A homotopy continuation mapping for the Steiglitz-McBride adaptive algorithm

In the last years, adaptive infinite-duration impulse response filters (IIR) have been studied as a possible alternative to adaptive finite-duration impulse response (FIR) filters. Some of the best known approaches for adaptive IIR filtering include the output error (OE), the equation error (EE), and the Steiglitz-McBride (SM) algorithms. In this paper, a homotopy continuation mapping (HCM) of the SM adaptive algorithm is proposed by using the OE and EE algorithms as basic schemes. The utilization of the homotopy factor results in a simple analysis of the general convergence behavior of the SM algorithm, allowing a direct comparison with the convergence properties of the OE and EE algorithms. Numerical examples are included in order to demonstrate the usefulness of the proposed mapping