The fast adaptive ROTOR´s RLS algorithm

A fast algorithm for implementation of the QR-factorization-based recursive-least-squares (RLS) adaptive filter is discussed. This fast adaptive rotors (FAR) algorithm can be implemented with a pipelined array of processors called ROTORs and CISORs. The ROTORs compute 2×2 orthogonal (Givens) rotations, and the CISORs compute the cosines and sines of the angles used in the ROTORs. The algorithm requires 4N ROTORs and 2N CISORs at each iteration to compute the solution to the RLS problem. The algorithm is numerically stable. The FAR algorithm is derived using a single generic updating formula for orthogonal matrices, which is introduced and derived. Whereas the generic updating formula is reminiscent of previous fast transversal filters and fast lattice algorithms, the set of internally propogated adaptive filter quantities is entirely different and constitutes yet another complete characterization of the RLS covariance and the forward, backward, and pinning estimation problems