Fast Newton transversal filters-a new class of adaptive estimation algorithms

A class of adaptive algorithms for the estimation of FIR (finite impulse response) transversal filters is presented. The main characteristic of this class is the fast computation of the gain vector needed for the adaptation of the transversal filters. The method for deriving these algorithms is based on the assumption that the input signal is autoregressive of order M, where M can be much smaller than the order of the filter to be estimated. Under this assumption the covariance matrix of the input signal is estimated by extending in a min-max way the M order sample covariance matrix. This estimate can be regarded as a generalization of the diagonal covariance matrix used in LMS and leads to an efficient computation of the gain needed for the adaptation. The new class of algorithms contains the LMS and the fast versions of LS as special cases. The complexity changes linearly with M, starting from the complexity of the LMS (for M=0) and ending at the complexity of the fast versions of LS