Vibration-Induced Micro-Doppler Estimation in Spaceborne SAR Images Using Doppler Centroid Tracking Across Azimuth Sub-Apertures

This paper introduces a workflow for vibrationinduced micro-Doppler estimation in spaceborne SAR images for infrastructure monitoring. The processing begins by dividing a complex SAR image into azimuth sub-aperture images with partially overlapping Doppler spectra. A fast correlation-based Doppler estimator is applied on a sliding boxcar window to each sub-aperture image, producing a time series of Doppler Centroid (DC) images, where each pixel represents the instantaneous frequency of the target. The vibration frequencies of targets are estimated by analyzing the time series of DC images. Subsequently, a Fourier transform along the sub-apertures dimension provides the vibration spectrum for each pixel. The vibration spectrum usually exhibits distinct frequencies, and pixels corresponding to vibrating targets are identified by assessing the sparsity of the spectrum using the complementary normalized entropy. The vibration frequencies are then extracted by selecting the most significant peak on the amplitude spectrum. The frequency estimates are validated on real data acquired over a bridge and a water tower from Basilicata region, Italy, by comparing them with in situ measurements obtained from a ground-based Kuband radar, which estimates vibrations based on time-range maps of line-of-sight displacements.