radar 2009 a_15 parameter estimation and tracking part 1
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IEEE New Hampshire SectionRadar Systems Course 1Parameter Estimation 1/1/2010 IEEE AES Society
Radar Systems Engineering Lecture 15
Parameter Estimation And Tracking
Part 1Dr. Robert M. O’Donnell
IEEE New Hampshire SectionGuest Lecturer
Radar Systems Course 2Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
PulseCompressionReceiver Clutter Rejection
(Doppler Filtering)A / D
Converter
Block Diagram of Radar System
Antenna
PropagationMedium
TargetRadarCross
Section
Transmitter
General Purpose Computer
Tracking
DataRecording
ParameterEstimation
WaveformGeneration
Detection
PowerAmplifier
T / RSwitch
Signal Processor Computer
Thresholding
User Displays and Radar Control
Photo ImageCourtesy of US Air Force
Radar Systems Course 3Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Tracking Radars
MOTR MPQ-39
TRADEX
BMEWS
Courtesy of Lockheed Martin.Used with permission.
Courtesy of US Air Force
FPS-16
Courtesy of MIT Lincoln Laboratory, Used with Permission
Courtesy of Raytheon, Used with Permission
Courtesy of FAACourtesy of FAA
FAA ASR
Radar Systems Course 4Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Outline
• Introduction
• Observable Estimation
• Single Target Tracking
• Multiple Target Tracking
• Summary
Radar Systems Course 5Parameter Estimation 1/1/2010
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Radar Parameter Estimation
Radar
Target • Location– Range– Azimuth Angle– Elevation Angle
• Size– Amplitude (RCS)– Radial Extent – Cross Range Extent
• Motion– Radial Velocity (Doppler)– Acceleration – Angular Motion about Center
of Mass– Ballistic Coefficient
Quantities in Blue
Are Usually Measured Directly
Measured Radar Observables
Radar Systems Course 6Parameter Estimation 1/1/2010
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Accuracy, Precision and Resolution
• Precision:– Repeatability of a measurement
• Accuracy:– The degree of conformity of measurement to
the true value– Bias Error : True value-
Average measured value
• Resolution:– Offset (angle or range) required for two
targets to be recognized as separate targets
Am
plitu
de (d
B)
Angle (deg) Angle (deg)
Am
plitu
de (d
B)
Targets at 0°
and 6° Targets at 0°
and 3°
Example Accuracy vs. Precision
Low Accuracy Low Precision
Low Accuracy High Precision
High Accuracy High Precision
-10 0 10 20 -10 0 10 20
0 0
-10
-20
-30-30
-20
-10
Radar Systems Course 7Parameter Estimation 1/1/2010
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Outline
• Introduction
• Observable Estimation– Range– Angle– Doppler– Amplitude of reflected echo from target
• Single Target Tracking
• Multiple Target Tracking
• Summary
Radar Systems Course 8Parameter Estimation 1/1/2010
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Observable Accuracy
• Observable to be discussed– Range– Angle– Doppler Velocity
• After bias errors are accounted for, noise is the key limiting factor in accurately measuring the above observables
– The exception is angle measurement, where for low angle tracking multipath errors can predominate
• The theoretical rms
error of a measurement is of the form
– Where is a constant between .5 and 1
Mδ M
N/SMkM =δ
k
Radar Systems Course 9Parameter Estimation 1/1/2010
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Limitations on Range Estimation
• Estimation of the range of a target is based upon using A/D sampled measurements of the round trip time to and from the target
• For time delay measurements , such as range, the value of the constant depends on the shape of the radar pulse’s spectrum and the pulse’s rise time.
