Radar detection for non-stationary time-Doppler signal based on Fréchet distance of geodesic curves on covariance matrix information geometry manifold

New challenge in Radar is the processing of non-stationary signal corresponding to fast time variation of Doppler Spectrum in one burst. We can observe this phenomenon for high speed or abrupt Doppler variations of clutter or target signal but also in case of target migration during the burst duration due to high range resolution. We will assume that each non-stationary target signal in one burst can be split into several short signals with less Doppler resolution but stationary, represented by time sequence of stationary covariance matrices or a geodesic polygon on covariance matrix manifold. For micro-Doppler analysis of these cases, we adapt the Fréchet distance between two curves in the plane with a natural extension to more general geodesic curves in abstract metric spaces used for covariance matrix manifold. This new approach could be used for robust detection of target with non-stationary Time-Doppler spectrum (NS-OS-HDR-CFAR: Non-Stationary Ordered Statistic High Doppler Resolution CFAR), False Alarm filtering for inhomogeneous clutter (statistics of plots Time-Doppler fluctuation), but also emerging civil applications like wind-shear, micro-burst, downdraft and wake-vortex detection.