Airborne SAR systems possess remote information of real time obviating the weather and time of the day. Unlike Satellites SAR, airborne SAR must oppose against the perturbation motion on troposphere of the Earth. As great progress of the electronic technology today, precious and precise sensors acquire the motion to be redeemed. By these techniques, a generalized motion compensation approach applicable to all SAR mapping modes can be accomplishable. Beyond this, the antenna on the aircraft executes the stabilization automatically to avoid miss-pointing of the target. Integrating the inertial navigation and recommending antenna gimbals tie in with the motion cleverly to operate the front-end of motion compensation. Design of the antenna gimbals also plays an important role on this work. The photograph of antenna and gimbals used in this thesis was taken in Figure 6-1.
In addition, the digital signal processing on radar system is another key to be concerned. The PGA algorithm has been shown to be an effective and robust tool for correcting radar phase errors in SAR imagery. It is also shown that it can accommodate phase error functions of arbitrary complexity spatial-frequency content. Currently, PGA is being adopted into a significant number of operational SAR systems even in other communication systems.
In future, there are many researches and developments in the topic of SAR.
It takes a milestone in such topic and gives new challenges of radar system.
References
[1] George W. Stimson, Introduction to Airborne Radar, Second Edition, Scitech, New Jersey, 1998
[2] Walter G. Carrara, Ron S. Goodman, Ronald M. Mfajewski, Spotlight Synthetic Aperture Radar, Signal Process Algorithms, Artech House, Boston/London, 1995
[3] Roger J. Sullivan, Microwave Radar Image and Advanced Concepts, Artech House, 2000
[4] Chris Oliver, Shaun Quegan, Understanding Synthetic Aperture Radar Images, Artech House, Boston/London, 1998
[5] Giorgio Franceschetti, Riccardo Lanari, Synthetic Aperture Radar Processing, Boca Raton/London/New York/Washington D.C., 1999
[6] G. J. A. Bird, Radar Precision and Resolution, John Wiley & Son , New York, 1974
[7] Byron Edde, RADAR Principle, Technology, Applications, Prentice-Hall International, 2nd Editions, 1993
[8] Bassem R. Mahafza, Radar Systems Analysis and Design Using MATLAB, Chapman and Hall/CRC, Boca Raton/London/New York/Washington D.C., 2000
[9] Mehrdad Soumekh, Synthetic Aperture Radar Signal Processing with MATLAB algorithms, Wiley-Interscience Publication, 1999
[10] Mohinder S. Grewal, Lawrence R. Weill, Angus P. Andrews, Global Positioning System, Inertial Navigation, and Integration, John Wiley &
Sons, US, 2001
[11] John C. Kirk Jr., Motion Compensation for Synthetic Aperture Radar, IEEE
Transactions on Aerospace and Electronic Systems, Vol. AES-11, No.3, May 1975
[12] John C.Kirk Jr., SAR, ISAR and Motion Compensation, Goleta Engineering, February 1998
[13] Motion Control, FlexMotion Software Reference Manual, National Instruments, November 1998
[14] Alan V. Oppenheim, Ronald W. Schafer, John R. Buck, Discrete-Time Signal Processing, Prentice-Hall, 2nd Edition, 1999
[15] Jae Sok Son, Gabriel Thomas, Benjamin C. Flores, Range-Doppler Radar Imaging and Motion Compensation, Artech House, Boston London, 2000 [16] Guy Morris, Linda Harkness, Airborne Pulsed Doppler Radar, Artech
House, 2nd Edition, 1996
[17] John C.Kirk Jr., Russ Lefevre, Randy van Daalen Wetters, Don Woods, Brendan Sullivan, Signal Based Motion Compensation, IEEE international radar conference, 2000
[18] D. E. Wahl, C. V. Jakowatz, Jr., P. A. Thompson, D. C. Ghiglia, New approach to strip-map SAR autofocus, Digital Signal Processing Workshop, 1994 Sixth IEEE, pp.53-56 , Oct. 1994
[19] C. V. Jakowatz, Jr., D. E. Wahl, Eigenvector method for maximum -likelihood estimation of phase errors in synthetic aperture radar imagery, Journal of the Optical Society of America, A, vol.10 No.12, pp.2539-2546, December 1993
[20] Charles V. Jakowatz, Jr., Daniel E. Wahl, Dennis C. Ghiglia, Paul A.
