On bias removal and unit norm constraints in equation error adaptive IIR filters

We develop two simple gradient-based algorithms for unbiased adaptive IIR filtering in the presence of zero-mean output noise. The algorithms are derived according to a constrained minimization problem that is known to have a unique solution and are generalizations of bias removal techniques for equation-error-based filters for uncorrelated output noise. We propose simple methods for estimating the noise correlation statistics within the algorithm. Our stochastic analyses of these algorithms yield necessary conditions on the step sizes for the stability of the mean values of the coefficients. In addition, we give a more accurate mean-square analysis of one of the algorithms assuming jointly Gaussian input and desired response signals. Simulations indicate that the algorithms can achieve unbiased parameter estimates at least as accurately as other, more-complex techniques.