Maximum Likelihood Recursive Identification Methods Based On The Information Filtering

Due to the interference of many factors in the process of industrial production,the identification of the system with colored noise becomes more and more difficult.By maximizing the likelihood function,this dissertation studies the parameter identification problem of a class of linear and nonlinear systems with colored noise based on the information filtering technique.Thus the research has theoretical significance and application prospects.The following results are obtained.(1)For the scalar equation error ARMA system,a maximum likelihood extended gradient algorithm is developed based on the information filtering technique;In order to improve the convergence speed of the gradient algorithm,the information filtering based maximum likelihood multi-innovation extended stochastic gradient algorithm is proposed by expanding the innovation length.In order to obtain high parameter estimation accuracy,a maximum likelihood extended least squares algorithm is proposed based on the information filtering.Furthermore,the derived algorithms are extended to the parameter estimation of the multivariable equation error ARMA systems and obtain good parameter estimation properties.(2)For the controlled autoregressive autoregressive moving average-like system,since the multivariable system has many variables and high dimension,decomposing the system into m(m is the dimension of the system output)subsystems,then using the information filtering technique to filter the input and output data for each subsystem,a information filtering based maximum likelihood extended gradient algorithm is developed for each subsystem.Compared with the maximum likelihood generalized extended gradient algorithm,the influence of the colored noise on parameter estimation is reduced,and the accuracy of parameter identification is improved.(3)For the multiple-input nonlinear Box-Jenkins system,in order to overcome its characteristics of nonlinearity and the interference of the colored noise,using the decomposition technique,a maximum likelihood generalized extended least squares algorithm is developed based on the decomposition technique.For the interference of the colored noise,select an appropriate filter to pre-process the system input and output data,combined with the maximum likelihood method,a maximum likelihood generalized extended gradient algorithm is proposed based on the information filtering for the aim of reducing the parameter estimation error.This dissertation verifies the effectiveness of each algorithm by giving numerical simulation examples.