UNIT III TRACKING RADAR.pptx

UNIT III TRACKING RADAR
Tracking with Radar, Monopulse Tracking, Conical Scan,
Sequential Lobing, Limitations to Tracking Accuracy, Low-Angle
Tracking - Comparison of Trackers, Track while Scan (TWS)
Radar- Target Prediction, state estimation, Measurement models,
alpha – beta tracker, Kalman Filtering, Extended Kalman filtering.
CEC347 - RADAR
TECHNOLOGIES

Tracking Radars
Measure the spatial position and provide
data that may be used to determine the target
path and predict the future position, in range,
elevation angle, azimuth angle, and Doppler
frequency shift.
Types of Tracking radars
- Continuous Tracking Radar
- Discrete (or) Track While Scan (TWS)
Radar
CEC347 - RADAR TECHNOLOGIES

Tracking Radars
 The tracking radar utilizes a pencil beam to find its
target first before it can track.
 A separate search radar is needed to facilitate target
acquisition by the tracker.
 The search radar or the acquisition radar designates
targets to the tracking radar by providing the
coordinates where the targets are to be found.
 The tracking radar acquires a target by performing a
limited search in the area of the designated target

Real Life Tracking Radars

Tracking can be done using
- Range
- Angle
- Doppler Frequency

Angle Tracking
Angle tracking is concerned with
generating continuous measurements
of angular position in the azimuth and
elevation coordinates.

Angle Tracking
 Involves the use of information obtained from offset
antennas to develop signals related to angular errors
between the target position and the boresight axis of the
tracking antenna.
 The resultant error signal indicates how much the target
has deviated from the axis of the main beam.
 The antenna beam in the angle tracking radar is
continuously positioned in an angle by a servomechanism,
actuated by the error signal, in an attempt to generate a
zero error signal.

Error Signal Generating
Methods
 Sequential Lobing
 Conical Scan Tracking
 Monopulse Tracking

Sequential Lobing
 Sequential lobing is often referred to as lobe switching or
sequential switching.
 The antenna pattern commonly employed with sequential
lobing is the symmetrical pencil beam
 The difference in the target position and the reference
direction is the angular error.
 The tracking radar attempts to position the antenna
continuously to make the angular error zero.
 When the angular error becomes zero, the target is
located along the reference direction implying that the

Sequential Lobing
 To obtain the direction and magnitude of the angular error,
the antenna beam is alternately switched between two
predetermined symmetrical positions around the reference
direction.
 In each position, target strength is measured and converted
into a voltage.
 The difference in amplitude between the voltages obtained
in the two switched positions is a measure of angular
displacement of the target from the switching axis.

Sequential Lobing
 The polarity of the voltage difference determines
the direction in which the antenna beam must be
moved in order to align the switching axis with
the direction of the target.
 When the voltages in the two switched positions
are equal, the target is on the axis and its
position may be determined from the direction of
the antenna axis.

Sequential Lobing

Sequential Lobing
 An important feature of sequential lobing
is the accuracy of the target position.
 Accuracy can be improved by
- carefully determining the equality of
the signals in the switched positions,
- limiting the system noise

Conical Scan Lobing
 Logical extension of the sequential lobing technique
 The offset antenna beam is continuously rotated
about the antenna axis.

Conical Scan Lobing
 The angle between the axis of rotation and the axis of
the antenna beam (LOS of the antenna beam) is
called the squint angle, denoted by a symbol θq.
 The echo signal will be amplitude modulated at a
frequency equal to the frequency of rotation of the
antenna beam.

Conical Scan Lobing
 The amplitude of the echo signal depends on the shape
of the antenna beam pattern, the squint angle, and the
angle between the target LOS and the rotation axis.
 The phase of the modulation is a function of the angle
between the target and the rotation axis.
 The conical-scan modulation is extracted from the echo
signal, and applied to a servo-control system, which
continually positions the antenna on the target.
 When the antenna is on the target, the LOS to the target
and the rotation axis coincide, and the modulation is zero

Conical Scan Tracking
As the antenna rotates about the rotation
axis, the echo signal will have zero modulation
indicating that the target is tracked and no
further action is needed.

