A deconvolution technique based on nonlinear estimation of hidden Markov chains

A novel, suboptimal, nonlinear recursive algorithm for the estimation of filtered Markov chains from noisy observations is presented. The expression of the estimator is formally identical to the Kalman filter solution when the error covariance matrix is replaced by the conditional covariance matrix. Starting from the Martingale-difference (MD) representation theorem, a recursive expression for the conditional covariance matrix that can be reasonably approximated by means of the Markov property is derived. Thus the obtained estimator is suboptimal in the sense that the conditional covariance matrix is evaluated only approximately