MA estimation in polynomial time

摘要: The parameter estimation of moving-average (MA) signals from second-order statistics was deemed for a long time to be difficult nonlinear problem which no computationally convenient and reliable solution possible. We show how the MA sample covariances can formulated as semidefinite program that solved in is polynomial function order. Two methods are proposed rely on two specific (over) parametrizations covariance sequence, whose use makes minimization fitting criterion convex problem. algorithms here fast, statistically accurate, reliable. None previously available (methods based higher-order included) shares all these desirable properties. Our also used obtain optimal least squares approximant an invalid (estimated) spectrum (that takes negative values at some frequencies), another long-standing signal processing literature awaiting satisfactory solution.