• For a rectangular pulse, whose width is
– Which yields
• For a train of pulses it becomes:
2TcR R=
k
N/S2TT ≈δT
N/S2TcR =δ
Adapted from Barton and WardReference 6
( ) ( ) DTPRFN/S2TcR =δ
DT = Dwell Time
Radar Systems Course 10Parameter Estimation 1/1/2010
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Theoretical vs. Practical Accuracy Limitations
• General– Section 6.3 of Skolnik
reference 1 derives the theoretical limitations for each of the pertinent observables
Time, frequency, and angle
• Range– S/N, pulse shape and width, effective bandwidth, number of
pulses
• Doppler Frequency– S/N, pulse shape, integration time
• Angle– S/N, type of measurement technique, antenna illumination
distribution, antenna size, frequency
Radar Systems Course 11Parameter Estimation 1/1/2010
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Angle Estimation Issues
Prob
abili
ty D
ensi
ty F
unct
ion
Angle of ArrivalBiasedEstimators
UnbiasedEstimators
TargetLocation
LOW SNR
HIGH SNR
CALIBRATIONERRORS
MULTIPATHERRORS
Courtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 12Parameter Estimation 1/1/2010
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Limitation on Angle Estimation
Sources of Error
Signal to NoiseRatio
Monopulse
vs.Conical Scan
Servo Noise
AmplitudeFluctuationsR
MS
Ang
ular
Tra
ckin
g Er
ror
(RM
S)
Relative Radar Range
Total ErrorMonopulse Receiver Noise
(monopulse)
AmplitudeFluctuationsServo
Noise
Receiver Noise(conical scan)
Total ErrorConical
Scan
0.3
0.001
0.03
0.01
0.03
0.1
1 3 10 30 100
300 1000
Glint
N/S7. DB3θ
≈δθAdapted from Skolnik
Reference 1
Radar Systems Course 13Parameter Estimation 1/1/2010
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Angular Accuracy with ASR Radar
• Angular beam splitting with Track While Scan Radar
– ~10 : 1 splitting measuredToradar
1/16 nmi
Target DetectionsFrom 4 CPI’s
1 Beamw
idth
Accuracy of 100 tracks
Azimuth Error (deg)
Sample Tracker Output
Num
ber o
f Tra
cks
0.0 0.2 0.4
Average Error 0.14°10 nmi
20 nmi
Track Used
Radar Systems Course 14Parameter Estimation 1/1/2010
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Doppler Estimation
Doppler Frequency-50
-40
-30
-20
-10
0
-50
-40
-30
-20
-10
0
Doppler Frequency
Filte
r Res
pons
e [d
B]
fd
=2vr
λDoppler Frequency
Radial Velocity
Wavelength
• Filter-bank spans entire radar system Doppler frequency band
• Detections are isolated within a single Doppler filter
• Use two closely spaced frequency filters offset from the center frequency of the Doppler filter containing the detection
• Doppler estimation procedure is similar to angle estimation with angle and frequency interchanged
Detect Estimate
Courtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 15Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Radar Cross Section Measurement Accuracy
• Measurement of the radar cross section (RCS) of a target in a test environment was discussed in detail in the lecture on Radar Cross Section (Lecture10)
• When one wants to measure the RCS of a target, the radar needs to be calibrated
– How do A/D counts relate to RCS values?
