Tracking properties of a convex combination of two adaptive filters

Combination approaches provide a useful way to improve adaptive filter performance. In this paper, we study the tracking performance of an adaptive convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination is adapted to minimize the error of the overall structure. We show the universality of the approach with respect to the component filters, i.e., that the overall filter is able to track changes at least as well as the best component filter. Using energy conservation arguments, we then specialize the results to a combination of two LMS filters