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Optimal MAP estimation of bilinear systems via the EM algorithm

We present a finite dimensional iterative algorithm for optimal maximum a posteriori (MAP) state estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. We show that several bilinear models previously considered in the literature are special cases of the general bilinear model we propose. Our iterative algorithm for state estimation is based on the expectation-maximization (EM) algorithm and outperforms the widely used extended Kalman filter (EKF). Unlike the EKF our algorithm is an optimal (in the MAP sense) finite-dimensional solution to the state sequence estimation problem for bilinear models.