Thompson, Spotlight-Mode Synthetic Aperture Radar, a signal processing approach, Kluwer Academic Publishers, Boston/London/Dordrecht, 1996
[21] 歐彥甫, 航空雷達之運動補償, 碩士論文, 國立交通大學, 機械工程研 究所, 2002
[22] Francois Le Chevalier, Principles of Radar and Sonar Signal Processing, Artech House, Boston/London, 2002
[23] Mehrdad Soumekh, Fourier Array Imaging, Prentice-Hall, New Jersey, 1994
Figures
Antenna
Duplexer
Figure 2-1 A Radar System Architecture Transmitter
Receiver rotection P
Device
Host mpute
Co r
Antenna Servo
Antenna Command
Reference Function r(t)
Signal Processor Aircraft Motion Sensor System
Stable Oscillator
Receiver
s(t)
Radar Gimbals Controller
∫
Display
v (Hz)
Figure 2-2 Electromagnetic Spectrum and Microwave Frequency Bands Useful for Imaging
10-16 10-14 10-12 10-10 10-8 10-6 10-4 10-2 100 102 104 λ(m) v (Hz)
104 1024 1022 1020 1018 1016 1014 1012 1010 108 106
Gamma Rays Ultraviolet
X-Rays Infrared
Elevation
Azimuth
Flight path
SAR VR
θL
Figure 2-3 Geometry of SAR
Ground range Ground path
Nadir
Swath
Slant range R
x
Footprint
VJK
uK
0
uK
Scene Reference Point
Figure 2-4 Spotlight Mapping
VJK
Figure 2-5 Strip Mapping Scene Center Line
0
K u Second Strip Map
K u
First Strip Map
VJK
0
uK K
u
Figure 2-6 Doppler Beam Sharpening (DBS) Mapping
Figure 3-1 Synthetic Array and Real Array Real Array
RxRx TxTx
1 2 3 n M
" "
1
Σ Σ
Synthetic Array Switch
Store
2 3 n M
" "
T Txx
RxRx
-80 -60 -40 -20 0 20 40 60 80
Figure 3-2 Beam Pattern in Synthetic and Real Array
-80 -60 -40 -20 0 20 40 60 80
Figure 3-3 Beam Pattern of Removing Grating Lobe
Figure 3-4 Signal Processing Function Block
Figure 3-5 SAR Array Sampling Diagram (0,r)
IF filter Heterodyne detector
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
x (normalized azimuth position)
Image intensity (dB)
Point target spread function f(x) , d = 1.2L
Mainlobe
x (normalized azimuth position)
Image intensity (dB)
Point target spread function f(x) , d = L/2
Mainlobe
Figure 3-6 Point Target Spread Function in Azimuth Direction
Figure 3-7 Focusing Diagram
300 400 500 600 700 800 900 1000
0 2 4 6 8 10 12 14 16 18 20
Distance r (m)
resolution (m)
X-band, L=80cm circular antenna
:Real (circular) antenna :Unfocused SAR :Focused SAR
Figure 3-8 Resolution of Focused and Unfocused SAR r
: Actual element position rn
∆
: Corrected position of nth element
Figure 3-9(a) Raw data Image after Range Compression
Figure 3-9(b) Azimuth Compression without Focusing
Figure 3-9(c) Azimuth Compression with Focusing
Figure 3-10 Ground Data Processing Unit Interface
-100 -50 0 50 100
-200 -150 -100 -50 0 50 100 150 200
Active target views - two X-Y planes
X-axis in meters
Ground/Slant Y-axis in meters
: Ground Plane : Slant Plane
Figure 3-11 Targets on Ground and Slant Plane
video data of <1corner200x400.pat>
Down-range (meters)
Cross-range (meters)
500 1000 1500 2000 2500 3000 3500 4000 500
1000
1500
2000
Figure 3-12 Video Data Image
DDC after video data of <1corner200x400.pat>
Down-range (meters)
Cross-range (meters)
500 1000 1500 2000 2500 3000 3500 4000
500
1000
1500
2000
Figure 3-13 Image after DDC (RFG1)
video data of <1corner200x400.pat> after range processing
Range Compressed (meters)
Cross-range (meters)
10 20 30 40 50 60 70 80
500
1000
1500
2000
Figure 3-14 Image after Range Compression
1corner200x400 final image
Down-range (meters)
Cross-range (meters)
0.99 0.992 0.994 0.996 0.998 1 1.002 1.004 1.006 1.008 1.01 x 104
Figure 3-15 Processing Final Image
Figure 4-1 Motion Measurement System GPS
Receiver
Host Computer
RS232 (Motion Compensation
Computer) 100Hz Update Data Rate
RS422
x y
z
(a) Inertial Measurement Unit (IMU)
(b) Navigation Computer
Figure 4-2 Actual Pictures of Motion Measurement System
