State-Space Realization of Adaptive IIR Notch Digital Filters with Unbiased Parameter-Estimation

A state-space approach for adaptive second-order IIR notch digital filters is explored. A simplified iterative algorithm is derived from the gradient-descent method to minimize the mean-squared output of an adaptive notch digital filter. The stability and parameter-estimation bias are then analyzed by employing a first-order linear dynamical system. As a consequence, it is clarified that the resulting parameter estimate is unbiased. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the adaptive state-space notch digital filter and bias analysis of parameter estimation.