NMSE DECONVOLUTION VIA POLYNOMIAL METHODS AND ITS DUAL LQG REGULATION

The problem of linear minimum mean-square error (MMSE) multichannel de convolution of sampled signals from noisy observations is approached v ia 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 opti mality of the deconvolution filter whereas the second ensures stabilit y of the filter, should the signal model be unstable. The proposed sol ution encompasses classical Wiener as well as stationary Kalman filter ing, prediction and fixed-lag smoothing. The duality with the polynomi al equations for LQG regulation is also discussed.