1. CE347 – RADAR TECHNOLOGIES
Prepared by
M. JANANI, M.E.,
Assistant Professor/ECE,
TPGIT,Vellore.
UNIT III –TRACKING RADAR
2. UNIT IIITRACKING 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.
3. 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 ofTracking radars
- ContinuousTracking Radar
- Discrete (or)Track While Scan (TWS) Radar
4. 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 coordinates.
6. Tracking can be done using
- Range
- Angle
- Doppler Frequency
7. AngleTracking
Angle tracking is concerned with
generating continuous measurements of
angular position in the azimuth and
elevation coordinates.
8. 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.
The error signal needs to be a linear function of the deviation
angle.
10. 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 target is tracked
11. 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.
12. 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.
14. 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
15. Conical Scan Lobing
Logical extension of the sequential lobing technique
The offset antenna beam is continuously rotated
about the antenna axis.
16. 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.
17. 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
18. 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.
19. Conical Scan Tracking
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
positionA.
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
21. 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).
22. Conical-scan radar system
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
23. Conical-scan radar system
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.
24. MonopulseTracking 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.
25. MonopulseTracking 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
26. 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.
27. Amplitude Comparison 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 focus.
28. Amplitude Comparison 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.
29. Amplitude Comparison 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.
30. 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
Amplitude Comparison Monopulse
31. 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.
Amplitude Comparison Monopulse
32. 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.
Amplitude Comparison Monopulse
34. 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.
Amplitude Comparison Monopulse
35. 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.
Range information is extracted from the output of the sum
channel after envelope detection.
Amplitude Comparison Monopulse
36. 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
37. 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
38. 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.
40. 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.
41. A phase comparison monopulse tracking radar using a two-
element array antenna operating at 600 MHz measures a
phase difference of 25° between the signal outputs of the
antenna elements. Assume that the antenna elements are
separated by 1.5 m. Determine the angular error of the
target it makes with the antenna axis.
42. The phase comparison monopulse tracking radar is now
used as a half-angle tracker. The radar measurement
shows that the amplitude of the sum signal is four times
that of the difference signal. Find the angular error of the
target it makes with the antenna axis.
44. Low AngleTracking
A radar that tracks at low elevation angles illuminates the target
via two paths.
One is the direct path from radar to target. Other is the path
that includes a reflection from the earth’s surface.
It is as though the radar were illuminating two targets, one above
the surface and the other its image below the surface.
45. At low grazing angles over a perfectly smooth reflecting surface,
the reflection coefficient from the surface is approximately –1.
That is , its phase is in the vicinity of 180o and its magnitude is
approximately unity so that the signal amplitude reflected from
the surface is almost equal to the signal amplitude incident on the
surface.
This is close to worse condition for the angle error due to glint.
For this reason, the tracking of targets at low elevation angles can
produce significant errors in the elevation angle and can cause
loss of target track.
Low Angle Tracking
46. Comparison ofTacking Systems
Conical ScanTracking 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
47. TrackWhile 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.
48. 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.
Track While Scan (TWS) Radar
49. 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.
Track While Scan (TWS) Radar
50. 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.
Track While Scan (TWS) Radar
52. The basic operations ofTWS
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.
Track While Scan (TWS) Radar
53. Target positions inherently performed in polar
coordinates are converted to the direction cosines
(N, E, andV) 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.
Track While Scan (TWS) Radar
54. 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.
Track While Scan (TWS) Radar
56. 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.
Track While Scan (TWS) Radar
57. 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.
Track While Scan (TWS) Radar
58. 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 cosines.
Track While Scan (TWS) Radar
59. 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:
Track While Scan (TWS) Radar
60. 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.
61. 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.
62. 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
63. 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
64. 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.
65. 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
66. 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
70. 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,
while smaller α and β gains reduce the level of noise in the estimate.
The α-β Tracker
71. 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
72. Smoothing equations can be rewritten in state space as
where the gain Κ is represented by
The α-β Tracker
73. 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
74. 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
consideration because it directly affects the error-reduction capability.
75. 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 )
76. 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
The α-β-γ Tracker (Kalman Filtering )
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.
78. Prediction equations can be rewritten in state space as
follows:
where the state vectors Xp and Xs are
TheTransition Matrix is given by
The α-β-γ Tracker (Kalman Filtering )
79. Smoothing equations can be rewritten in state space as
follows:
where the gain K is represented as
The Output Matrix Γ is given by
The α-β-γ Tracker (Kalman Filtering )
80. 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.
81. The α-β-γ Tracker (Kalman Filtering )
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
82. Similarly, If only the smoothed estimates are considered,
The α-β-γ Tracker (Kalman Filtering )
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
