Robust Identification and Smoothing for Linear System with Outliers and Missing Data

Abstract

An iterative identification method for a linear state-space model with outliers and /or missing data is proposed by applying the Expectation-Maximization (EM) algorithm . The EM algorithm yields a simple identification procedure to facilitate the maximum likelihood (ML) estimation for the state-space models. The missing data case is easily manipulated by the EM algorithm. The outliers arc treated as missing data, and the outliers are detected by maximum a posteriori (MAP) estimate of the occurrence of outlier which is modeled by a Bernoulli sequence, EM algorithm is also applied to the MAP estimation, The fixed-interval smoothed estimate of the state vector is simultaneously obtained, since it is used for the parameter identification, The presen: algorithm is applied to real data to show that the accuracy of the dynamic model is greatly improved by introducing the possibility that the observed data contains outliers.