• This calibration process is usually accomplished by launching a balloon with a sphere (RCS independent of orientation) attached by a lengthy tether and measuring the amplitude in A/D counts and the range of the balloon
Radar Systems Course 16Parameter Estimation 1/1/2010
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Radar Cross Section Measurement Accuracy
• The calibration process (continued)– Measurement is performed in the far field– A radiosonde
is usually balloon launched separately to measure the pressure, temperature, etc. (index of refraction of the atmosphere vs. height) so that propagation effects, such as, ducting, multipath, etc., may be taken into account properly and accurately
• High power radars could use spherical satellites to perform the same function as the balloon borne sphere
• RCS accuracy is usually limited by the ability to measure atmospheric (properties) losses as a function of the sphere’s range and elevation angle
Radar Systems Course 17Parameter Estimation 1/1/2010
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Outline
• Introduction
• Observable Estimation
• Single Target Tracking– Angle tracking techniques
Amplitude monopulse Phase comparison monopulse Sequential lobing Conical scanning
– Range tracking– Servo systems
• Multiple Target Tracking
• Summary
Courtesy of MIT Lincoln Laboratory.Used with permission
TRADEX
FPS-16
Courtesy of US Air Force
Radar Systems Course 18Parameter Estimation 1/1/2010
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Single Target Tracking -
General
• Usually after a target is initially detected, the radar is asked
to:
– Continue to detect the target as it moves through the radar’s coverage
– Associate the different detections with the specific target “All these detections are from the same target” Use range, angle, Doppler measurements
– Use these detections to develop a continually more accurate estimate of the targets observables
Position, velocity, etc– Predict where the target will be is the future
• These are the functions of a “Tracker”
Radar Systems Course 19Parameter Estimation 1/1/2010
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Basics of Continuous Angle Tracking
• For radars with a dish antenna, the purpose of the tracking function is to keep the antenna beam axis aligned with a selected target.
• Illustration at left – Two overlapping beams -
target is to the right of antenna boresight
• Illustration at right – Two overlapping beams -
target is to the right of antenna boresight
. Target is located at boresight
position.
Beam ABeam A Beam B Beam B
Angle
AaBa
AaBa
0θ T0 θ=θTθ Angle
Boresight Boresight Target DirectionTarget Direction
BA aa <
BA aa =
Adapted from SkolnikReference 1
Radar Systems Course 20Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Outline
• Introduction
• Observable Estimation
• Single Target Tracking– Angle tracking techniques
Amplitude monopulse Phase comparison monopulse Sequential lobing Conical scanning
– Range tracking– Servo systems
• Multiple Target Tracking
• Summary
Radar Systems Course 21Parameter Estimation 1/1/2010
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Amplitude Comparison Monopulse
• Amplitude Comparison Monopulse
Method: – Use pairs of slightly offset beams to determine the location of
the target relative to the antenna boresight
(error signal)– Use this information to re-steer the antenna (or beam) to keep
the target very close to the antenna boresight
• For dish antennas, two offset receive beams are generated by using two feeds slightly displaced in opposite directions from the focus of a parabolic reflector
• The sum and difference of the two squinted beams are used to generate the error signal
• Each channel (sum, azimuth difference, and elevation difference) requires a separate receiver
Radar Systems Course 22Parameter Estimation 1/1/2010
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Monopulse
Antenna Patterns and Error Signals
θ θθ
Overlapping Antenna Patterns
DifferencePattern
SumPattern
Error Signal vs. Angle
Angle
Erro
r Sig
nal
)(cosSignalError ΔΣ φ−φΣΔ
