Parameter estimation of a target-directed dynamic system model with switching states

Abstract

In this paper, we describe an implementation of the extended Kalman filter (EKF) for joint state and parameter estimation for a target-directed, switching state-space nonlinear system model and compare its performance with a maximum-likelihood parameter estimation procedure based on the expectation–maximisation (EM) algorithm. The model parameters consist of the target one and the time-constant one. Simulation experimental results are presented for individual and joint estimation of all model parameters for both algorithms. The results show that both algorithms are able to converge to the true target parameter in the model, with the EKF algorithm exhibiting faster convergence. This is true even under the target-undershoot condition when the observation sequence is relatively short. However, convergence to the true time-constant parameter is not evident, possibly due to the non-unique nature of the parameter estimation problem. We also show empirically that in the case of joint estimation of the parameters, the EM algorithm diverges shortly after a small number of iterations whereas the EKF algorithm gives more desirable convergence properties.