Joint recursive optimality—a non-probabilistic approach to adaptive transversal filter design

Abstract

It is common practice to design and interpret adaptive filter algorithms in terms of some optimality principle. The predominant approach purports to miminize a quadratic measure of the filter's error signal. This approach is, however, tied to the assumption of a time-invariant applications environment so that operational algorithm structures (such as LMS) are only obtained from ad hoc modifications aiming at continuous tracking. Joint recursive optimality is a unified framework for the “optimal” design of adaptive transversal filters. It covers a wide class of adaptation algorithms including standards like least mean squares and recursive least squares algorithms. Contrary to existing optimality principles, a deterministic criterion is proposed which operational algorithms meet exactly for each time step. The criterion features a trade-off between time variance of the filter coefficients and error signal power. The paper discusses implications for the interpretation of a variety of algorithms and concludes with guidelines for the incorporation of prior statistical or coefficient modeling information into the adaptation algorithm.