Unbiased LMS filtering in the presence of white measurement noise with unknown power

This paper presents a new modified least mean squares (LMS) adaptive filtering algorithm for autoregressive (AR) modeling in the presence of white measurement noise with unknown power. In the proposed algorithm, a first-order filter is used to filter the noise-corrupted signal. In this way, the AR model is augmented to have a known pole which can, based on asymptotic analysis, be used to extract and eliminate the noise-induced bias in the standard LMS filtering result, and thus the unbiased parameter estimation can be achieved.