=
Δ Σ
Adapted from SkolnikReference 1
Radar Systems Course 23Parameter Estimation 1/1/2010
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Four Horn Monopulse
Block Diagram
A
DC
B
Antenna Feed
Sum
Hybrid Junction
A
D
C
B
ReceiverAzimuth Diffe
rence
T/R Device
Transmitter
Elevation Difference
SumΣ
Σ
Σ
Δ
Δ Σ Δ
Front
ElevationDifference
Sum
AzimuthDifference
Adapted from SkolnikReference 1
Radar Systems Course 24Parameter Estimation 1/1/2010
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Two Dimensional-
Four Horn Monopulse
B DA C
B DA C
B+A –
(C+D)
B DA C
A+B+C+D
Sum beamΣ
Elevation difference beamΔ EL
Azimuth difference beamΔ AZ
B DA C
B+D –
(A+C)
Radar
AntennaFeed
AntennaDish
•
Σ
= Sum channel signal Δ
= Difference channel signal φ
= phase difference between Σ
and
Δ• Error signal e =
Note that the lower feeds generate the
upper beams
| Δ
| cos
φ
| Σ
|
A
C
B
D
Radar Systems Course 25Parameter Estimation 1/1/2010
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Monopulse
Error Pattern
Off-Axis Angle0
0
1.0
1.0
-1.0-1.0
0.5
0.5
- 0.5
-0.5
Volta
ge P
atte
rn
Sum =
Difference = Δ
Σ
)(cos ΔΣ φ−φΣΔ
Radar Systems Course 26Parameter Estimation 1/1/2010
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Functional Diagram of Monopulse
Radar
MicrowaveCombining
Network
Duplexer
Transmitter
AntennaDrive
Servos
CoordinateTransformation
AzimuthDifferenceReceiver
SumReceiver
ElevationDifferenceReceiver
ElevationMonopulseProcessor
AzimuthMonopulseProcessor
From Antenna
Feed Horns
D
C
B
AΣ
AZΔ
)(cos)el&az(Error ΔΣ φ−φΣΔ
=
AntennaMechanical
Drive
For Detection and Range Measurement
ELΔ
Azimuth
Elevation
Adapted from ShermanReference 5
Radar Systems Course 27Parameter Estimation 1/1/2010
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Microwave Combining Network (Four Horn Monopulse
Feed)
HybridJunction
1
HybridJunction
2
HybridJunction
4
HybridJunction
3φ
φ
B
A C
D
C
A
D
B
Arrangement Of Horns
90°
-90°
1
11
1
2
3
4
2
2
2
3
33
44
4
jB
-jC
2/)BA( −
2/)BA(j +
2/)DC(j −−
2/)DC( +
[ ])DB()CA(2/1 +−+[ ])DC()BA(2/1 −−−
Diagonal Difference(terminated, not used)
Elevation Difference
Azimuth Difference
Sum
[ ]DCBA2/1 +++[ ])BA()DC(2/1 +−+
Adapted from ShermanReference 5
Radar Systems Course 28Parameter Estimation 1/1/2010
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Three Types of Hybrid Junctions
3 dBDirectional
CouplerPort D
Port C
Port B
Port A
Primary Waveguide
Secondary Waveguide
Waves Add
Waves Cancel
4/gλ
Magic -
T
4/3 gλ
4gλ
4gλ
4gλ
PortD
PortA
PortC
PortB
ab
HybridRing Junctionor “Rat-Race”
Courtesy of Courtesy of CobhamCobham
Sensor Systems.Sensor Systems.Used with permission.Used with permission.
Radar Systems Course 29Parameter Estimation 1/1/2010
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Hybrid Junctions for Monopulse
Radars
• A signal input at port A divides equally in amplitude and phase between ports C and D, but does not appear at port B
– Port B cannot support that propagation mode• A signal input to port B divides equally but with opposite
phases between ports C and D– Does not appear at port A
• If inputs are applied simultaneously to ports A and B, their sum will appear at port C and the difference at the D
Photograph of C -
Band Magic -
T (Ridged waveguide)
A
D
C
BΔ
Σ
Magic -
T
Courtesy of Courtesy of CobhamCobham
Sensor Systems.Sensor Systems.Used with permission.Used with permission.
Radar Systems Course 30Parameter Estimation 1/1/2010
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Hybrid Junctions Used in Monopulse Radar
HybridRing Junctionor “Rat-Race”
• A signal input at port A reaches output port D
by two separate paths, which have the same path length ( 3λ/4)
– The two paths reinforce at port D
• An input signal at port B reaches output port D through paths differing by one wavelength ( 5λ/4 and λ/4)
– The two paths reinforce at port D
• Paths from A to D and B to D differ by 1/2 wavelength– Signal at port A -
signal at port B will appear at port D
• If signals of the same phase are entered at A and , the outputs C and D are the sum (Σ)
and difference (Δ).
