Abstract
This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.
Highlights
The parameter estimation errors given by the recursive generalized extended least squares (RGELS), PC-subsystem recursive generalized extended least squares (S-RGELS) and PC-RGELS algorithms become smaller as s increasing
We have dealt with the parameter identification problems of the M-OEARMA-like systems
A partially-coupled recursive generalized extended least squares algorithm is presented based on the hierarchical identification principle and the coupling identification concept
Summary
System identification is an important branch in the field of modern control and is an important method to establish systematic mathematical models from the combination of observation data and prior knowledge [1,2,3,4,5,6,7,8], and has been applied in many fields for decades, such as controller design [9,10,11,12,13,14,15]. Sudied the parameter estimation problems of multivariate output-error autoregressive systems and derived a filtering-based auxiliary model recursive generalized least squares algorithm based on the data filtering technique and the auxiliary model identification idea [64]. For multivariate output-error systems, Wang et al proposed a decomposition based recursive least squares identification algorithm by using the auxiliary model, and analyzed its convergence through the stochastic process theory [67]. Different from the methods in [67,68], this paper studies the parameter identification problems of multivariable output-error-like (M-OE-like) systems with colored noises which is described by the autoregressive moving average (ARMA) model by means of the decomposition technique and the coupling identification concept [69,70].
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