Abstract
A lot of algorithms have been proposed to solve the least squares (LS) problem for transversal adaptive filters, that is, finding the tap-weights of the filter which minimizes the exponentially weighted sum of the squared errors. However, some are computationally consuming as the recursive LS (RLS) algorithm and others are numerically unstable as the fast RLS(FLS) and RLS algorithms. The predictor-based LS (PLS) algorithm [9] gives the exact solution of the LS problem and its numerical stability has been proven by the linear time-variant state-space method. its computational complexity comparable to the RLS algorithm can be reduced to the linear order when the input signal is sufficiently modeled by an autoregressive of rather small order, since it is based on the predictors which can be truncated. We call it the fast PLS algorithm. Its good numerical properties have been confirmed, however, its convergence properties are not elucidated yet. This paper shows that the fast PLS algorithm has almost the same convergence properties as the PLS and RLS algorithms though its computational complexity is much smaller than them.
