A new least squares adaptation scheme for the affine combination of two adaptive filters

Adaptive combinations of adaptive filters are an efficient approach to alleviate the different tradeoffs to which adaptive filters are subject. The basic idea is to mix the outputs of two adaptive filters with complementary capabilities, so that the combination is able to retain the best properties of each component. In previous works, we proposed to use a convex combination, applying weights lambda(n) and 1-lambda(n), with lambda(n) isin (0,1), to the filter components, where the mixing parameter lambda(n) was updated to minimize the overall square error using stochastic gradient descent rules. In this paper, we present a new adaptation scheme for lambda(n) based on the solution to a least-squares (LS) problem, where the mixing parameter is allowed to lie outside range [0,1]. Such affine combinations have recently been shown to provide additional gains. Unlike some previous proposals, the new LS combination scheme does not require any explicit knowledge about the component filters. The ability of the LS scheme to achieve optimal values of the mixing parameter is illustrated with several experiments in both stationary and tracking situations.