4/3 gλ
4gλ
4gλ
4gλ
PortD
PortA
PortC
PortB
ab
Radar Systems Course 31Parameter Estimation 1/1/2010
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• This coupler is made by aligning two rectangular waveguides with their walls touching
• Microwave energy from one of the waveguides is coupled to the other by means of appropriate holes or slots between the two waveguides
– Because of the quarter wave spacing between the two slots, this configuration is frequency sensitive
– A 90 degree phase shift has to be inserted in either port A or B in order to provide the sum and difference at ports C and D
Hybrid Junctions Used in Monopulse Radar
3 dBDirectional
CouplerPort D
Port C
Port B
Port A
Primary Waveguide
Secondary Waveguide
Waves Add
Waves Cancel
4/gλ
Radar Systems Course 32Parameter Estimation 1/1/2010
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Monopulse
Processor
)(cos ΔΣ φ−φΣΔ
Computer
2QQIIRe
Σ
ΣΔ+ΣΔ=⎟
⎠⎞
⎜⎝⎛
ΣΔ
2Q
2I Σ+Σ=Σ
2Q
2I Δ+Δ=Δ
2QIIQIm
Σ
ΣΔ−ΣΔ=⎟
⎠⎞
⎜⎝⎛
ΣΔ
ΣA/D
A/D
A/D
A/D
90°PhaseShift
ReferenceOscillator
Δ
QΣ
IΣ
IΔ
QΔ
Adapted from ShermanReference 5
Radar Systems Course 33Parameter Estimation 1/1/2010
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S Band Monopulse Feed with X Band Center Feed
From S and X Band Transmitters
Four Horn Monopulse
S band Feed
(X band Feed at center)
Output
Front Viewof
Output
Side View
Courtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 34Parameter Estimation 1/1/2010
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Twelve Horn Monopulse
Feed
Photograph of 12 Horn Monopulse
FeedCourtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 35Parameter Estimation 1/1/2010
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Glint (Angle Noise)
• Glint, or angle noise, is a fluctuation or error in the angle measurement caused by the radar’s energy reflecting from a complex target with multiple scattering centers
– It causes a distortion of the echo wavefront– The result of having a non-uniform wavefront
from a complex target, when the radar was designed to process a planar echo wavefront, is an error in the measurement of the angle of arrival
– The measured angle of arrival can often cause the boresight of the tracking antenna to point outside the angular extent of the target, which can cause the radar to break track
• Glint can be a major source of error when making angle measurements
– Short range where angular extent of target is large
• Problem for all tracking radars with closed loop angle tracking– Monopulse, conical scan, sequential lobing
Radar Systems Course 36Parameter Estimation 1/1/2010
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Low Angle Tracking
• The target is illuminated via two paths (direct and reflection)
• Error in measured elevation angle occurs because of glint– At low grazing angles, reflection coefficient close to -1
• Tracking of targets at low elevation angles can produce significant errors in the elevation angle and can cause loss of track
• The surface reflected signal is sometimes called the multi-path
signal
and the glint error due to this geometry a multi-path error
Radar
Direct path
Multipath Ray
Target
Radar Systems Course 37Parameter Estimation 1/1/2010
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Measured Low Angle Tracking Error
Track Time (Minutes)
Aircraft Tracked by S-Band Phased Array radar (FPS-16 provided “Truth)
Elev
atio
n Er
ror (
Deg
rees
)
0
2
1
-1
-2
Azimuth (deg) 32.5 30.7 30.4
30.3 30.3
30.2 Elevation (deg) 3.0 2.4 2.0 1.7 1.4 1.3Range (km) 19.9 24.3 28.9 33.5 38.1 42.7
Adapted from SkolnikReference 1
Radar Systems Course 38Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Outline
• Introduction
• Observable Estimation
• Single Target Tracking– Angle tracking techniques
Amplitude monopulse Phase comparison monopulse Sequential lobing Conical scanning
– Range tracking– Servo systems
• Multiple Target Tracking
• Summary
Radar Systems Course 39Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Phase Comparison Monopulse
