Gordon Davidson

A chirp scaling approach for processing squint mode SAR data

Image formation from squint mode synthetic aperture radar (SAR) is limited by image degradations caused by neglecting the range-variant filtering required by secondary range compression (SRC). Introduced here is a nonlinear FM chirp scaling, an extension of the chirp scaling algorithm, as an efficient and accurate approach to range variant SRC. Two methods of implementing the approach are described. The nonlinear FM filtering method is more accurate but adds a filtering step to the chirp scaling algorithm, although the extra computation is less than that of a time domain residual compression filter. The nonlinear FM pulse method consists of changing the phase modulation of the transmitted pulse, thus avoiding an increase in computation. Simulations show both methods significantly improve resolution width and sidelobe level, compared with existing SAR processors for squint angles above 10 deg for L-band and 20 deg for C-band.

Signal properties of spaceborne squint-mode SAR

This paper presents signal properties of spaceborne, strip-map SAR for very large squint angles. Doppler centroid, azimuth bandwidth, and exposure time are derived in terms of the platform attitude and elevation angle. This allows a description of the Doppler centroid variation with range and terrain height, and explains a possible range dependence of azimuth bandwidth at high squint. The yaw and pitch required to minimize Doppler centroid and azimuth bandwidth variation are derived, and residual Doppler centroid variation in the presence of antenna pointing errors is presented. The SAR constraint on the relationship between swath width and azimuth bandwidth is revisited for high squint, and is used to present a fundamental limit on squint angle. Finally, processing considerations arising from the shape of the two-dimensional (2D) spectrum with high squint are discussed.

Multiresolution phase unwrapping for SAR interferometry

An approach to two-dimensional (2D) phase unwrapping for synthetic aperture radar (SAR) interferometry is presented, based on separate steps of coarse phase and fine phase estimation. A technique called adaptive multiresolution is introduced for local fringe frequency estimation, in which difference frequencies between resolution levels are estimated and summed such that a sufficiently conservative phase gradient field is maintained. A coarse unwrapped phase of the full terrain height is then constructed using weighted least-squares based on coherence weighting. This coarse phase is used in a novel approach to slope-adaptive spectral shift filtering and to reduce the phase variation of the interferogram. The resulting interferogram can be more accurately multilooked and unwrapped with any algorithm. In this paper, fine phase construction is done with weighted least-squares and with weights determined by simple morphological operations on residues. The approach is verified on a simulated complex interferogram and real SAR data.

Noise-induced slope distortion in 2-D phase unwrapping by linear estimators with application to SAR interferometry

This paper explains the underestimation of phase slope and the consequent distortion of the phase surface, observed in two-dimensional (2-D) phase unwrapping by linear estimators, like least squares methods applied to synthetic aperture radar (SAR) interferometry. These methods minimize the difference between the gradient of the unwrapped phase and the wrapped differences of the measured wrapped phase. Using the probability distributions of phase noise and phase differences for a given coherence, the probability of a phase gradient error giving rise to a nonconservative vector field is derived. It is shown that this phase gradient error has nonzero mean in the presence of phase slopes. Linear phase estimators cannot distinguish the mean phase gradient error from a true phase slope; hence, the unwrapped phase shows a slope bias. This bias is quantified as a function of coherence and the number of independent samples that are averaged. The theoretical results are confirmed by simulations.

A multiresolution approach to improve phase unwrapping

A method is presented for robust phase unwrapping based on instantaneous frequency estimation at multiple resolutions. Estimation is done of the frequency difference between resolution levels, resulting in asymptotically zero bias in the aliasing error. The frequency for the highest resolution level is found by the sum of difference frequencies, and the final frequency estimates are input to a least squares phase reconstruction algorithm. A hierarchical algorithm for frequency estimation at all resolution levels, based on the correlation Doppler centroid estimator, is derived. Also, an adaptive multiresolution approach is presented, in which the highest resolution level required for a frequency estimate without aliasing and thus a smooth phase reconstruction, is determined at each point. The method is investigated by simulations, and results show successful phase unwrapping without slope bias, even in the presence of undersampling and low coherence.

Multiresolution signal representation for phase unwrapping and interferometric SAR processing

Phase unwrapping requires-implicitly or explicitly-phase gradient estimates for phase reconstruction. An asymptotically unbiased local frequency estimator based on multiresolution signal representation is presented. The proposed estimator is able to automatically trade-off resolution against estimation error. It is shown that interferometric SAR processing can be improved by employing a smoothed version of the unwrapped phase. Particularly, a novel method for slope-adaptive spectral shift filtering is introduced.

An approach for improved processing in squint mode SAR

Processing SAR signal data into an image requires correlation with a range-variant focussing operator. Current SAR processing algorithms make approximations to the exact focussing operator, which causes a noticeable degradation in image quality when the squint angle is large. The difficulty arises from higher order phase terms in the operator known as secondary range compression (SRC). While recent approaches to high squint SAR processing allow accurate focussing for points at a fixed slant range, the range-variance of SRC has remained a problem. The approach presented in this paper is based on the chirp scaling technique, and accommodates the range-variance of SRC by modifying the phase modulation of the transmitted pulse.<<ETX>>

The effect of pulse phase errors on the chirp scaling SAR processing algorithm

The chirp scaling (CS) SAR processing algorithm uses the linear FM property of the transmitted pulses to provide accurate range cell migration correction. However, when the transmitted pulse is not linear FM, or if the FM rate is not known exactly, processing errors due to chirp scaling will result. This paper presents the resulting processing error in the CS algorithm, given pulse phase errors that exceed those expected in SAR systems. The registration and phase error that result in chirp scaling are negligible for typical or stable pulse phase errors, or can be avoided if phase modulation coefficients are estimated from the replica. A fast Fourier transformed pulse replica is sufficient to form the range matched filter in the CS algorithm, giving slightly better range resolution than the range/Doppler (R/D) algorithm.

Nature of noise in 2D phase unwrapping

This paper reviews the concept of noise in 2D phase unwrapping of SAR interferograms. It is shown that phase gradient estimates derived as wrapped phase differences of adjacent samples are biased, leading to an underestimation of phase slopes. Hence, linear estimators like least squares methods operating on such gradient estimates tend to globally distort the reconstructed terrain. The slope bias is quantified as a function of coherence and number of looks both theoretically and via simulations. The particular type of noise under discussion also may lead to impulse-like errors in the phase unwrapped by a linear method. In order to avoid these errors the support of reconstruction must be restricted in the same way as with so-called branch-cut methods.

Robust 2D phase unwrapping based on multiresolution

An approach to 2D phase unwrapping for SAR interferometry is presented, based on separate steps of coarse phase and fine phase estimation. The coarse phase is constructed from instantaneous frequency estimates obtained using adaptive multiresolution, in which estimation is done of difference frequencies between resolution levels, and the frequency differences are summed over resolution levels such that a conservative phase gradient field is maintained. This allows a smoothed coarse unwrapped phase, which achieves the full terrain height, to be obtained with an unweighted least squares phase construction. The coarse phase is used to remove the bulk of the phase variation of the interferogram, allowing more accurate multilooking, and the resulting fine phase in unwrapped with weighted least squares. The unwrapping approach is verified on simulated interferograms.