A Robust Identification of a Linear System with Observation Outliers by the EM Algorithm

Abstract

An iterative identification method for a multivariable linear system with outliers in the observations is proposed by applying the EM (Expectation-Maximization) algorithm. The outliers are detected by a likelihood ratio test using residuals computed from the smoothed state estimates obtained in the previous iterations, while the parameter estimation is performed by treating outliers as missing data. As an example, we identify a simple COD model based on the real data of three points of the lower reaches of the Lake Biwa. We show that the accuracy of the model is greatly improved by introducing the probability p_j specifying the observation outliers. We also show that the algorithm can be applied when many data are missing.