A minimum misadjustment adaptive FIR filter

The performance of an adaptive filter is limited by the misadjustment resulting from the variance of adapting parameters. This paper develops a method to reduce the misadjustment when the additive noise in the desired signal is correlated. Given a static linear model, the linear estimator that can achieve the minimum parameter variance estimate is known as the best linear unbiased estimator (BLUE). Starting from classical estimation theory and a Gaussian autoregressive (AR) noise model, a maximum likelihood (ML) estimator that jointly estimates the filter parameters and the noise statistics is established. The estimator is shown to approach the best linear unbiased estimator asymptotically. The proposed adaptive filtering method follows by modifying the commonly used mean-square error (MSE) criterion in accordance with the ML cost function. The new configuration consists of two adaptive components: a modeling filter and a noise whitening filter. Convergence study reveals that there is only one minimum in the error surface, and global convergence is guaranteed. Analysis of the adaptive system when optimized by LMS or RLS is made, together with the tracking capability investigation. The proposed adaptive method performs significantly better than a usual adaptive filter with correlated additive noise and tracks a time-varying system more effectively.