 Consider the amplitude of the echo signal is
maximum for the target lying along the beam’s
axis at position B, and is minimum for the
beam at position A.
 Between these two positions, the amplitude of
the target return will vary between the
maximum and minimum values.
 Thus the extracted amplitude modulated signal
can be fed to the servo-control system in order
to position the target on the desired tracking
axis

Conical-scan radar system

 The AM signal out of the range gate is
demodulated by the azimuth and elevation
reference signals to produce the two angle error
signals.
 These angle errors drive the angle servos, which in
turn control the position of the antenna, and drive it
to minimize the error (a null tracker).

 Since the conical-scan system utilizes amplitude changes
to sense position, amplitude fluctuations at or near the
conical-scan frequency will adversely affect the operation
of the conical-scan radar system by inducing tracking
errors.
 Three major causes of amplitude fluctuations
- inverse-fourth-power relationship between the echo
signal and range
- conical-scan modulation
- amplitude fluctuations in the target cross section

 The function of the AGC is to maintain a
constant level of the receiver output and to
smooth amplitude fluctuations as much as
possible without disturbing the extraction of
the desired error signal.
 Two/three stages of IF amplifiers are normally
used to stabilize the dynamic range of the
system. CEC347 - RADAR TECHNOLOGIES

Monopulse Tracking Radar
 More than one antenna beam is used simultaneously in
these methods
 The angle of arrival of the echo signal may be
determined in a single-pulse system by measuring the
relative amplitude of the echo signal received in each
beam.
 The tracking systems that use a single pulse to extract
all the information necessary to determine the angular
errors are called monopulse systems.

Monopulse Tracking Radar
 Angular errors are obtained by
◦ Amplitude comparison monopulse
◦ Phase comparison monopulse.
 Advantages
◦ Greater efficiency
◦ Higher data rate
◦ Reduced vulnerability to gain inversion and AM
jamming.
◦ More accurate, and is not susceptible to lobing
anomalies CEC347 - RADAR TECHNOLOGIES

Amplitude Comparison
Monopulse
 The generation of angular track errors in an
amplitude comparison monopulse angle tracking
is similar to lobing
 Multiple squinted antenna beams and the relative
amplitude of the echoes in each beam are
required to determine the angular error.
 The difference is that the beams are produced
simultaneously rather than sequentially.

Monopulse
 Monopulse tracking radars can employ both
reflector antennas as well as phased array
antennas to generate four partially overlapping
antenna beams.
 In the case of reflector antennas, a compound feed
of four horn antennas is placed at the parabolic

Monopulse
 The distances between horns are small and the phases of the
four signals A, B, C, and D are within a few degrees of one
another.
 It is assumed that the phases are identical for all practical
purposes.
 Amplitude comparison monopulse tracking with phased array
antennas is more complex than with reflectors.

Monopulse
 All four feeds generate the sum pattern.
 The difference pattern in one plane is formed by taking the sum of
two adjacent feeds and subtracting this from the sum of the other
adjacent feeds.
 The difference pattern in the orthogonal planes is obtained by
adding the differences of the orthogonal adjacent pairs.

 A total of four hybrid junctions generate the sum channel, the
azimuth difference channel, and the elevation difference
channel.
 The hybrids perform phasor additions and subtractions of the
RF signal to produce output signals
Monopulse

 Monopulse processing consists of computing a sum ∑ and two
difference ∆ (one for azimuth and the other for elevation)
antenna patterns.
 The difference patterns provide the magnitude of the angular
error, while the sum pattern provides the range measurement,
and is also used as a reference to extract the sign of the error
signal.
 The difference patterns ∆AZ and ∆EL are produced on reception
using a microwave hybrid circuit called a monopulse
comparator.
Monopulse

