THE UNIVERSITY OF BRITISH COLUMBIA Digital Processing Algorithms

THE UNIVERSITY OF BRITISH COLUMBIA Digital Processing Algorithms for Bistatic Synthetic Aperture Radar Data Presented by Prof. Ian Cumming, UBC Based on the Ph. D. slides of Dr. Yewlam Neo, DSO National Labs (Singapore) Industrial Collaborator : Dr. Frank Wong 1

Agenda • • • Bistatic SAR principles A Review of Processing Algorithms Contributions 1. 2. 3. 4. • Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions 2

Bistatic SAR • In a Bistatic configuration, the Transmitter and Receiver are spatially separated and can move along different paths. • Bistatic SAR is important as it provides many advantages – Cost savings by sharing active components – Improved observation geometries – Passive surveillance and improved survivability 3

Imaging geometry of monostatic SAR RT Monostatic SAR Platform Target Platform flight path 2 x 4

Imaging geometry of bistatic SAR 5

Focusing problems for bistatic algorithms • Traditional monostatic SAR algorithms based on frequency domain methods make use of 2 properties 1. Azimuth-invariance 2. Hyperbolic Range Equation • Bistatic SAR data, unlike monostatic SAR data, is inherently azimuth-variant – targets having the same range of closest approach do not necessarily collapse into the same trajectory in the azimuth frequency domain. • Difficult to derive the spectrum of bistatic signal due to the double square roots term (DSR). 6

Agenda • • • Bistatic SAR principles A Review of Processing Algorithms Contributions 1. 2. 3. 4. • Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions 7

Overview of Existing Algorithms • Time domain algorithms are accurate as it uses the exact replica of the point target response to do matched filtering • Time based algorithms are very slow – BPA, TDC • Traditional monostatic algorithms operate in the frequency domain – RDA, CSA and ωKA – Efficiency achieved in azimuth frequency domain by using azimuth-invariance properties 8

Existing Bistatic Algorithms • Frequency based bistatic algorithms differ in the way the DSR is handled. • Majority of the bistatic algorithms restrict configurations to fixed baseline. • Three Major Categories 1. 2. 3. Numerical Methods – ωKA, Nu. SAR – replace transfer functions with numerical ones Point Target Spectrum – LBF Preprocessing Methods – DMO 9

LBF (Loffeld’s Bistatic Formulation) • Solution for the stationary point in azimuth time is given in terms of azimuth frequency (f ) • LBF derived an approximation solution for the stationary phase: Approximate Solution to Stationary phase Using this relation, the LBF analytical spectrum can be formulated Quasi-monostatic Term Bistatic Deformation Term 10

DMO (Dip and Move Out) • Transform Bistatic data to Monostatic (using Rocca’s Smile Operator) • Assumes a Leader-Follower flight geometry (azimuth-invariant) Phase modulator RT+RR 2 RM Migration operator Rocca’s smile operator transforms Bistatic Trajectory to Monostatic Trajectory 11

Agenda • • • Bistatic SAR principles A Review of Processing Algorithms Contributions 1. 2. 3. 4. • Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions 12

Major Contributions of the Thesis #1 Derived an accurate point target spectrum using MSR (Method of Series Reversion) #3 Derived Bistatic RDA Applicable to Parallel flight cases with fixed baseline #2 Compare Spectrum Accuracy MSR is more accurate than Existing point target Spectrum – LBF and DMO #4 Derived NLCS Algorithm – Applicable to Stationary Receiver & Non-parallel Flight cases Focused Real bistatic data. Collaborative work with U. of Siegen (airborne-airborne data) 13

Derivation of the analytical bistatic point target spectrum • Problem : To derive an accurate analytical Point Target Spectrum • POSP: Can be used to find relationship between azimuth frequency f and azimuth time f = [1/(2 )] d ( )/d • But we have to find = g(f ). Difficulty: phase ( ) is a double square root. # 1 2 3 4 Result 14

Our Approach to Solving for the Spectrum • Approach to problem: – Azimuth frequency, f , can be expressed as a polynomial function of azimuth time . – Using the reversion formula, can be expressed as a polynomial function of azimuth frequency, f • Journal Paper Published : Y. L. Neo. , F. H. Wong. and I. G. Cumming A two-dimensional spectrum for bistatic SAR processing using Series Reversion, Geoscience and Remote Sensing Letters, January 2007. # 1 2 3 4 Result 15

Series Reversion • Series reversion is the computation of the coefficients of the inverse function, given the coefficients of the forward function: reversion formula forward function inverse function # 1 2 3 4 Result 16

New Point Target Spectrum by the Method of Series Reversion (MSR) • An accurate point target spectrum is derived, based on power series • A solution for the point (time) of stationary phase is given by • The accuracy is controlled by the degree of the power series • The MSR can be used to adapt monostatic algorithms to process bistatic data – e. g. , RDA and NLCS # 1 2 3 4 Result 17

