On unbiased adaptive IIR filtering algorithms

Some properties of a recently proposed unbiased criteria for adaptive IIR filtering, namely the Master-slave Expanded Numerator Algorithm (XNA), is investigated. The XNA algorithm combines the minimization of two criteria that are quadratic in the parameters. Although the XNA method achieves an unbiased behavior in sufficient-order system identification applications, it generates undesired stationary points. Through the study presented in this paper, explicit expressions for the unwanted stationary points can be obtained. By closely examining the obtained results, a new unbiased adaptive IIR filtering algorithm is presented. Using similar ideas to the Steiglitz-McBride method, the new algorithm is based on the minimization of an off-line error function. After the proposal of the new unbiased (off-line) algorithm, which is quadratic in the parameters, we present the analysis of the possible stationary points. Some examples are shown illustrating the performance of the new algorithm in a system identification application.