Monopulse

 If a target is on boresight, then the amplitudes of the signals
received in the four channels (A, B, C, D) will be equal, and so the
difference signals will be zero.
 As the target moves off boresight, the amplitude of the signals
received will differ, and the difference signal will take on the sign and
magnitude proportional to the error that increases in amplitude with
increasing displacement of the target from the antenna axis.
 The difference signals also change 180° in phase from one side of
center to the other.
 The sum of all four horn outputs provides the video input to the
range tracking system and establishes the AGC voltage level for
automatic gain control.
Monopulse

 The cluster of four feed horns generate four partially overlapping
(squinted) antenna beams.
 All four feeds are used to generate the sum pattern
 The difference pattern in one plane is formed by taking the sum
of two adjacent feeds and subtracting this from the sum of the
other two adjacent feeds.
 The difference pattern in the orthogonal plane is obtained
similarly.
 A total of four hybrid junctions are needed to obtain the sum
pattern and the two difference patterns.
Monopulse

 Three separate mixers and IF amplifiers, one for each
channel.
 All three mixers operate from a single local oscillator in
order to maintain the phase relationships between the
three channels.
 Two phase-sensitive detectors extract the angle-error
information; one for azimuth and the other for elevation.
 Phase comparison is made between the output of the sum
channel and each of the difference channel, so the phase
shifts introduced by each of the channels must be almost
identical.
Monopulse

 The phase of the signal received in different antenna
elements determines the angular errors.
 The major difference is that the four signals produced
in amplitude comparison monopulse have similar
phases but different amplitudes, however, in phase
comparison monopulse; the signals have the same
amplitudes but different phases.
Phase Comparison
Monopulse

 Phase comparison monopulse tracking radar uses
an array of at least two antennas separated by some
distance from one another.
 Separate arrays are required for azimuth and
elevation, with a complete phase comparison
monopulse tracking radar needing at least four
antennas.
Phase Comparison
Monopulse

Phase Comparison
Monopulse
 The phases of the signals received by elements are
compared.
 If the antenna axis is pointed at the target, the phases
are equal; if not, they differ.
 The amount and the direction of the phase difference
are the magnitude and direction of the error and are
used to drive the antenna.

Phase Comparison
Monopulse

Phase Comparison
Monopulse
Assumes two-element array antenna for each of azimuth and
elevation, which includes two antenna separated by a distance d.
The target is located at a range R and is assumed large compared
with antenna separation.

Limitations to Tracking
Accuracy
 Target Amplitude Fluctuations (scintillation)
 Target Phase Fluctuations (glint)
 Atmospheric Fluctuations
 Servo system Noise
 Receiver Noise

Comparison of Tacking
Systems
Radar
Monopulse Tracking
Radar
Sequential scanning system
Simultaneous scanning
system
It requires minimum 4 pulses. It requires single pulse.
Less Expensive Expensive
Less Complex More Complex
It has single feed. It has two feeds.
Less accurate
Gain, data rate and overall
accuracy is high

Track While Scan (TWS)
Radar
 The straight-tracking mode, when the radar directs all
its power to tracking the acquired targets.
 The track-while-scan (TWS) is a mode of radar
operation in which the radar allocates part of its power
to tracking the target or targets while part of its power is
allocated to scanning.
 In the TWS mode the radar has a possibility to acquire
additional targets as well as providing an overall view of
the airspace and helping maintain better situational
awareness.

 Modern scanning radar - modes of operation
◦ Simultaneous tracking of multiple targets
◦ Prediction of future target location,
◦ Airborne radars - ground mapping, weather detection,
and aircraft surveillance.
 Depending on the configuration, the TWS radar
can either provide full hemispherical coverage or
cover a limited angular segment.
Radar

 Because of the complexity of the TWS
process and the necessity for storing
both present and past target positions
and velocities for multiple targets, digital
computers or phased-array radars are
generally required to provide TWS
processing.
Radar

 TWS radars became possible with the introduction
of two new technologies: phased-array radars and
computer memory devices.
 Phased-array antennas - shifting the phase slightly
between a series of antennas, the resulting
additive signal can be steered and focused
electronically.
 Digital computers and their associated memories
allows the radar data to be remembered from scan
to scan.
Radar

