On parameter estimation of ARMAX model via BCLS method

This paper studies the problem of parameter estimation of ARMAX model from a novel point of view. An efficient bias compensation least squares algorithm is proposed to provide consistent parameter estimate for ARMAX model. The main feature of our proposed algorithm is to introduce the auxiliary least squares linear backward predictors to construct the cross-correlations of least-squares (LS) error and backward prediction (BWP) errors. And with the help of the cross-correlations of LS error and BWP errors, estimate of the bias resulted from LS solution can be obtained. Consequently the consistent estimate for ARMAX model can be obtained via compensating the estimated bias of LS estimate. The batch-processing approach and the recursive processing approach for the proposed method are given. Theoretical analysis that compares the proposed method with the other existing methods such as bias-eliminated least-squares (BELS) method proposed by Zheng and instrumental variables (IV) method is carried out.