Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection

Adaptive detection of signals embedded in Gaussian or non-Gaussian noise is a problem of primary concern among radar engineers. In this paper, we propose a recursive algorithm to estimate the structure of the covariance matrix of either a set of Gaussian vectors that share the spectral properties up to a multiplicative factor or a set of spherically invariant random vectors (SIRVs) with the same covariance matrix and possibly correlated texture components. We also assess the performance of an adaptive implementation of the normalized matched filter (NMF), relying on the newly introduced estimate, in the presence of compound-Gaussian, clutter-dominated, disturbance. In particular, it is shown that a proper initialization of the recursive procedure leads to an adaptive NMF with the constant false alarm rate (CFAR) property and that it is very effective to operate in heterogeneous environments of relevant practical interest.