Parameter Estimation Using Unscented Smoother and EM Algorithm

Abstract

This paper describes a new method for parameter estimation of dynamical systems expressed by nonlinear state and observation equations. The developed method employs the Unscented Rauch-Tung-Striebel Smoother (URTSS), which estimates the state and unknown parameters, combined with Expectation-Maximization (EM) algorithm to estimate the unknown statistics, i.e., the mean and covariance of the initial state, and the noise covariances. In order to approximate the expectation values with a reasonable number of sample points, the unscented transform based on the estimation results of URTSS is employed. Moreover, it is possible to calculate analytical solutions of the unknown statistics at each maximization step, and hence the developed method circumvents the use of non-convex numerical optimization software. Effectiveness of the developed method is confirmed by using an example.