Robust Burg estimation of radar scatter matrix for autoregressive structured SIRV based on Fréchet medians

The authors address the estimation of the scatter matrix of a scale mixture of Gaussian stationary autoregressive (AR) vectors. This is equivalent to consider the estimation of a structured scatter matrix of a spherically invariant random vector whose structure comes from an AR modelisation. The Toeplitz structure representative of stationary models is a particular case for the class of structures they consider. For Gaussian AR processes, Burg method is often used in case of stationarity for its efficiency when few samples are available. Unfortunately, if they directly apply these methods to estimate the common scatter matrix of N vectors coming from a non‐Gaussian distribution, their efficiency will strongly decrease. They propose then to adapt these methods to scale mixtures of AR vectors by changing the energy functional minimised in the Burg algorithm. Moreover, they study several approaches of robust modification of the introduced Burg algorithms, based on Fréchet medians defined for the Euclidean or the Poincaré metric, in presence of outliers or contaminating distributions. The considered structured modelisation is motivated by radar applications, the performances of their methods will then be compared with the very popular fixed point (FP) estimator and OS‐CFAR detector through radar simulated scenarios.