On the equivalence of the extended Kalman smoother and the expectation maximisation algorithm for polynomial signal models

TitleOn the equivalence of the extended Kalman smoother and the expectation maximisation algorithm for polynomial signal models
Publication TypeConference Paper
Year of Publication1999
AuthorsJohnston, L. A., and V. Krishnamurthy
Conference NameInformation, Decision and Control, 1999. IDC 99. Proceedings. 1999
Pagination303 -308
Keywordsapproximate conditional mean state estimates, discrete time cubic sensor problem, expectation maximisation algorithm, extended Kalman smoother, Kalman filters, maximum a posteriori state sequence estimator, nonlinear signal models, polynomial dynamics, polynomial signal models, polynomials, SAGE algorithm, smoothing methods, state estimation
Abstract

The iterated extended Kalman smoother (IEKS) is shown to be equivalent to one iteration of the expectation maximisation (EM)-based SAGE algorithm for the class of nonlinear signal models containing polynomial dynamics. Thus the IEKS is a maximum a posteriori (MAP) state sequence estimator for this class of systems. The iterated extended Kalman filter (IEKF) can be thought of as a heuristic, online version of a SAGE algorithm, derived via EM formalism rather than via linearisation around approximate conditional mean state estimates. We apply the polynomial SAGE algorithm to the discrete time, cubic sensor problem and show that it outperforms the standard extended Kalman smoother

URLhttp://dx.doi.org/10.1109/IDC.1999.754174
DOI10.1109/IDC.1999.754174

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