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

Author

Johnston, Leigh A. ; Krishnamurthy, Vikram

Author_Institution

Centre for Syst. Eng. & Appl. Mech., Univ. Catholique de Louvain, Belgium

Volume

49

Issue

9

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

1899

Lastpage

1909

Abstract

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

Keywords

Kalman filters; iterative methods; nonlinear filters; optimisation; sequential estimation; smoothing methods; tracking filters; AECM algorithm; EM algorithm; alternating expectation conditional maximization; expectation-maximization algorithm; frequency tracking; iterated extended Kalman smoother; nonlinear signal models; numerical simulations; sawtooth iterated extended Kalman smoother; sequence estimate; smoothing algorithms; suboptimal extended Kalman filter; suboptimal extended Kalman smoother; Approximation algorithms; Convergence; Displays; Frequency; Gaussian processes; Kalman filters; Numerical simulation; Parameter estimation; Signal processing algorithms; Smoothing methods;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.942619

Filename

942619