A State-Space Approach for Adaptive Notch Digital Filters with Unbiased Parameter-Estimation

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