SAR-Based Vibration Estimation Using the Discrete Fractional Fourier Transform

Abstract

A vibration estimation method for synthetic aperture radar (SAR) is presented based on a novel application of the discrete fractional Fourier transform (DFRFT). Small vibrations of ground targets introduce phase modulation in the SAR returned signals. With standard preprocessing of the returned signals, followed by the application of the DFRFT, the time-varying accelerations, frequencies, and displacements associated with vibrating objects can be extracted by successively estimating the quasi-instantaneous chirp rate in the phase-modulated signal in each subaperture. The performance of the proposed method is investigated quantitatively, and the measurable vibration frequencies and displacements are determined. Simulation results show that the proposed method can successfully estimate a two-component vibration at practical signal-to-noise levels. Two airborne experiments were also conducted using the Lynx SAR system in conjunction with vibrating ground test targets. The experiments demonstrated the correct estimation of a 1-Hz vibration with an amplitude of 1.5 cm and a 5-Hz vibration with an amplitude of 1.5 mm.

Performance analysis on synthetic aperture radar-based vibration estimation in clutter

“…As a result, the instantaneous vibration accelerations are estimated and the vibration frequencies are estimated from the spectrum of estimated instantaneous accelerations. The reader may refer to [4] for more details.…”

“…In synthetic aperture radar (SAR), low-level target vibrations can be estimated by estimating the instantaneous vibration displacements (in range), ∆x, from [4] …”

“…The target vibration can be estimated through successive chirp-rate estimations using the discrete fractional Fourier transform (DFrFT), which is inherently geared toward chirprate estimation [3], [4], [5], [6], [7]. Later on, a subspace method was incorporated into the DFrFT-based method and it provides better performance than the direct DFrFT-based method in noise [8], [9].…”

Clutter suppression in synthetic aperture radar targets using the DFRFT and subspace methods with rank reduction

“…In recent years, the DFRFT [7], [8], [9], [6] has become a useful time-frequency tool for multiple chirp parameter estimatiolin [5] and in particular it has been successfully applied to the problem of vibration estimation using SAR [2], [3], [4]. Direct DFRFT based estimation of the vibration frequency involves application of the DFRFT to the target return signal, peak coordinate location and translation of the peak coordinates to center-frequency and chirp-rate estimates using the peak-to-parameter mapping.…”

“…(1). Prior work in [2], [3] did not incorporate rank-reduction and filtering of the subspace signals to remove clutter that manifests as high-frequency noise in the center-frequency and chirp-rate slices. Rank reduction employs correlation matrices that retain just the signal or noise subspace, thereby rejecting noise and clutter prevalent in the other subspaces [1].…”