Non-linear smoothers for discrete-time, finite-state Markov chains

The problem of enhancing the quality of system state estimates is considered for a special class of dynamical systems. Specifically, a system characterized by a discrete-time, finite-state Markov chain state and observed via conditionally Gaussian measurements is assumed. The associated mean vectors and covariance matrices are tightly intertwined with the system state and a control input selected by a controller. Exploiting an innovations approach, finite-dimensional, non-linear approximate MMSE smoothing estimators are derived for the Markov chain system state. The resulting smoothers are driven by a control policy determined by a stochastic dynamic programming algorithm, which minimizes the MSE filtering error, and was proposed in our earlier work. An application of the smoothers derived in this paper is presented for the problem of physical activity detection in wireless body sensing networks, which illustrates the performance enhancement due to smoothing.