Identification of linear systems with input and output noise: the Koopmans-Levin method

The Koopmans-Levin (KL) method of parameter estimation of discrete-time linear systems with input and output noise is based on the spectral decomposition of a covariance matrix, which gives approximately maximum likelihood estimates (MLE) if the noise is white Gaussian. In the paper, three robust algorithms, namely the batch method, the sequential updating of the batch solution and the sequential square-root estimation using an information matrix, are developed, based on the singular-value decomposition of matrices. Coding of these algorithms is relatively straightforward using matrix routines available in standard program libraries. The procedures and the properties of the methods are illustrated using published examples.