Polynomial MMSE Deconvolution and its Duality with LQGR
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. Its duality with the polynomial equations for LQG regulation (LQGR) is discussed.
KeywordsPolynomial Matrix Diophantine Equation Polynomial Solution Kalman Gain Polynomial Matrice
Unable to display preview. Download preview PDF.
- Ahlen A. and M. Sternad (1989). Optimal deconvolution based on polynomial methods. IEEE Trans. Acoust., Speech, Signal Processing, 37, 217–226.Google Scholar
- Mendel J. (1983). Optimal seismic deconvolution, Academic Press, New York.Google Scholar
- Chisci L. and E. Mosca (1991). Polynomial equations for the MMSE state estimation. IEEE Trans. Aui. Control, to appear.Google Scholar
- Kucera V. (1979). Discrete Linear Control, J. Wiley, Chichester.Google Scholar
- Chisci L and E. Mosca (1991). Polynomial approach to MMSE multichannel deconvolution. Tech. Rep. DSI 17/91, DSI, Universitâ, di Firenze, Firenze, Italy.Google Scholar