Bias removal in equation-error adaptive IIR filters

In the equation-error formulation of adaptive IIR filters, the estimated parameters contain bias when there is noise in the desired response. A method that can eliminate this bias is investigated. The idea is to maintain a quadratic constraint on the feedback coefficients so that the noise contributes only a constant term to the mean-square error. This term does not affect minimization and thus the bias is eliminated. A quadratically constrained stochastic gradient search method is applied for optimization and convergence behavior, when the noise is white, is analyzed. Adaptation of the feedback FIR filter in second-order cascade form, useful for stability monitoring, is also considered. When the noise is nonwhite, the technique requires an adaptive whitening filter. Simulation results are included to demonstrate the bias removal capability of the method, corroborate the theoretical developments, and compare with existing techniques