Bias Compensation Based Recursive Least Squares Identification For Multi-input Multi-output Errors-in-variables Models

Multi-input multi-output errors-in-variables(MIMO-EIV)models are widely used in industrial control process,aerospace,economic systems and other fields.MIMO-EIV models have more complex structure,larger dimension and more parameters to be identified than single input and single output models,which results in a large amount of calculation during the parameter identification process.By using the hierarchical identification principle,the MIMO models can be decomposed into several multi-input single-output models whose parameters are identified respectively.By this means,we can reduce the calculation loads.Besides,the parameters estimate of MIMO-EIV models is biased by the least squares identification algorithm.The unbiased estimate can be obtained with the help of the bias compensation technique.This thesis,studying the parameter identification problem of MIMO-EIV models,aiming at improving the accuracy of parameter estimation and combining with hierarchical identification principle and bias compensation technique,establishes a new parameter estimation algorithm.For two types of MIMO-EIV models,the least square identification algorithm and the partially coupled least square identification algorithm are proposed respectively.Two cases are considered respectively.One is that the input and output measurements are both corrupted by white noise,another one is that the input measurements are corrupted by white noise and the output measurements are corrupted by colored noise.MIMO-EIV models are decomposed into several multi-input single-output models and then the parameters are identified respectively by the least square identification algorithm.By using the parameter coupling phenomenon,the estimation of the coupling parameters in the current subsystem is corrected based on the estimated values of the coupling parameters in the previous subsystem,and then a partially coupled least squares identification algorithm is obtained.The numerical simulation of the algorithm shows that the partially coupled least squares identification algorithm can improve the identification accuracy of the coupling parameters.For MIMO-EIV models in the case where the input measurements corrupted by white noise and output measurements corrupted by colored noise,a bias compensation based recursive least square(BC-RLS)algorithm is proposed.The bias term of the least square estimate is analyzed,the relation between the bias term and the white noise variance is deduced and the whole frame of the least square compensation algorithm is obtained.Then the estimation of the variance of white noise is calculated by introducing the zero parameter vector so as to calculate the bias term and establish the BC-RLS algorithm.Numerical simulation shows that the BC-RLS algorithm has the highest identification accuracy.For MIMO-EIV models whose input measurements are corrupted by input and output measurements are corrupted by colored noise,a bias compensation based recursive least square(BC-RLS)algorithm is established.The relation between the bias term and the white noise variance and the autocorrelation function of colored noise is analyzed and the expression of bias term is derived.Combining LS algorithm and estimate of white noise variance and the autocorrelation function value of colored noise,the BC-RLS algorithm are established.numerical simulation shows that the BC-RLS algorithm obtains unbiased estimation and has high identification accuracy.