Noisy Autoregressive System Identification Based on Repeated Autocorrelation Function

This paper presents an identification approach for the minimum-phase autoregressive (AR) systems in the presence of heavy noise based on a repeated autocorrelation function (RACF) of observed data. It is shown that RACF retains poles of the original system and in noisy environment if it is used instead of single ACF in the modified least-squares Yule-Walker equations the effect of additive noise can be reduced. A termination criterion for the repeated operations is proposed based on the decaying nature of correlation values. The length of ACF, which is kept fixed in all RACFs, is determined from the decorrelation time of the single ACF. Simulation results show the superiority of performance by the proposed method in comparison to some of the existing methods in estimating the AR parameters even at a very low SNR of -5 dB