Multivariate spectral reconstruction of stap covariance matrices: Toeplitz-block solution

In space-time adaptive processing (STAP) applications, temporally stationary clutter results in a Toeplitz-block clutter covariance matrix. In the reduced-order parametric matched filter STAP technique, this covariance matrix is reconstructed from a small number of estimated parameters, resulting in a much more efficient use of training samples. This paper and a companion one [1] addresses the issue of STAP filter performance from covariance matrices reconstructed with a strict adherence to the Toeplitz-block structure versus a ldquorelaxedrdquo reconstruction which employs a maximum entropy completion criteria, but does not enforce a strict Toeplitz-block structure on that completion. Both techniques analyzed use a multivariate spectral reconstruction approach which preserve the Burg spectrum. In this paper, the reconstruction is constrained to result in a Toeplitz-block covariance matrix model, and the solution requires positive definite matrix-valued stable polynomial factorization that can be derived via the multivariate Levinson algorithm. Performance of the reconstructed covariance matrix model as a STAP filter is evaluated using the DARPA KASSPER dataset in the companion paper.