Stochastic algorithms for computing p-means of probability measures, geometry of radar Toeplitz covariance matrices and applications to HR Doppler processing

A new geometric approach for HR Doppler processing is developed, which is based on the notion of Riemannian p-means and the information geometry of radar Toeplitz covariance matrices. First of all, we give the definition of Riemannian p-means and a simple stochastic algorithm to compute it. We show the almost sure convergence of this algorithm and give some simulation examples. Under a further regularity condition, the rate of convergence is given by a central limit theorem. After that, we give a short introduction to the Riemannian geometry of radar Toeplitz covariance matrices. Finally, some simulation examples are given to illustrate the performance of this new method.