gain')

Output and results:

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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 GatesThe 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 gateb- Tracking gatec- Turning gate

a) Acquisition gateThis 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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