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.

Synthetic-aperture radar (SAR) can be used to remotely estimate ground target vibrations by exploiting the Doppler in the returned signals. Recent studies suggest that timefrequency signal-processing tools can retrieve the vibration signature from the returned SAR signals. A vibration estimation method based on the fractional Fourier transform (FRFT) was reported earlier and it was tested on simulated SAR data. In this paper, a first-time demonstration of the FRFT-based vibration estimation method is reported using real SAR data collected by the Lynx (K u -band) SAR system. The vibrating target is an aluminum triangular trihedral with lateral length of 15 inches. The FRFT-based algorithm is shown to successfully retrieve a 3 mm peak-to-peak amplitude, 5 Hz vibration of the target from real SAR data.

Target vibrations introduce nonstationary phase modulation, which is termed the micro-Doppler effect, into returned synthetic aperture radar (SAR) signals. This causes artifacts, or ghost targets, which appear near vibrating targets in reconstructed SAR images. Recently, a vibration estimation method based on the discrete fractional Fourier transform (DFrFT) has been developed. This method is capable of estimating the instantaneous vibration accelerations and vibration frequencies. In this paper, a deghosting method for vibrating targets in SAR images is proposed. For single-component vibrations, this method first exploits the estimation results provided by the DFrFT-based vibration estimation method to reconstruct the instantaneous vibration displacements. A reference signal, whose phase is modulated by the estimated vibration displacements, is then synthesized to compensate for the vibration-induced phase modulation in returned SAR signals before forming the SAR image. The performance of the proposed method with respect to the signal-to-noise and signalto-clutter ratios is analyzed using simulations. Experimental results using the Lynx SAR system show a substantial reduction in ghosting caused by a 1.5-cm 0.8-Hz target vibration in a true SAR image.

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Recently, a time-frequency method based on the discrete fractional Fourier transform (DFrFT) was proposed for estimating target vibrations using synthetic aperture radar (SAR). Later on, a subspace method was incorporated into the DFrFT-based method. It is shown that the subspace method provides better performance than the direct DFrFT-based method in noise. However, the performance of these two methods has not been studied in clutter that cause strong interference with signals from vibrating targets in real-world applications. In this paper, the performance of the two vibration estimation methods in clutter is characterized and compared via simulations. Simulation results demonstrate that the DFrFT-based method, that yielded reliable results when signal-to-clutter ratios (SCR) exceeds 18 dB, now yields reliable results when SCR exceeds 8 dB with the incorporation of the subspace method. Experimental results show that the subspace method correctly estimates the vibration frequency of a 7 Hz vibration from actual SAR data at an estimated SCR of 14 dB.