SAR vibrometry using the pseudo-subspace approach based on the discrete fractional Fourier transform
Qi Wang, Balu Santhanam, Matthew P. Pepin, Tom Atwood, Majeed M. Hayat · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
In synthetic-aperture radar (SAR), ground-target vibrations introduce a phase modulation in the returned signals, a phenomenon often referred to as the micro-Doppler effect. Earlier work has shown that the problem of estimating common ground-target vibrations can be transformed into the problem of successively estimating chirp parameters of the returned signal in properly sized subapertures. Recently, a method based on the discrete fractional Fourier transform (DFRFT) was proposed, in conjunction with the subaperture framework, to estimate target vibrations in the absence of noise. In this paper a pseudo-subspace approach is employed to extend the applicability of the DFRFT-based vibration-estimation method to signals that are corrupted by white noise. The new algorithm first calculates the inverse discrete Fourier transform of row and column projections of the magnitude of the DFRFT spectrum of the SAR returned signal to obtain two vectors. Next, covariance matrices are estimated from the sample covariance matrices of the two vectors. A pseudo-subspace approach is then applied to the covariance matrices to yield the pseudo-spectra. The chirp rate of the signal is estimated by finding the principle frequency component in the corresponding pseudo-spectrum. Monte-Carlo simulations demonstrate that the proposed method generally offers improved mean-square-error performance in the presence of noise compared to the direct DFRFT-based method.