TWS data processing

The basic operations of TWS
 Computation of the target’s initial coordinates
and measurements
 Correlating and Associating target observations
with existing target tracks to avoid redundant
tracks,
 Computation of the information for displays or
other system inputs.
Radar

 Target positions inherently performed in polar
coordinates are converted to the direction
cosines (N, E, and V) of the inertial coordinate
systems
 inertial coordinate systems - More convenient
for computer processing of target tracks.
 The inertial angular position of each target
specifies the inertial target position.
Radar

 To convert the radar measurements to the inertial coordinate
system, the measured range to the target must be computed
by the following expressions:
 RN, RE and RV are in the northerly, easterly, and vertical
components of the target positions
 R - Target range
 Nˆ , Eˆ and Vˆ - Unit directional cosines in the respective
inertial coordinate system.
Radar

Radar

 After the coordinate transformation has been
performed, the observed target position must be
correlated with the established target tracks stored
in the computer.
 If the target position is near the predicted target
position for one of the previously established
tracks and the difference between the observed
and predicted position is within the preset error
bound, a positive correlation is obtained.
Radar

 If the observed target does not correlate with any of the
existing tracks, then a new track is established for the
target.
 If the observed target correlates with two or more of the
established tracks, then an established procedure such
as that described by Hovanessian must be followed in
assigning the observation to a particular track.
 The process of assigning observations to the proper
track is referred to as association.
Radar

 After the observed targets are associated with established or
new tracks, estimated target positions must be computed for
each target along with predictions of the target positions for the
next radar scan.
 The current estimated target positions are computed by digital
filtering of the current observed target position along with a
weighted estimate of previous target observations associated
with the target track.
 The predicted target positions for each track are then computed
based on the current target position estimate, the time between
scans, velocity components along each of the directional
Radar

 The predicted target positions are then used in the
correlation process for each target observation on the
next radar scan.
 For a newly established target track, if Doppler
information is available from the radar, the computer can
determine the radial velocity of the moving target.
 The target velocity components in three inertial
coordinate directions can be obtained in terms of RN, RE
and RV . The target velocity Vt can then be computed
using the following equation:
Radar

Target Prediction &
Smoothing
 The tracking radar system has a wide
application in both the military and civilian
fields.
 In the military, tracking is essential for fire
control and missile guidance
 In civilian applications it is useful for controlling
traffic of manned maneuverable vehicles such
as ships, submarines, and aircrafts.

Target Prediction &
Smoothing
 Tracking filters play the key role of target state
estimation from which the tracking system is
updated continuously.
 One of the tracking filters in use today in many
applications is the α-β-γ filter, which is a
development of the α-β filter aimed in tracking an
accelerating target since the α-β filter is only
effective when input of the target model is a
constant velocity model.

 The α-β filter is popular because of its simplicity and
computational inexpensive requirements.
 This allows its use in limited power capacity
applications like passive sonobuoys.
 The α-β tracker is now recognized as a simplified
subset of the Kalman filter.
 Low-cost and high-speed digital computing
capability has made Kalman filters practical for
more applications.
Target Prediction &
Smoothing

 Smoothing and prediction of target coordinates take place
after the completion of correlation and association.
 Smoothing provides the best estimate of the present
target position, velocity, and acceleration to predict future
parameters of the target.
 Typical smoothing and prediction equations, for the
direction cosines and range, are implemented using the α-
β-γ filter, which is a simplified version of the Kalman filter.
 This α-β-γ filter can also provide a smoothed estimate of
the present position used in guidance and fire control
operation.
Target Prediction &
Smoothing

The α-β Tracker
 The α-β tracker (also called α-β filter, f-g filter,
or g-h filter) is a simplified form of observer
for estimation, data smoothing, and control
applications.
 It is closely related to Kalman filtering and to
linear state observers used in control theory.
 Its principal advantage is that it does not
require a detailed system model.

