Weighted Multi-information Least Squares Identification Based On Auxiliary Model

The least squares identification method is a basic and classical identification method in system identification.The output error model is a common stochastic system model,including output error model,output error autoregressive model,output error moving average model and output error autoregressive moving average model.The structure of the output error model is more complex,and the information vector needed in the identification contains the variables which cannot be measured.Therefore,the traditional least squares identification method cannot be directly used in the output error class model.The auxiliary model identification method is usually used to solve this problem,but the convergence speed and identification accuracy of the improved algorithm are still relatively poor.In order to solve this problem,the weighted matrix is introduced into the multi-innovation identification and the auxiliary model identification to improve the identification performance by choosing the appropriate parameter values.Based on the traditional recursive least squares identification algorithm and the auxiliary model identification method,the recursive least squares identification algorithm based on the auxiliary model is obtained.On the basis of the algorithm,the multi-innovation vector is constructed by using the multi-innovation identification method,and the multi-innovation least squares identification algorithm based on the auxiliary model is obtained.Compared with the recursive least squares identification algorithm based on the auxiliary model,the algorithm improves the utilization of the data,and makes the algorithm have higher identification accuracy.For the multi-innovation least squares identification algorithm based on the auxiliary model,the weighted matrix is introduced into the algorithm to redefine the error criterion function of the multi-innovation identification.Based on the auxiliary model,the weighted multi-innovation least squares identification algorithm is proposed to minimize the error criterion function.The simulation results of the proposed algorithm verify that the weighted multi-innovation least squares identification algorithm based on the auxiliary model can improve the convergence speed and the identification accuracy.The auxiliary model of colored noise term is established to deal with the interference of input data by colored noise.At the same time,the estimation of the noise is used to replace the unknown noise,and the identification algorithm based on the multi-innovation identification and the weighted matrix is proposed for the other three models.The simulation results of the three algorithms show the superiority and effectiveness of the weighted multi-innovation identification algorithm based on the auxiliary model proposed in this paper.