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Identification of linear systems with input and output noise: the Koopmans-Levin method. (English) Zbl 0554.93071
The Koopmans-Levin (KL) method [see M. J. Levin, IEEE Trans. Autom. Control AC-9, 229-235 (1964) and T. Koopmans ”Linear regression analysis of economic time series”, The Netherlands (1937)] of parameter estimation of discrete-time linear systems with input and output noise is based on the special 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.

MSC:
93E12 Identification in stochastic control theory
93C05 Linear systems in control theory
93E25 Computational methods in stochastic control (MSC2010)
62L12 Sequential estimation
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
93C55 Discrete-time control/observation systems
93E10 Estimation and detection in stochastic control theory
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