Two antennas radiating identical beams in the same direction
Geometry of the signals at the two antennas when received from a
target at an angle θ
The phase difference of the signals received from the two antennas is :
θλ
π=φΔ sind2
d
d
d
θ
Also known as “interferometer radar”
Radar Systems Course 40Parameter Estimation 1/1/2010
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• Amplitude Comparison Monopulse– Common phase center, beams squinted away from axis– Target produces signal with same phase but different amplitudes
(On axis amplitudes equal)
• Phase Comparison Monopulse– Beams parallel and identical– Lateral displacement of phase center much greater than – Target produces signal with same amplitude but different phase
(On axis phases equal)– Grating lobes and high sidelobes a problem
Comparison of Monopulse
Antenna Beams
Axis
Axis
λ
Radar Systems Course 41Parameter Estimation 1/1/2010
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Angle Estimation with Antenna Arrays
Wavefr
onts
Antenna Array
ReceivedPhasefront
θ
Direction ofPropagation
• Received signal varies in phase across array
• Phase rate of change related to direction of propagation
• Estimating phase rate of change indicates direction of propagation
– Angle-Of-Arrival (AOA)– Direction-Of Arrival (DOA)
Courtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 42Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Outline
• Introduction
• Observable Estimation
• Single Target Tracking– Angle tracking techniques
Amplitude monopulse Phase comparison monopulse Sequential lobing Conical scanning
– Range tracking– Servo systems
• Multiple Target Tracking
• Summary
Radar Systems Course 43Parameter Estimation 1/1/2010
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Sequential Lobing
Angle Measurement
• The Sequential Lobing
angle tracking technique time shares a single antenna beam to obtain the angle measurement in a sequential manner
V1
= voltage from upper
beam (lobe)V2
= voltage from lower
beam (lobe)
If V1
-V2
> 0 Antenna pointing to highIf V1
-V2
< 0 Antenna pointing to lowIf V1
-V2
= 0 Antenna pointed at target
Beam 1
Beam 2
Antenna pointed at target
Adapted from ShermanReference 5
Radar Systems Course 44Parameter Estimation 1/1/2010
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Sequential Lobing
Angle Measurement
• The differences in echo signals between the two switched beams is a measure of the angular displacement of the target from the switching axis
– The beam with the larger signal is closer to the target– A control loop is used to redirect the beam track locations
to equalize the beam response– When the echo signals in the two beam positions are equal,
the target is on axis
Antenna Patterns
Position 1
Time
Position 2Center ofBeam 2
Center ofBeam 1
SwitchingAxis
Target Position
Radar Systems Course 45Parameter Estimation 1/1/2010
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Outline
• Introduction
• Observable Estimation
• Single Target Tracking– Angle tracking techniques
Amplitude monopulse Phase comparison monopulse Sequential lobing Conical scanning
– Range tracking– Servo systems
• Multiple Target Tracking
• Summary
Radar Systems Course 46Parameter Estimation 1/1/2010
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Conical Scan Tracking Concept
• The angle between the axis of rotation and the axis of the antenna beam is the squint angle
• Because of the rotation of the squinted beam and the targets offset from the rotation axis, the amplitude of the echo signal will be
modulated at a frequency equal to the beam rotation
Typical Conical Scan Pattern
(8 Beam Positions per Scan)
Scan Pattern
BeamRotation
Target Axis
RotationAxis
Beam Axis
Antenna Pattern
Squint Angle
Radar Systems Course 47Parameter Estimation 1/1/2010
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Conical Scan Pulse Trains
• The amplitude of the modulation
is proportional to the angular distance between the target direction and the rotation axis