Linking – MSR, LBF and DMO • We established the link between the MSR, LBF and DMO spectra • Using the MSR, we derived a new form of the point target spectrum using two stationary points. • Similar to LBF, the phase of the MSR can be split into quasimonostatic and bistatic deformation terms. • Journal Paper Submitted: Yewlam Neo. , Frank Wong and Ian Cumming “A Comparison of Point Target Spectra Derived for Bistatic SAR Processing”, Trans. Geoscience and Remote Sensing, submitted for publication, 14 Dec 2006, resubmitted October 15, 2007. # 1 2 3 4 Result 18

Link between the MSR and LBF Stationary point solutions MSR LBF Split phase into quasi monostatic and bistatic components # 1 2 3 4 Result 19

LBF and DMO • Rocca’s smile operator can be shown to be LBF’s deformation term if the approximation below is used Approximation is valid when baseline is short when compared to bistatic Range # 1 2 3 4 Result 20

Alternative method to derive the Rocca’s Smile Operator # 1 2 3 4 Result 21

Link between MSR, LBF and DMO 2 D Point Target Spectrum MSR Expand about Tx and Rx stationary points Consider up to Quadratic Phase only Quasi-Monostatic Term LBF Leader - Follower Flight configuration Monostatic Term DMO # 1 2 3 4 Result Bistatic Deformation Term Baseline is short Compared to Range Rocca’s Smile Operator 22

Bistatic RDA • Developed from the MSR 2 D point target spectrum • Monostatic algorithms like RDA, CSA achieve efficiency by using the azimuth-invariant property • Bistatic range histories are azimuth-invariant by if baseline is constant • The MSR is required as range equation is not hyperbolic • Journal Paper Reviewed and Re-submitted: Y. L. Neo. , F. H. Wong. And I. G. Cumming Processing of Azimuth-Invariant Bistatic SAR Data Using the Range Doppler Algorithm, IEEE Transactions for Geoscience and Remote Sensing, re -submitted for publication, 12 Apr 2007. # 1 2 3 4 Result 23

Main Processing steps of bistatic RDA Baseband Signal # 1 2 3 4 Range FT Azimuth FT RCMC Range Compression Azimuth Compression SRC Azimuth IFT Range IFT Focused Image Result 24

Real Bistatic Data Focused using Bistatic RDA Copyright © FGAN FHR # 1 2 3 4 Result 25

Non-Linear Chirp Scaling • Existing Non-Linear Chirp Scaling – Based on paper F. H. Wong, and T. S. Yeo, “New Applications of Nonlinear Chirp Scaling in SAR Data Processing, " in IEEE Trans. Geosci. Remote Sensing, May 2001. – Assumes negligible QRCM (i. e. , for SAR with short wavelength) – Shown to work on Monostatic cases and the Bistatic cases where receiver is stationary • We have extended NLCS to handle Bistatic nonparallel tracks cases # 1 2 3 4 Result 26

Extended NLCS • Able to handle higher resolutions, longer wavelength cases • Corrects range curvature, higher order phase terms and SRC • Develop fast frequency domain matched filter using MSR • Solve registration to Ground Plane • Journal Paper written: F. H. Wong. , I. G. Cumming and Y. L. Neo, Focusing Bistatic SAR Data using Non-Linear Chirp Scaling Algorithm, IEEE Transactions for Geoscience and Remote Sensing, to be submitted for publication, May 2007. # 1 2 3 4 Result 27

Main Processing steps of Extended NLCS • NLCS applied in the time domain • SRC and Range Curvature Correction --- range Doppler/2 D freq domain • Azimuth matched filtering --- range Doppler domain Range compression Baseband Signal The NLCS scaling function is a polynomial function of azimuth time Focused Image # 1 2 3 Azimuth compression 4 Result LRCMC / Linear phase removal Range Non-Linear Curvature Correction Chirp Scaling and SRC Range Non-Linear Curvature Chirp Correction Scaling 28

Agenda • • • Bistatic SAR principles A Review of Processing Algorithms Contributions 1. 2. 3. 4. • Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions 29

Concluding Remarks • With our four contributions, a more general and accurate form of bistatic point target spectrum was derived. • Using this result, we were able to focus more general bistatic cases using several algorithms that we have developed. • We plan to work on future projects that make use of the results from this thesis – Interest express from several agencies – DRDC (Ottawa), DSO National Labs (Singapore) and U. of Siegen (Germany). – – Satellite – Airborne (Terra. SAR-X and PAMIR) Satellite/Airborne – stationary receiver (X and C band) using RADARSAT-2 or Terra. SAR-X 30

Thank You Q&A 31