Adaptive algorithms for joint time delay estimation and IIR filtering

A new class of gradient-based algorithms for joint adaptive time delay estimation and IIR filtering for the recursive identification of systems with long pure delays is introduced. The algorithms update an adaptive delay estimate and the coefficients of an IIR filter using familiar gradient-descent methods. In addition, interpolation of the input sequence is used to obtain delays that are not constrained to integer numbers of samples. Three algorithms using a direct form filter parametrization and one using a normalized lattice filter are derived, and computer simulations are used to demonstrate their convergence and tracking properties