SAR based vibration estimation using discrete Fractional Fourier transform (DFRFT) analysis methods has gained attention in recent work on vibrometry. In the presence of significant clutter however, this estimation becomes challenging due to the presence of clutter induced peaks in the vibration spectra. In this paper, we incorporate rank reduction and filtering into a subspace DFRFT approach that results in significant peak enhancement along with an accompanying reduction in the associated mean square estimation errors when applied to simulated SAR and synthetic chirp data. The approach is further applied to vibration data gathered from a real GA-Lynx system and shown to produce a corresponding peak enhancement and clutter suppression in the vibration spectrum.

The recently developed improved spectrograms that use the discrete fractional fourier transform (DFrFT) are used to evaluate multiple vibration signatures that represent targets in synthetic aperture radar (SAR) data. Multiple ground target vibrations that introduce phase modulation in the SAR returned signals are examined using standard pre-processing of the return waveform signal followed by the application of the DFrFT. In this paper, we study the capabilities of these spectrogram tools with the intent of extending their limits by varying the characteristic features associated with each vibrating target which result in different outputs. The performance of the fractional spectrogram tools, under the effects of various parameters is used to clarify the limitations and advantages of these modified fractional spectrograms for SAR-based vibrometry applications.

A fundamental assumption when applying Synthetic Aperture Radar (SAR) to a ground scene is that all targets are motionless. If a target is not stationary, but instead vibrating in the scene, it will introduce a non-stationary phase modulation, termed the micro-Doppler effect, into the returned SAR signals. Previously, the authors proposed a pseudosubspace method, a modification to the Discrete Fractional Fourier Transform (DFRFT), which demonstrated success for estimating the instantaneous accelerations of vibrating objects. However, this method may not yield reliable results when clutter in the SAR image is strong. Simulations and experimental results have shown that the DFRFT method can yield reliable results when the signal-to-clutter ratio (SCR) > 8 dB. Here, we provide the capability to determine a target's frequency and amplitude in a low SCR environment by presenting two methods that can perform vibration estimations when SCR < 3 dB. The first method is a variation and continuation of the subspace approach proposed previously in conjunction with the DFRFT. In the second method, we employ the dual-beam SAR collection architecture combined with the extended Kalman filter (EKF) to extract information from the returned SAR signals about the vibrating target. We also show the potential for extending this SAR-based capability to remotely detect and classify objects housed inside buildings or other cover based on knowing the location of vibrations as well as the vibration histories of the vibrating structures that house the vibrating objects.