A new quasi-Newton adaptive filtering algorithm

A new algorithm for FIR adaptive filters based on the quasi-Newton class of optimization algorithms is described. A series of theorems demonstrating the stability of the algorithm, boundedness and positive definiteness of the estimated autocorrelation matrix of the input signal are provided. The internal variables of the algorithm and their effect are also investigated in order to provide a better insight of the algorithm's behavior. Extensive simulation results are presented for fixed- and floating point implementation which show that the proposed algorithm has comparable convergence speed and superior robustness relative to other known Newton-type algorithms. Furthermore, robustness is guaranteed for highly correlated or even nonpersistently exciting input signals, which makes the proposed algorithm a powerful alternative to the LMS and the RLS algorithms.