T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 1 out of 55 University of Siegen Processing Algorithms For Bistatic SAR By Y. L. Neo Supervisor : Prof. Ian Cumming Industrial Collaborator : Dr. Frank Wong

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 2 out of 55 University of Siegen Agenda Bistatic SAR processing A Review Of Processing Algorithms Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 3 out of 55 University of Siegen 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

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 4 out of 55 University of Siegen Imaging geometry of bistatic SAR

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 5 out of 55 University of Siegen Bistatic SAR signal range azimuth

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 6 out of 55 University of Siegen A point target signal Two-dimensional signal in time and azimuth Simplest way to focus is using two- dimensional matched filtering

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 7 out of 55 University of Siegen Overview of Existing Algorithms Time domain algorithms are accurate but slow – BPA, TDC Monostatic algorithms make use –Azimuth-Invariance –Efficiency achieved in azimuth frequency domain Traditional monostatic frequency domain algorithms –RDA, CSA and ωKA

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 8 out of 55 University of Siegen Simple Illustration of Frequency based algorithms Rg time Az timeAz freqAz Time

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 9 out of 55 University of Siegen Focusing problems for bistatic algorithms Bistatic SAR data, unlike monostatic SAR data, is inherently azimuth-variant. Traditional monostatic SAR algorithms based on frequency domain methods are not able to focus bistatic SAR imagery, since 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).

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 10 out of 55 University of Siegen Agenda Bistatic SAR processing A Review Of Processing Algorithms Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 11 out of 55 University of Siegen Derivation of target spectrum POSP: 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.

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 12 out of 55 University of Siegen 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 –Numerical Methods – ωKA, NuSAR – replace transfer functions with numerical ones –Point Target Spectrum – LBF, MSR –Preprocessing Methods – Rocca’s Smile Operator (DMO)

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 13 out of 55 University of Siegen Loffeld’s Bistatic Formulation Derived by using Taylor’s expansion of the phase function about the two monostatic stationary points Approximate solution to the point target spectrum as it consider up to 2 nd order phase Results in two phase terms – bistatic deformation term and quasi-monostatic phase term.

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 14 out of 55 University of Siegen LBF Solution for the stationary point is a function of azimuth time In terms of azimuth frequency  (f  ). Using this relation, the analytical point target spectrum can be Formulated - LBF Approximate Solution to Stationary phase

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 15 out of 55 University of Siegen DMO Pre-processing technique – transform bistatic data to monostatic data Technique from seismic processing Transform special bistatic configuration (tandem configuration) to monostatic

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 16 out of 55 University of Siegen DMO (seismic processing) Tx Rx θdθd Mono survey tbtb tmtm

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 17 out of 55 University of Siegen θdθd Tx Rx θdθd Mono SAR θsqθsq tbtb tmtm DMO applied to SAR

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 18 out of 55 University of Siegen DMO Operator for bistatic SAR to Monostatic SAR transformation Phase modulator Migration operator DMO operator transform Bistatic Trajectory to Monostatic trajectory

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 19 out of 55 University of Siegen Agenda Bistatic SAR processing A Review Of Processing Algorithms Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 20 out of 55 University of Siegen New Point Target 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 

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 21 out of 55 University of Siegen Our Approach - solve the point target spectrum The signal of a point target in the range Doppler domain and 2-D frequency domain are derived using the Principle of Stationary Phase (POSP), and reversion of power series

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 22 out of 55 University of Siegen New Point Target Spectrum – Method Of Series Reversion (MSR) An accurate point target spectrum based on power series is derived Solution for the point of stationary phase is given by The accuracy is controlled by the degree of the power series Spectrum can be used to derive other Algorithms – RDA and NLCS

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 23 out of 55 University of Siegen Agenda Bistatic SAR processing A Review Of Processing Algorithms Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 24 out of 55 University of Siegen MSR, LBF and DMO Link between MSR, LBF and DMO Phase of MSR can be split into quasi- monostatic and bistatic deformation terms. This new formulation is called the Two Stationary Phase Points (TSPP), derived from MSR by Taylor Series Expansion Found to be the same as the LBF, when considering phase terms up to 2 nd order LBF can be considered a special case of this formulation

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 25 out of 55 University of Siegen TSPP (MSR) and LBF Stationary point solution Split phase into quasi monostatic and bistatic components

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 26 out of 55 University of Siegen LBF and DMO Rocca’s smile operator (DMO) can be shown to be LBF’s deformation term if the approximation below is used

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 27 out of 55 University of Siegen Alternative method to derive Rocca’s Smile Operator

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 28 out of 55 University of Siegen Summary MSR is the most general of the three spectra – MSR, DMO and LBF DMO is accurate when short baseline/Range ratio LBF is accurate under conditions – higher order bistatic deformation terms are negligible and

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 29 out of 55 University of Siegen Typical example X band example Squint angles θ sqT = -θ sqR Large baseline to range Ratio of 2h/R = 0.83

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 30 out of 55 University of Siegen Agenda Bistatic SAR processing A Review Of Processing Algorithms Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 31 out of 55 University of Siegen Bistatic RDA Monostatic algorithms like RDA, CSA achieve efficiency by using the azimuth-invariant property Bistatic range histories can be made azimuth-invariant by if baseline is constant Point target spectrum required as range equation is not hyperbolic

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 32 out of 55 University of Siegen Main Processing steps of bistatic RDA Range FT Azimuth FT SRC RCMC Azimuth IFT Baseband Signal Focused Image Range Compression Range IFT Azimuth Compression