– Beam displacement
• The phase of the modulation
relative to the beam scanning position contains the direction information
– Angle error
Received Pulse Trainwith
Conical-Scan Modulation
Rec
eive
d Pu
lse
Am
plitu
de
Time
Envelope of Received Pulses
Received Pulses
Radar Systems Course 48Parameter Estimation 1/1/2010
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Block Diagram of Conical Scan Radar
RangeGateDuplexer Receiver
Transmitter
ElevationServo
Amplifier
ElevationServoMotor
AzimuthServo
Amplifier
ElevationAngle
Error Detector
AzimithAngle
Error Detector
AzimuthServoMotor
ReferenceGenerator
To Rotary JointOn Antenna
In Pedestal
tf2sin sπtf2cos sπ Error
SignalScanMotor
Radar Systems Course 49Parameter Estimation 1/1/2010
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Beam-Splitting
At typical detection threshold levels (~13 dB) the resolution cell can be approximately split by a factor of ten; i.e. 10:1 antenna beam splitting
-10 0 10 20 300
0.2
0.4
0.6
0.8
1
Conical Scan , 1 pulseMonopulse, 1 pulseConical Scan, 4 pulsesMonopulse, 4 pulses
Signal-to-noise ratio [dB]
Erro
r/Bea
mw
idth
SNR = 13 dB
10:1 Beam splitting
Legend
Courtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 50Parameter Estimation 1/1/2010
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Angle Estimation with Scanning Radar (Multiple Pulse Angle Estimation)
Scan Angle
Target
Pow
er
AntennaPattern
(e.g. azimuth)
Scan Angle
Target
Pow
er
Antenna Pattern Antenna Pattern
Scan Angle
DeclaredTarget
Pow
er
Scanned Output Power
DetectionThreshold
DetectionThreshold
Courtesy US Dept of Commerce
Airport Surveillance Radar Courtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 51Parameter Estimation 1/1/2010
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Angle Estimation with Scanning Radar (Multiple Pulse Angle Estimation)
Scan Angle
Target
Pow
er AntennaPattern
Scan Angle
Target
Pow
er
Antenna Pattern Antenna Pattern
Scan Angle
DeclaredTarget
Pow
er
Scanned Output Power
DetectionThreshold
• For a “track-while scan”
radar, the target angle is measured by:
– Fitting the return angle data from different angles to the known antenna pattern, or
– Using the highest amplitude target return as the measured target angle location
DetectionThreshold
Courtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 52Parameter Estimation 1/1/2010
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Angle Estimation with Array Antennas
• Phased array radars are well suited for monopulse
tracking
– Amplitude Comparison Monopulse Radiating elements can be combined in 3 ways Sum, azimuth difference, and elevation difference
patterns– Phase Comparison Monopulse
Use top and bottom half of array for elevation Use right and left half of array for azimuth
• Lens arrays (e.g. MOTR) would use amplitude monopulse
– Four-port feed horn would be same as for dish reflector
MOTR
BMEWS
Courtesy of MIT Lincoln Laboratory, Used with Permission
Radar Systems Course 53Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Outline
• Introduction
• Observable Estimation
• Single Target Tracking– Angle tracking techniques
Amplitude monopulse Phase comparison monopulse Sequential lobing Conical scanning
– Range tracking– Servo systems
• Multiple Target Tracking
• Summary
Radar Systems Course 54Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Split Gate Range Tracking
EarlyGate
Signal
Difference Signal betweenEarly and Late Range Gates
Late Gate
Early Gate
Echo Pulse
LateGate
Signal
• Two gates are generated; one is an early gate, the other is a late gate.
• In this example, the portion of the signal in the early gate is less than that of the late gate.
• The signals in the two gates are integrated and subtracted to produce the difference error signal.
• The sign of the difference indicates the direction the two gates have to be moved in order to have the pair straddle the echo pulse
• The amplitude of the difference determines how far the pair of gates are from the centroid.
