QR-decomposition based algorithms for adaptive Volterra filtering

The authors present an approach to the development of fast and numerically stable recursive least squares (RLS) algorithms for adaptive nonlinear filtering using QR-decomposition of the data matrix. They introduce a pair of QR-RLS adaptive algorithms for second-order Volterra filtering. Both the algorithms are based solely on Given´s rotation. Hence both are numerically stable and highly amenable to parallel implementations using arrays. One of the algorithms is a block processing algorithm in the sense that it processes all the channels simultaneously. The other processes the channels sequentially. The sequential algorithm is computationally much more efficient than the block algorithm and is comparable to that of fast RLS Volterra filters. Another attractive feature of sequential processing is that knowledge of the single-channel algorithm can be applied to the multichannel case