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 33 out of 55 University of Siegen Analytical Development Start with the 2D point target spectrum Replace 1/(fo + fτ) with power series expansion

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 34 out of 55 University of Siegen Phase terms of spectrum Range Modulation – range chirp Range Doppler Coupling – removed in the 2D frequency domain, evaluated at the reference range. For wider scene, requires range blocks. Range Cell Migration term – linear range frequency term, removed in the range Doppler domain Azimuth Modulation – removed by azimuth matched filter in range Doppler domain Residual phase – range varying but can be ignored if magnitude is the final product

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 35 out of 55 University of Siegen Real Bistatic Image Copyright © FGAN FHR

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 36 out of 55 University of Siegen Approximate RDA For coarse range resolution and lower squint, the range Doppler coupling has only a small dependency on azimuth frequency. Thus, SRC is evaluated at Doppler centroid and can be combined with Range Compression (as in Monostatic Case). Range FT Azimuth FT Azimuth Compression With Azimuth IFT Baseband Signal Focused Image Range Compression And SRC Range IFT RCMC

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 37 out of 55 University of Siegen Agenda Bistatic SAR processing A Review Of Processing Algorithms Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 38 out of 55 University of Siegen Non-Linear Chirp Scaling Existing Non-Linear Chirp Scaling –Based on paper by F. H. Wong, and T. S. Yeo, “New Applications of Nonlinear Chirp Scaling in SAR Data Processing," in IEEE Trans. Geosci. Remote Sensing, May –Assumes negligible QRCM (for SAR with short wavelength) –shown to work on Monostatic case and the Bistatic case where receiver is stationary

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 39 out of 55 University of Siegen NLCS We have extended NLCS to handle non parallel tracks cases Able to higher resolutions, longer wavelength cases Correct range curvature, higher order phase terms and SRC Develop fast frequency domain matched filter using MSR Registration to Ground Plane

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 40 out of 55 University of Siegen Applying QRCMC and SRC Range compression LRCMC / Linear phase removal Azimuth compression Baseband Signal Focused Image Non-Linear Chirp Scaling Residual QRCMC The scaling function is a polynomial function of azimuth time NLCS applied in the time domain SRC and QRCMC --- range Doppler/2D freq domain Azimuth matched filtering --- range Doppler domain Residual QRCMC and SRC Non-Linear Chirp Scaling

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 41 out of 55 University of Siegen Monostatic Case Az time Range time A B C FM Rate Difference –The trajectories of three point targets in a squinted monostatic case is shown –Point A and Point B have the same closest range of approach and the same FM rate. –After range compression and LRCMC, Point B and Point C now lie in the same range gate. Although they have different FM rates

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 42 out of 55 University of Siegen After LRCMC, trajectories at the same range gate do not have the same chirp rates, an equalizing step is necessary This equalization step is done using a perturbation function in azimuth time Once the azimuth chirp rate is equalized, the image can be focused by an azimuth matched filter. FM Rate Equalization (monostatic)

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 43 out of 55 University of Siegen FM Rate Equalization (monostatic or nonparallel case) – cubic perturbation function Azimuth Phase

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 44 out of 55 University of Siegen Longer wavelength experiment Without residual QRCMC (20 % range and azimuth broadening) With residual QRCMC, resolution and PSLR improves Uncorrected QRCM will lead to broadening in range and azimuth QRCMC is necessary in longer wavelength cases Higher order terms can be ignored in most cases

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 45 out of 55 University of Siegen Expansion of phase up to third order necessary - e.g. C band 55deg squint 2m resolution Azimuth Frequency Matched Filter Accuracy is attained by including enough terms. Second order Third order

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 46 out of 55 University of Siegen Requirement for SRC L-band 1 m resolution

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 47 out of 55 University of Siegen Simulation results C-band Non-parallel tracks range resolution of 1.35m and azimuth resolution of 2.5m Unequal velocities Vt = 200 m/s Vr = 221 m/s track angle difference 1.3 degree 30° and 47.3 ° squint

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 48 out of 55 University of Siegen Simulation results with NLCS processing Accurate compression Registration to ground plane

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 49 out of 55 University of Siegen NLCS (Stationary Receiver) D F’ E’ –Data is inherently azimuth-variant –Targets D E’ F’ lie on the same range gate but have different FM rates –Point E’ and Point F’ have the same closest range of approach and the same FM rate but different from Point D

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 50 out of 55 University of Siegen FM Rate Equalization (stationary receiver case) – quartic perturbation function Azimuth Phase F’ D E’ D F’ Stationary Receiver Azimuth Range DE’ F’

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 51 out of 55 University of Siegen Simulation Experiment S-band Transmitter at broadside Range resolution of 2.1m and azimuth resolution of 1.4m Unequal velocities Vt = 200 m/s Vr = 0 m/s

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 52 out of 55 University of Siegen Simulation results with NLCS processing Focused Image Registration to Ground plane

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 53 out of 55 University of Siegen Agenda Bistatic SAR processing A Review Of Processing Algorithms Point Target Spectrum Relationship Between Spectra Bistatic Range Doppler Algorithm Non Linear Chirp Scaling Algorithm Conclusions

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 54 out of 55 University of Siegen Conclusions Reviewed Several Bistatic Algorithms Derived Point target Spectrum (MSR) Linked LBF, DMO and MSR Developed Bistatic RDA Developed NLCS for non parallel case and stationary receiver

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 55 out of 55 University of Siegen Das Ende Danke!

T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A 56 out of 55 University of Siegen POSP