MMSE deconvolution via polynomial methods and its dual LQG regulation

Abstract

The problem of linear minimum mean-square error (MMSE) multichannel deconvolution of sampled signals from noisy observations is approached via matrix polynomial equations. The general solution is given in terms of a left spectral factorization and a pair of bilateral Diophantine equations. The first Diophantine equation is obtained by imposing optimality of the deconvolution filter whereas the second ensures stability of the filter, should the signal model be unstable. The proposed solution encompasses classical Wiener as well as stationary Kalman filtering, prediction and fixed-lag smoothing. The duality with the polynomial equations for LQG regulation is also discussed.