Hierarchical Algorithm for the Identification of Parameter Estimation of Linear System

Abstract

A novel technique to identification of autoregressive moving average (ARMA)systems is proposed to increase the accuracy and speed of convergence for the system identification. The convergence speed of recursive least square algorithm (RLS) is solved under differential equations that needs all necessary information about the asymptotic behavior. Using RLS estimation, the convergence of parameters is able to the true values if the data of information vector growing to infinite. Therefore, the convergence of the parameters of the RLS algorithm takes time or needs a large number of sampling. In order to improve the accuracy and convergence speed of the estimated parameters, we propose a technique that modifies the QARXNN model by running two steps to identify the system hierarchically. The proposed method performs two steps: first, the system is identified by least square error (LSE) algorithm. Second, performs multiinput multi-output feedforward neural networks (MIMO-NN) to refine the estimated parameters by updating the parameters based on the residual error of LSE. The residual error by using LSE is set as target output to train NN. Finally, we illustrate and verify the proposed technique with an experimental studies. The proposed method can find the estimated parameters faster with = 0.935129 % in tenth sampling. The results is almost consistence which the accuracy of the identified parameters did not change significantly with the increasing number of sampling or the number of data points.