Research On The Maximum Likelihood Identification Method Of Hammerstein Model

This paper introduces the purpose and significance of nonlinear systems identification, outlines in detail the Hammerstein model which occupy an important position in the field of nonlinear identification. Hammerstein model is a kind of modular nonlinear system model, which is composed of a static nonlinear sub-module and a dynamic linear sub-module in series,to describe the nonlinear characteristics of the system. Since the model has a structurally simple mathematical model, it could effectively describe the actual characteristics of the controlled system, and easy realization of on-line identification. Therefore, the model has became a research hotspots for experts and scholars in domestic and overseas, and have been applied to lots of fields in practical engineering.As we all know, the theory and methods of research to identify univariate Hammerstein model is relatively mature, the paper focused on multivariable Hammerstein model to study the Hammerstein system identification method based on maximum likelihood identification method performed. It based on the maximum likelihood principle, this paper proposes some different identification methods to multivariable Hammerstein models which are also based on maximum likelihood method, and the simulation experiment is carried out by Matlab simulation software. The main contents of this paper are as follows:1. Describe the Hammerstein model and its mathematical description, the main contents and basic steps of the model identification, and lists the two commonly used models, namely, equation error model and output error model.2. Introduce the principle and the identification steps of the maximum likelihood identification algorithm, and the maximum likelihood parameter estimation is carried out by using the controlled autoregressive model as a simulation example.3. Based on maximum likelihood identification algorithm, propose recursive maximum likelihood least squares identification method of multivariable Hammerstein model to identify multivariable Hammerstein controlled moving average model(CMA Hammerstein model) and multivariate Hammerstein output error moving average model(for Hammerstein OEMA model) which are under colored noise.4. Make the Matlab simulation, and the simulation results show that the approach taken in this paper effectively solves the multivariate Hammerstein model online identification of high dimension, large amount of calculation and difficult to calculate the parameters of the problem.