Robust Burg Estimation of Radar Scatter Matrix for Mixtures of Gaussian Stationary Autoregressive Vectors

We address the estimation of the scatter matrix of a scale mixture of Gaussian stationary autoregressive vectors. This is equivalent to consider the estimation of a structured scatter matrix of a Spherically Invariant Random Vector (SIRV) whose structure comes from an autoregressive modelization. The Toeplitz structure representative of stationary models is a particular case for the class of structures we consider. For Gaussian autoregressive processes, Burg methods are often used in case of stationarity for their efficiency when few samples are available. Unfortunately, if we directly apply these methods to estimate the common scatter matrix of N vectors coming from a non-Gaussian distribution, their efficiency will strongly decrease. We propose then to adapt these methods to scale mixtures of autoregressive vectors by changing the energy functional minimized in the Burg algorithm. Moreover, we study several approaches of robust modification of the introduced Burg algorithms in presence of outliers or contaminating distributions. The considered structured modelization is motivated by radar applications, our methods will then be illustrated through radar simulated scenarios.