Figure 4-3 Mapping Geometry in Geographic Coordinates
Figure 4-4 Lever Arm Phase Correction VK
N HM
uK
-ES North
East
Map Being Imaged
Center Ground Point O
PK Another Point n
Antenna Phase
Center ANT
RK Antenna gimbals
axis
I
RK
α l K
L =lcosα
RK φANT =φI −φL
INS Axis
Figure 4-5 Hardware Implementation Diagram of Motion Compensation
Figure 4-6 SAR Azimuth Mechanism Prototype
MMS VLOS = ⋅K K
Received raw data input
Cos
Motion compensation function
R
Stepper Motor
Encoders
Elevation Gear Head
Azimuth Axis Elevation Axis
Designed by Wu-Zhang Yu and Yong-Chieng Tong in IMLab
Figure 4-7 SAR Antenna Gimbals 1stG Overview
Figure 4-8 SAR Antenna Gimbals 4thG Overview Wave Guide
Motor Driver Elevation
Axis
Azimuth Axis
Array Antenna IMU
Designed by Yong-Chieng Tong in IMLab
Figure 4-9 NI 7334 Motion Control Card and Extending Board
Figure 4-10 Power and Signal Flows of Antenna Gimbals 2 axes
8 signals Gimbals
Motors
Encoders
+24V +24V
+5V
NI Extending Board
2 AZ signals 6 EL signals
Drivers
+28V 2 axes
4 signals
NI 7334 Motion Control Card
Limitswitches
Figure 4-11 Console Program and User Interface of Antenna Gimbals
Figure 4-12 Polynomial Curve Fitting
Figure 4-13 InterSense Gyroscope
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0
50 100
Yaw(°)
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 -50
0 50 100
Pitch(°)
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 -100
-50 0
Time(msec)
Roll(°)
Figure 4-14 InterSense Gyroscope Data with Sampling Frequency 100Hz t
Position X
Extrapolated
T: Sampling period 5th order polynomial fitting
0 T 2T 3T 4T 5T 6T
7500 7550 7600 7650 7700 7750 7800 7850 7900
5700 5750 5800 5850 5900 5950 6000 6050 6100
40 50 60 70
Pitch(°)
5950 6000 6050 6100 6150 6200 6250 6300 6350
-75
Figure 4-15 3rd Tracking in InterSense Gyroscope
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 -5
0 5
Yaw(°)
Tracking Errors
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 -5
0 5
Pitch(°)
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 -5
0 5
Roll(°)
Time(msec)
Figure 4-16 Tracking Errors of InterSense Gyroscope
5 10 15 20 25 30 35 40 45 50 0
0.05 0.1
Magnitude
Spectrum of InterSense Gyro
5 10 15 20 25 30 35 40 45 50
Figure 4-17 Spectrum of InterSense Gyroscope
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-100 -50 0 50
Normalized Frequency (×π rad/sample)
Phase (degrees)
Normalized Frequency (×π rad/sample)
Magnitude (dB)
(1-3rd order highpass) Filter Bode Diagram
Figure 4-18 Bode Diagram of (1-3rd Order Highpass) Butterworth Filter
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
IMU Sa pling Datam
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 -100
-50 0 50
Pitch(°)
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 -50
Figure 4-19 IMU Sampling Data with 100Hz Sampling Frequency
5 10 15 20 25 30 35 40 45 50
Figure 4-20 Spectrum of IMU
6400 6450 6500 6550 6600 6650 6700 6750 6800 40
60 80
Yaw(°)
3rd Tracking in IMU
3500 3550 3600 3650 3700 3750 3800 3850 3900
-60
2200 2250 2300 2350 2400 2450 2500 2550 2600
50
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 -1
0 1
Yaw(°)
Trackin Errors of IMUg
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 -1
0 1
Pitch(°)
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 -1
0 1
Roll(°)
Time(msec)
Figure 4-22 Tracking Errors of IMU
Random Phase Errors Images
Figure 5-1 Algorithmic Steps in PGA
Figure 5-2 Input Image of PGA Step 1
Input complex image-domain data
Step 2
Center shift largest target
Step 3
Determine window width and apply
Step 4
Fourier transform in azimuth dimension (to range domain)
Step
Apply phase correction 6
Step 7
Inverse Fou sform back NoNo
YYeess Step 5
Estimated phase error function across aperture
rier tran to image domain
RMS Done errors ok?
