Improvement Instrumental Variables Method for Output Error Model

Abstract

The identification of parameters system can be done in multiple ways by alternating methods (Least Squares, Instrumental Variables) and models (ARX, OE). The Ordinary Least Squares method which was presented in several research papers gives biased estimates for Output Error model. For example, the interpretation results in the first order OE model, the autocorrelation function shows that the residuals are not white noise, and the LS estimator is well biased, and it is not a suitable estimator for identification of output error model. In this paper, we will present a detailed study of Recursive Instrumental Variables method and its instruments choice to identify the parameters of Output Error model with unbiased estimates. The idea is simultaneously to identify the parameters system similar to an ARX model with Least Squares method. It is a successfully applied to identify with unbiased estimates parameters of a second order system based on whitening error prediction, and we showed that, if the instruments are weak, then the estimator may be biased and confidence intervals and hypothesis tests unreliable. Also, for every data observation set, the estimates parameters can be compared with those originally generated by MATLAB functions. Finally, a numerical example illustrates the efficiency and performances of the proposed method.