Median burg robust spectral estimation for inhomogeneous and stationary segments

In order to estimate parameters of Gaussian autoregressive processes, Burg method is often used in case of stationarity for its efficiency when few samples are available. We are interested in the case when multiple inhomogeneous (not necessarily Gaussian) segments of time series are available. We then study robust modification of Burg algorithms, especially based on Frechet medians defined for the Euclidean or the Poincare metric, to estimate the parameters of autoregressive processes in presence of outliers and/or contaminating distributions. Moreover, we will show that the introduced estimators are robust with respect to the power distribution of the time series. The considered modelization is motivated by radar applications, the performances of our methods will then be compared to the very popular Fixed Point and OS-CFAR estimators through radar simulated scenarios.