 The α-β filter presumes that a system is
adequately approximated by a model having
two internal states, where the first state is
obtained by integrating the value of the second
state over time.
 This very low order approximation is adequate
for many simple systems, for example,
mechanical systems where position is obtained
as the time integral of velocity.
The α-β Tracker

 Based on a mechanical system analogy, the two
states can be called position x and velocity v.
 Assuming that velocity remains approximately
constant over the small time interval T between
measurements, smoothing is performed to reduce the
errors in the predicted position through adding a
weighted difference between the measured and
predicted position.
The α-β Tracker

The α-β Tracker
PREDICTION
SMOOTHING

The α-β Tracker

Implementation of α-β Tracker

 The performance of the tracker depends on the choice of α and β,
but choices are dependent.
 For stability and convergence, the values of α and β constant
multipliers should be positive and small according to the following
relations:
 Noise is suppressed only if 0 < β < 1, otherwise noise increases
significantly.
 In general, larger α and β gains tend to produce a faster response
for tracking transient changes,
The α-β Tracker

 Prediction equations can be rewritten in state space as
 where the state vectors Xp and Xs are
 The corresponding transition matrix Φ is defined by
The α-β Tracker

 Smoothing equations can be rewritten in state
space as
 where the gain Κ is represented by
The α-β Tracker

Consider an α-β filter used in a tracking radar with a
scanning time interval of 1.2 ms between samples that
assumes α = 0.75, β = 1.5. Estimate the predicted values
of position and velocity of a target corresponding to the
desired estimated values of the target at 10 km moving
with a velocity of 300 m/s

The α-β-γ Tracker (Kalman
Filtering )
 The α-β-γ tracker estimates the values of state variables and
corrects them in a manner similar to α-β filter.
 The α-β-γ tracker is a steady-state Kalman filter, which assumes
that the input model of the target dynamics is a constant
acceleration model.
 The model has a low computational load, since the two steps are
involved, that is the estimation and updating of position, velocity,
and acceleration.
 In addition, smoothing coefficients of the filter are constants for a
given sensor, which further contributes to its design simplicity.
 The selection of the weighting coefficients is an important design

 The α-β-γ Tracker is a one-step forward position
predictor that uses the current error, called the
innovation, to predict the next position.
 The innovation is weighted by the smoothing
parameters α, β and γ
 These parameters influence the behavior of the
system in terms of stability and ability to track the
target.
The α-β-γ Tracker (Kalman Filtering
)

 Based on these weighting parameters, the α-β-γ equations applied in
estimating predicted and smoothed values of position x, velocity v, and
acceleration a are expressed as
)
Prediction
Smoothing
where the subscripts 0, p, and s denote the observed, predicted, and
smoothed state parameters, respectively;
x, v, and a are the target position, velocity, and acceleration,
respectively;
T - simulation time interval;
K - sample number as used in the analysis of the α-β tracker.

Implementation of α-β-γ Tracker
Parameter Constraints

 Prediction equations can be rewritten in state
space as follows:
 where the state vectors Xp and Xs are
 The Transition Matrix is given by
)

 Smoothing equations can be rewritten in state
space as follows:
 where the gain K is represented as
 The Output Matrix Γ is given by
)

Consider an α-β-γ tracker with a scanning time interval of 2 ms
between samples that assumes α = 1.7, β = 0.75, and γ = 5.
Estimate the predicted values of position, velocity, and acceleration
of the target corresponding to the desired estimated values of the
target at 10 km having a velocity of 300 m/s and an acceleration of
18 m/s2.

)
The predicted and smoothed positions are the first element of the
vector Xs and Xp, respectively, which can be computed as:
If only the predicted estimates are considered

Similarly, If only the smoothed estimates are considered,
)
Xp(k) and Xs(k) can be expressed in the frequency domain
using z- transform as
The transfer function for the predicted and smoothed state
variables can be determined by simply substituting the proper
values of Η,Η′,P , and Κ in above equations

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