A numerically stable fast Newton type adaptive filter based on order update fast least squares algorithm

The numerical property of an adaptive filter algorithm is the most important problem in practical applications. Most fast adaptive filter algorithms have the numerical instability problem and the fast Newton transversal filter (FNTF) algorithms are no exception. In this paper, we propose a numerically stable fast Newton type adaptive filter algorithm. Two problems are dealt with in the paper. First, we derive the proposed algorithm from the order-update fast least squares (FLS) algorithm. This derivation is direct and simple to understand. Second, we give a stability analysis using a linear time-variant state-space method. The transition matrix of the proposed algorithm is given. The eigenvalues of the ensemble average of the transition matrix are shown to be asymptotically all less than unity. This results in a much improved numerical performance compared with the FNTF algorithms. The computer simulations implemented by using a finite-precision arithmetic have confirmed the validity of our analysis.