Accurate estimation of AR model by tapered SVD without rank determination

This paper presents a new method to increase the accuracy in the estimates of the autoregressive (AR) model obtained by the Kumaresan-Tuft (KT) method proposed in 1982. In the KT method, there are the following two problems to be solved. (1) It is necessary to select the appropriate order of the AR-model before truncating the non-significant singular values obtained by the singular-value-decomposition (SVD). (2) There are errors in the selection of the signal- and noise-subspaces, which are determined by the noisy data matrix. Thus, the resultant singular values cannot be neglected even for the higher orders. Thus, truncation of the high order singular values by the predetermined order causes the bias error in the resultant AR parameter estimates. By introducing a tapering window into the truncation of high order non-significant singular values, the mean squared error of the estimates is certainly reduced. This paper also presents a new procedure to design an optimum tapering window for estimating AR model parameters without using any non-linear optimisation procedure