A simplified FTF-type algorithm for adaptive filtering

Fast RLS algorithms are known to present numerical instability and this instability is originated in the backward prediction parameters. In this paper, a simplified FTF-type algorithm for adaptive filtering is presented. The basic idea behind the proposed algorithm is to avoid using the backward variables. By using only forward prediction variables and adding a small regularization constant and a leakage factor, we obtain a robust numerically stable FTF-type algorithm that shows the same performances as the numerically stable FTF algorithms. The computational complexity of the proposed algorithm is 7N when used with a full size predictor, which is less complex than the 8N numerically stable FTF algorithms and this computational complexity can be significantly reduced to 2N+5P when used with a reduced P-size forward predictor.