EM Algorithm for State-space Identification with Observation Outliers

An Initialization by Subspace Methods

Abstract

This paper considers an improvement of estimates of a state space model obtained by subspace system identification methods via the EM algorithm in the presence of observation outliers. To initialize the EM algorithm the initial estimates are obtained by two subspace identification methods : MOESP [1] and ORT [2]. The E- and M-steps in the EM algorithm are calculated when outliers are detected, by computing the conditional expectation under the assumption that the output data is incompletely observed. The outliers are detected and deleted in the EM algorithm by a simple scheme in robust statistics by using the median of the residuals, which are defined as the difference between the observed outputs and the estimated outputs computed from the initial estimates by subspace methods. Numerical examples show that the EM algorithm can monotonically improve the initial estimates obtained by subspace identification methods.