Derivation of a sawtooth iterated extended Kalman smoother via the AECM algorithm

TitleDerivation of a sawtooth iterated extended Kalman smoother via the AECM algorithm
Publication TypeJournal Article
Year of Publication2001
AuthorsJohnston, L. A., and V. Krishnamurthy
JournalSignal Processing, IEEE Transactions on
Pagination1899 -1909
Date Publishedsep.
KeywordsAECM algorithm, alternating expectation conditional maximization, EM algorithm, expectation-maximization algorithm, frequency tracking, iterated extended Kalman smoother, iterative methods, Kalman filters, nonlinear filters, nonlinear signal models, numerical simulations, optimisation, sawtooth iterated extended Kalman smoother, sequence estimate, sequential estimation, smoothing algorithms, smoothing methods, suboptimal extended Kalman filter, suboptimal extended Kalman smoother, tracking filters

The iterated extended Kalman smoother (IEKS) is derived under expectation-maximization (EM) algorithm formalism, providing insight into the behavior of the suboptimal extended Kalman filter (EKF) and smoother (EKS). Through an investigation of smoothing algorithms that result from variants of the EM algorithm, the sawtooth iterated extended Kalman smoother (SIEKS) and its computationally inexpensive counterparts are proposed via the alternating expectation conditional maximization (AECM) algorithm. The SIEKS is guaranteed to produce a sequence estimate that moves up the likelihood surface. Numerical simulations including frequency tracking examples display the superior performance of the sawtooth EKF over the standard EKF for a range of nonlinear signal models


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