MA estimation in polynomial time

The parameter estimation of moving-average (MA) signals from second-order s tatistics was deemed for a long time to be a difficult nonlinear problem fo r which no computationally convenient and reliable solution was possible. L n this paper, we show how the problem of MA parameter estimation from sampl e covariances can be formulated as a semidefinite program that can be solve d in a time that is a polynomial function of the MA order. Two methods are proposed that rely on two specific (over)parametrizations of the MA covaria nce sequence, whose use makes the minimization of a covariance fitting crit erion a convex problem. The MW estimation algorithms proposed here are comp utationally fast, statistically accurate, and reliable. None of the previou sly available algorithms for MA estimation (methods based on higher-order s tatistics included) shares all these desirable properties. Our methods can also be used to obtain the optimal least squares approximant of an invalid (estimated) MA spectrum (that takes on negative values at some frequencies) , which was another long-standing problem in the signal processing literatu re awaiting a satisfactory solution.