Innovative tools for radar signal processing Based on Cartan’s geometry of SPD matrices & Information Geometry

Abstract

New operational requirements for stealth targets detection in dense & inhomogeneous clutter are emerging (littoral warfare, low altitude asymmetric threats, battlefield in urban area...). Classical radar approaches for Doppler & array signal processing have reached their limits. We propose new improvements based on advanced mathematical studies on geometry of SPD matrix (symmetric positive definite matrix) and information geometry, using that radar data covariance matrices include all information of the sensor signal. First, information geometry allows to take into account statistics of radar covariance matrix (by mean of Fisher information matrix used in Cramer-Rao bound) to built a robust distance, called Jensen, Siegel or Bruhat-Tits metric. Geometry on ldquosymmetric conesrdquo, developed in frameworks of Lie group and Jordan algebra, provides new algorithms to compute matrix geometric means that could be used for ldquomatrix CFARrdquo. This innovative approach avoids classical drawbacks of Doppler processing by filter banks or FFT in case of bursts with very few pulses.