Adaptive AR modeling in white Gaussian noise

Autoregressive (AR) modeling is widely used in signal processing. The coefficients of an AR model can be easily obtained with a least mean square (LMS) prediction error filter. However, it is known that this filter gives a biased solution when the input signal is corrupted by white Gaussian noise. Treichler suggested the -LMS algorithm to remedy this problem and proved that the mean weight vector can converge to the Wiener solution. In this paper, we develop a new algorithm that extends works of Vijayan et al. for adaptive AR modeling in the presence of white Gaussian noise. By theoretical analysis, we show that the performance of the new algorithm is superior to the -LMS filter. Simulations are also provided to support our theoretical results.