A posteriori updates for adaptive filters

In adaptive FIR filters, the least-mean-square (LMS) adaptive algorithm uses the a priori error signal to update the filter coefficients. We study the forms and properties of a posteriori adaptive filter coefficient´s updates in a general context. We provide a technique by which the stability of an adaptive filter´s coefficient update can be easily analyzed using the relationship between the a priori and a posteriori error signals. Using this knowledge, we then develop methods for choosing the algorithm step size to guarantee the robustness and stability of the system and to provide fast adaptation behavior. Simulations verify the usefulness of a posteriori-error-based adaptive algorithms for unbiased adaptive IIR filtering.