Finite dimensional smoothers for MAP state estimation of bilinear systems

In this paper, we present two finite-dimensional iterative algorithms for m aximum a posteriori (MAP) state sequence estimation of bilinear systems, Bi linear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. Our iterative algorithms for state estima tion are based on the expectation-maximization (EM) algorithm and outperfor m the widely used extended Kalman smoother (EKS), Unlike the EKS, these EM algorithms are optimal (in the MAP sense) finite-dimensional solutions to t he state sequence estimation problem for bilinear models. We also present r ecursive (on-line) versions of the two algorithms and show that they outper form the extended Kalman filter (EKF), Our main conclusion is that the EM-b ased algorithms presented in this paper are novel nonlinear filtering metho ds that perform better than traditional methods such as the EKF.