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Finite dimensional smoothers for MAP state estimation of bilinear systems

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2 Author(s)
Johnston, L.A. ; Dept. of Electr. & Electron. Eng., Melbourne Univ., Parkville, Vic., Australia ; Krishnamurthy, V.

In this paper, we present two finite-dimensional iterative algorithms for maximum a posteriori (MAP) state sequence estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. Our iterative algorithms for state estimation are based on the expectation-maximization (EM) algorithm and outperform the widely used extended Kalman smoother (EKS). Unlike the EKS, these EM algorithms are optimal (in the MAP sense) finite-dimensional solutions to the state sequence estimation problem for bilinear models. We also present recursive (on-line) versions of the two algorithms and show that they outperform the extended Kalman filter (EKF). Our main conclusion is that the EM-based algorithms presented in this paper are novel nonlinear filtering methods that perform better than traditional methods such as the EKF

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Signal Processing, IEEE Transactions on  (Volume:47 ,  Issue: 9 )