Efficient Positivity Test Algorithms for Parametric and Nonparametric Sequences of Covariance Estimates

In statistical signal processing problems involving second-order information of data such as covariance estimation, spectral factorization, and optimal filtering, one often needs to test positivity of a real sequence obtained from the finite length of data as covariance estimates. In this correspondence, we present efficient time-domain algorithms for testing nonnegativity of real finite nonparametric and linearly parametric sequences as valid covariance estimates. For a parametric sequence, the algorithm searches entire parameter space to find a unique set of parameters for which the sequence is positive-definite. Examples show performance of the proposed algorithms versus direct use of DFT/FFT.