Convex Combination of Two Recursive Least Squares-type Algorithms for Adaptive Whitening

The recursive least squares (RLS)-type whitening algorithm is shown to be a useful solution for improving the convergence rate of the least mean square (LMS)-type whitening algorithm, but the RLStype algorithm with a constant forgetting factor requires a tradeoff between the convergence speed and steady-state misadjustment. By using a convex combination of two RLS algorithms with different forgetting factor, we present an effective method to solve the tradeoff problem of the RLS-type whitening algorithm. Firstly, two RLS-type whitening algorithms with different forgetting factor are convex combined in a reasonable manner to put together the best properties of them. Then, a mixing parameter is introduced to adjust the proportion of the two RLS algorithms, and the adaptive updating rule of the mixing parameter is obtained based on the stochastic gradient of the cost function. Finally, the weight transfer procedure and momentum term technique are developed to further improve the convergence performance of the convex combination algorithm. Since two RLS algorithms with different forgetting factor are applied and the best properties of them are acquired, the proposed combination algorithm work more efficiently than the existing adaptive whitening algorithms, as is verified by computer simulations in both stationary and non-stationary environments.