Stochastic EM algorithm for nonlinear state estimation with model uncertainties

Amin Zia; Thiagalingam Kirubarajan; James P. Reilly; Shahram Shirani

doi:10.1117/12.506603

5 January 2004 Stochastic EM algorithm for nonlinear state estimation with model uncertainties

Amin Zia, Thiagalingam Kirubarajan, James P. Reilly, Shahram Shirani

Proceedings Volume 5204, Signal and Data Processing of Small Targets 2003; (2004) https://doi.org/10.1117/12.506603
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

In most solutions to state estimation problems like, for example, target tracking, it is generally assumed that the state evolution and measurement models are known a priori. The model parameters include process and measurement matrices or functions as well as the corresponding noise statistics. However, there are situations where the model parameters are not known a priori or are known only partially (i.e., with some uncertainty). Moreover, there are situations where the measurement is biased. In these scenarios, standard estimation algorithms like the Kalman ﬁlter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the problem with uncertain model parameters is considered as a special case of maximum likelihood estimation with incomplete-data, for which a standard solution called the expectation-maximization (EM) algorithm exists. In this paper a new extension to the EM algorithm is proposed to solve the more general problem of joint state estimation and model parameter identiﬁcation for nonlinear systems with possibly non-Gaussian noise. In the expectation (E) step, it is shown that the best variational distribution over the state variables is the conditional posterior distribution of states given all the available measurements and inputs. Therefore, a particular type of particle filter is used to estimate and update the posterior distribution. In the maximization (M) step the nonlinear measurement process parameters are approximated using a nonlinear regression method for adjusting the parameters of a mixture of Gaussians (MofG). The proposed algorithm is used to solve a nonlinear bearing-only tracking problem similar to the one reported recently with uncertain measurement process. It is shown that the algorithm is capable of accurately tracking the state vector while identifying the unknown measurement dynamics. Simulation results show the advantages of the new technique over standard algorithms like the EKF whose performance degrades rapidly in the presence of uncertain models.

Citation Download Citation

Amin Zia, Thiagalingam Kirubarajan, James P. Reilly, and Shahram Shirani "Stochastic EM algorithm for nonlinear state estimation with model uncertainties", Proc. SPIE 5204, Signal and Data Processing of Small Targets 2003, (5 January 2004); https://doi.org/10.1117/12.506603

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