Least squares-based identification methods for a class of multivariable systems with autoregressive noises

This paper focuses on the identification of a class of multivariable systems with autoregressive noises. Two least squares-based algorithms are provided. One is the recursive generalized least squares algorithm. The idea is to integrate the colored noise regression terms into the information matrix and the noise parameters into the parameter vector, respectively, using the Kronecker product, and then to identify the parameter vector. The unknown terms in the integrated information matrix are replaced with their estimates. The other is the filtering-based recursive least squares algorithm. The idea is to transfer the system with a colored noise into a system with a white noise by filtering the input-output data with a specific filter, and then to identify the filtered model and the noise model interactively to obtain the parameter estimates. The filter is selected according the noise model structure. A simulation example is given to illustrate the effectiveness and the performances of the two proposed algorithms.