Weighted Recursive Least Squares Identification For Hammerstein And Wiener Systems

Hammerstein and Wiener nonlinear systems belong to input nonlinear model and output nonlinear model respectively.Because of their simple structure and being flexible,they are widely used in the identification field.Least squares algorithm is a classical identification algorithm.This kind of algorithm has the advantages of high accuracy and fast convergence speed,and its parameter estimation is unbiased under the interference of white noises.This thesis is mainly based on the least squares algorithm for Hammestein and Wiener systems under white noises and colored noises.The basic least squares algorithm is improved by introducing the identification idea of weighted parameter,latest estimation and instrumental variables.It has higher identification accuracy and faster convergence speed.The main work of this thesis is as follows:For the Hammerstein ARX model,this thesis presents a weighted least squares identification algorithm which is the least squares algorithm combined with weighted prameter and the latest estimation.Because the correction term of least squares algorithm is fluctuating,the identification accuracy can be improved by proper weight selection.Using the idea of weight,the current correction item is rewritten to the weight sum of the current Amendment Item and the previous amendment item.In order to further improve the identification accuracy of the weighted least squares algorithm,the latest estimation is applied,which is the parameter estimation of the latest time is used instead of the parameter estimation of the previous time.The accuracy and anti-jamming ability of the weighted least squares identification algorithm are proved to be better than that of the least squares identification algorithm by simulation.For the Hammerstein ARMAX model,this thesis presents a weighted recursive instrumental variable least squares algorithm which is the least squares algorithm combined with instrumental variables,weighted paramter and latest estimation.The recursive least squares are biased under the interference of colored noise but the recursive instrumental variables least squares algorithm can be unbiased by applying instrumental variables.On this basis,the weight sum of the correction item and applying the latest estimate can improve accuracy more.The superiority of the accuracy and anti-interference ability of the weighted recursive instrumental variable over recursive least squares identification algorithm is verified by simulation.For the Wiener ARMAX model,this thesis presents a weighted recursive instrumental variable least squares identification algorithm.The supriority of the accuraty and anti-interference ability of the weighted recursive instrumental variable least squares identification algorithm over the recursive least squares identification algorithm is verified by simulation.