The fast Householder filters-RLS adaptive filter

A fast Householder filter (FHF) QR-RLS algorithm is presented that requires significantly less (by a factor of at least three) computation than previous fast QR-RLS adaptive algorithms. The essential feature of the new method is that it replaces the Givens rotations used in these fast QR algorithms by Householder transformations. A set of filters that characterize the QR factorization of a data matrix is derived, and time updates on this set are determined using a generic Householder updating identity. The FHF requires 7N computations per iteration for the standard prewindowed case, which is the same as the FTF (fast transversal filter) and FAEST fast (non-QR) RLS