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

• Published in: IEEE transactions on signal processing Vol. 49; no. 9; pp. 1899 - 1909
• Main Authors: Johnston, L.A., Krishnamurthy, V.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2001; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Approximation algorithms; Computer simulation; Convergence; Derivation; Detection, estimation, filtering, equalization, prediction; Displays; Exact sciences and technology; Formalism; Frequency; Gaussian processes; Information, signal and communications theory; Kalman filters; Mathematical models; Maximization; Numerical simulation; Parameter estimation; Signal and communications theory; Signal processing algorithms; Signal, noise; Smoothing methods; Telecommunications and information theory; Tracking; Performance evaluation; Non linear process; Simulation; Smoothing; Kalman filter; Signal estimation; Signal processing; Iterative method; EM algorithm
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.942619

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.