A CONVEX-OPTIMIZATION APPROACH TO THE RATIONAL COVARIANCE EXTENSION PROBLEM

In this paper we present a convex optimization problem for solving the rational covariance extension problem. Given a partial covariance seq uence and the desired zeros of the modeling filter, the poles are uniq uely determined from the unique minimum of the corresponding optimizat ion problem. In this way we obtain an algorithm for solving the covari ance extension problem, as well as a constructive proof of Georgiou's seminal existence result and his conjecture, a stronger version of whi ch we have resolved in [Byrnes et al., IEEE Trans. Automat. Control, A C-40 (1995), pp. 1841-1857].