Radar Systems Course 55Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Multi Target Tracking in Range, Angle, and Doppler
• Single target angle trackers (Dish radars) can be configured to track other targets in the radar beam
– Useful for radars with moderate to wide beamwidths– Favorable geometry helpful
• TRADEX and several other radars have multi-target trackers– Primary target is kept on boresight with standard monopulse
angle tracker
– Up to 10 other targets, in radar beamwidth, are tracked in range
• Some other radars track in Doppler and in range along with tracking in angle
Radar Systems Course 56Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Outline
• Introduction
• Observable Estimation
• Single Target Tracking– Angle tracking techniques
Amplitude monopulse Phase comparison monopulse Sequential lobing Conical scanning
– Range tracking– Servo systems
• Multiple Target Tracking
• Summary
Radar Systems Course 57Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Antenna Servo Systems
• The automatic tracking of a target in angle employs a servo system that utilizes the angle error signals to maintain the pointing of the antenna in the direction of the target
• The servo system introduces lag in the tracking that results in error
– The lag error depends on the target trajectory Straight line, gradual turn, rapid maneuver
• Type II Servo System often used in tracking radar– No steady state error when target velocity constant– Known as “zero velocity error system”
• The effect of velocity and acceleration on a servo system can be described by the frequency response of the tracking loop
Radar Systems Course 58Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Servo Bandwidth
• The tracking bandwidth of a servo system is that of a low pass filter
• The bandwidth should be narrow to: Minimize the effects of noise,or jitter, Reject unwanted signal components
Conical scan frequency or jet engine modulation Provide a smoothed output of the desired measured parameters
• The bandwidth should be wide to: Follow rapid changes in the target trajectory or in the vehicle
carrying the radar• The choice of servo bandwidth is usually a compromise
– Sensitivity vs. tracking of maneuvering target• Tracking bandwidth may be made variable or adaptive
Far range -
angle rates low, low S/N (narrow bandwidth) Short range -
angle rates large (wide bandwidth) Shorter ranges -
Glint can be an issue (narrow bandwidth)
Radar Systems Course 59Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Bounds on Servo Resonant Frequency
• The tracking bandwidth of a mechanical tracker should be small compared to the lowest natural frequency of the antenna and its structural foundation
– This prevents the antenna from oscillating at its resonant frequency
Serv
o R
eson
ant F
requ
ency
(Hz)
Antenna Diameter (ft)1 3 10 30 100 300
10
1
30
3
100
APG-66
SCR-584
FPS-16
FPQ-10
FPQ-6FPS-49
Goldstone
Haystack
Radar Systems Course 60Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Summary –
Part 1
• A detailed description of the different radar observables and their estimation was presented
– Observables -
Range, angle, and Doppler velocity– Radar cross section issues were presented in a previous lecture– Resolution, precision and accuracy were discussed
• The different techniques for single target angle tracking were discussed in detail, as well as their implementation
– Amplitude monopulse– Phase comparison monopulse– Sequential lobing– Conical scanning
• Range tracking techniques, as well as other related subjects were presented
Radar Systems Course 61Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Homework Problems
• From Skolnik, Reference 1
– Problems 4.1, 4.3, 4.5, 4.9, 4.11, and 4.15
Radar Systems Course 62Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
References
1.
Skolnik, M., Introduction to Radar Systems, McGraw-Hill, New York, 3rd
Ed., 20012. Barton, D. K., Modern Radar System Analysis, Norwood,
Mass., Artech
House, 19883. Skolnik, M., Editor in Chief, Radar Handbook, New York,
McGraw-Hill, 3rd
Ed., 20084. Skolnik, M., Editor in Chief, Radar Handbook, New York,
McGraw-Hill, 2nd
Ed., 19905. Sherman, S. M., Monopulse Principles and Techniques,
Norwood, Mass., Artech
House, 19846. Barton, D. K. and Ward, H. R, Handbook of Radar
Measurements, Norwood, Mass., Artech
House, 1984
Radar Systems Course 63Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Acknowledgements
• Dr Katherine A. Rink• Dr Eli Brookner, Raytheon Co.
Radar Systems Course 64Parameter Estimation 1/1/2010
IEEE New Hampshire SectionIEEE AES Society
Part 2
• Introduction
• Observable Estimation
• Single Target Tracking
• Multiple Target Tracking
• Summary