Finite dimensional smoothers for MAP state estimation of bilinear systems

TitleFinite dimensional smoothers for MAP state estimation of bilinear systems
Publication TypeJournal Article
Year of Publication1999
AuthorsJohnston, L. A., and V. Krishnamurthy
JournalSignal Processing, IEEE Transactions on
Pagination2444 -2459
Date Publishedsep.
Keywordsbilinear systems, EM algorithm, expectation-maximization algorithm, finite dimensional smoothers, finite-dimensional iterative algorithms, iterative methods, MAP state estimation, maximum a posteriori state sequence estimation, maximum likelihood sequence estimation, nonlinear filtering, nonlinear filters, nonlinear systems, optimal finite-dimensional solutions, recursive versions, smoothing methods, state estimation, state sequence estimation

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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