Polynomial MMSE Deconvolution and its Duality with LQGR

  • L. Chisci
  • E. Mosca
Part of the Progress in Systems and Control Theory book series (PSCT, volume 12)


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.


Polynomial Matrix Diophantine Equation Polynomial Solution Kalman Gain Polynomial Matrice 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • L. Chisci
    • 1
  • E. Mosca
    • 1
  1. 1.Dipartimento di Sistemi e InformaticaUniversitá. di FirenzeFirenzeItaly

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