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Least-squares identification of a class of multivariable systems with correlated disturbances. (English) Zbl 0967.93093

The paper is devoted to the problem of parameter estimation of a multivariable system, given by a certain type of model representation with known structure. The main objective of the paper is to extend the recently proposed new version of the bias-eliminated least-squares method [C.-B. Feng and the author, IEE Proc., Part D 138, No. 5, 484-492 (1991; Zbl 0753.93078); the author, “Unbiased identification of multivariable systems subject to colored noise”, Proc. 33rd IEEE Conf. on Decision and Control (CDC’94), Vol. 3, Lake Buena Vista, FL, USA, 2864-2865 (1994)] to the identification of a class of multivariable stochastic systems, namely, multi-input-single-output systems corrupted by correlated noise. It is shown that the bias in least-square estimators can be eliminated if the cross-covariance vector between the disturbance acting on the multivariable system and the vector of lagged observed input-output data can be estimated exactly. A set of digital prefilters has been designed and connected to the identified multivariable system at the multi-input channels. Certain linear equality constraints, with respect to the system parameters, have been derived, by the use of artificially inserted known zeros in the identified system. The consistent parameter estimates are obtained on the base of the established relations, in conjunction with the bias-correction principle.
The main advantage of the developed method is that there is no need to model the process noise, so the method can work well without a description of the correlated noise dynamic. A batch and recursive approach is applied in the estimation procedure presented here. It has been shown that the developed identification algorithm is straightforward, efficient and promising. The paper could be of interest to all specialists and experts involved in multivariable systems parameter identification.

MSC:

93E12 Identification in stochastic control theory
93E24 Least squares and related methods for stochastic control systems

Citations:

Zbl 0753.93078
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References:

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