A self-tuning NLMS adaptive filter using parallel adaptation

A new adaptive filter algorithm that explicitly self-tunes for enhanced random walk tracking is presented. This algorithm takes measurements of its environment as if it were a random walk, and modifies its convergence-controlling parameter accordingly. The resulting filter makes use of three distinct normalized least-mean-squares (NLMS) filters running on the same inputs and is consequently referred to as parallel adaptation (PA-NLMS). An analysis is provided that accurately predicts PA-NLMS performance in the random walk scenario. We also claim that this algorithm can interpret a far-from-convergence condition as a quickly varying random walk, resulting in nearly optimal NLMS convergence. The effectiveness of the interpretation of the adaptation state as a random walk in these and other environments is also examined by means of simulation. These simulations are also used to compare the performance of the PA-NLMS filter with that of an existing self-tuning algorithm as well as a benchmark NLMS process. Improvements in both convergence and misadjustment at convergence over these existing algorithms are demonstrated.