Cicular-shift
50 100 150 200 250
10
20
30
40
50
60
50 100 150 200 250
50 55 60 65 70 75
Aperture position
Non-coherent averaging (dB)
Figure 5-3 Center-shifted Image
Figure 5-4(a) Non-coherent Average
Windowed with 20dB
50 100 150 200 250
10
20
30
40
50
60
Image without Linear Phase Removal Figure 5-4(b) Windowed Image by 20dB
Figure 5-5 Image without Linear Phase Removal
After PGA Algorithm
50 100 150 200 250
10
20
30
40
50
60
Windowed with 10dB
50 100 150 200 250
10
20
30
40
50
60
Figure 5-6 Corrected Image with Estimating Phase by PGA
Figure 5-7(a) Center-shifting after PGA
50 100 150 200 250 50
55 60 65 70 75 80 85
Aperture position
Non-coherent averaging (dB)
Windowed with 20dB
50 100 150 200 250
10
20
30
40
50
60
Figure 5-7(b) Non-coherent Average after PGA
Figure 5-7(c) Windowed Image by 20dB after PGA
Image after PGA again (Iteration = 2)
Boeing B727 Transportor
Figure 5-8 Corrected Image by Second Iteration of PGA
Figure 5-9 Original Image
50 100 150 200 -5
0 5 10 15
Aperture position
Phase Error (rad)
Motion Phase Errors Estimation
Applied Phase Error Estimated Phase Error 2 Iterations
Figure 5-10 Estimated Phase Error Functions Low SNR image of Boeing B727
Figure 5-11 Low SNR Image for PGA Simulation
(a) Degrade Image
(b) Cicular-shift (f) Circular-shift (e) Image after PGA
20 40 60 80 100 120 76
78 80 82 84
(c)
Non-coherent averaging (dB)
(d) Windowed with 20dB
20 40 60 80 100 120 75
80 85
dBNon-coherent averaging () (g)
(h) Windowed with 13dB
Figure 5-12 PGA Steps
Low SNR Image after 2 Iterations PGA
Figure 5-13 Low SNR Image after 2 Iterations PGA
20 40 60 80 100 120
-15 -10 -5 0 5 10
Aperture position
Phase Error (rad)
Motion Phase Errors Estimation
Applied Phase Error Estimated Phase Error 2 Iterations
Figure 5-14 Estimated Phase Erro Functions of Low SNR Imagery r
Figure 6-1 Actual Antenna and Gimbals
Tables
Designation Assigned Frequencies
VHF 138~144 MHz
216~225 MHz
UHF 420~450 MHz
890~942 MHz
L 1.215~1.4 GHz
S 2.3~2.5 GHz
2.7~3.7 GHz
C 5.25~5.925 GHz
X 8.5~10.68 GHz
Ku 13.4~14.0 GHz
15.7~17.7 GHz
K 24.05~24.25 GHz
Ka 33.4~36.0 GHz
Table 2-1 Radio Frequency Bands
Longitudinal (pitch ) frequency 0.630Hz (-3dB)
Lateral (roll) frequency 0.913Hz (-3dB)
Directional (yaw) frequency 0.331Hz (-3dB) Table 4-1 Motion Cutoff Frequency of a UAV
Tracking RMS Errors (degree)
Before filtering of InterSense gyro
After filtering of
InterSense gyro IMU
Yaw 0.8655° 0.1058° 0.0520°
Pitch 1.1070° 0.1360° 0.0249°
Roll 1.0077° 0.1241° 0.0088°
Table 4-2 Tracking RMS Errors of InterSense Gyroscope and IMU