Multi-stage adaptive signal processing algorithms

In this paper, we explore the use of multi-stage adaptation algorithms for a variety of adaptive filtering applications where the structure of the underlying process to be estimated is unknown. These algorithms are "multi-stage" in that they comprise multiple adaptive filtering algorithms that operate in parallel on the observation sequence, and adaptively combine the outputs of this first stage to form an overall signal estimate. Several examples of this class of algorithms are demonstrated and analyzed in both a deterministic and stochastic context with respect to their convergence and mean squared error. The first example of this class, a "universal" linear predictor, was recently introduced and shown to asymptotically achieve the performance of the best linear predictor for each sequence, (up to some maximal order). Two new algorithms have been developed that generalize this universal linear predictor, and explore the use of the LMS algorithm in each stage of adaptation. Each of these algorithms are compared through theoretical analysis of their behavior.