Two-stage Recursive Identification For Multivariate Output-error Systems

Multivariate systems widely exist in many scientific and engineering fields.Different from scalar systems,multivariate systems have more complex structures which can describe both linear multivariable systems and nonlinear multivariable systems.Therefore,the identification of multivariate systems is an important branch of system identification.Based on the gradient search,the least squares search and the decomposition technique,this thesis focuses on the multivariate output-error system and researchs a series of recursive identification algorithms.The main works are as follows.1.To deal with the identification problem of the multivariate output-error moving average system,by converting the original model containing both the parameter vectors and the parameter matrices into a model containing one parameter vector,this thesis derives an auxiliary model recursive extended least squares identification algorithm and an auxiliary model extended stochastic gradient identification algorithm.Then by using decomposition techniques,the original model is decomposed into two sub-models for identification.One of them contains one parameter vector and the other contains several parameter matrices.A two-stage auxiliary model recursive extended least squares identification algorithm and a two-stage auxiliary model extended stochastic gradient identification algorithm are proposed for the purpose of reducing the computational load and enhancing the parameter estimation accuracy.2.For the identification problem of the multivariate output-error autoregressive moving average system,this thesis proposes an auxiliary model recursive generalized extended least squares identification algorithm and an auxiliary model generalized extended stochastic gradient identification algorithm.With the help of the decomposition technique,the original model is decomposed into a system model and a noise model for identification,and a two-stage auxiliary model recursive generalised extended least squares identification algorithm is obtained.Then,combining the decomposition technique with the filtering technique,a filtering-based two-stage auxiliary model extended stochastic gradient identification algorithm is derived in order to reduce the interference of the colored noise and enhance the identification accuracy.3.For the identification problem of the multivariate output-error autoregressive moving average system,in order to improve the utilization rate of the observed input-output data in the stochastic gradient identification algorithm,this thesis combines the multiinnovation identification theory with the stochastic gradient identification algorithm and expands the innovation to make full use of the input-output data.Then,a filtering-based two-stage auxiliary model multi-innovation extended stochastic gradient identification algorithm is proposed so as to further improve the identification accuracy of the filteringbased two-stage auxiliary model extended stochastic gradient identification algorithm.This thesis gives relevant calculation procedure of the above identification algorithms for multivariate output-error systems and shows the effectiveness of the proposed algorithms through some simulation examples.Finally,some conclusions are made.