Numerically Stable Fast Transversal Filters for Recursive Least-Squares Adaptive Filtering

Abstract

In this paper, a solution is proposed to the long-standing problem of the numerical instability of Fast Recursive Least-Squares Transversal Filter (FTF) algorithms with exponential weighting, which is an important class of algorithms for adaptive filtering. A framework for the analysis of the error propagation in FTF algorithms is first developed; within this framework, we show that the computationally most efficient 7N form is exponentially unstable. However, by introducing redundancy into this algorithm, feedback of numerical errors becomes possible; a judicious choice of the feedback gains then leads to a numerically stable FTF algorithm with complexity 9N. The results are presented for the complex multichannel joint-process filtering problem.

This work was supported in part by the Joint Services Program at Stanford University (US Army, US Navy, US Air Force) under Contract DAAG29-85-K-0048 and the SDI/IST Program managed by the Office of Naval Research, under Contract N00014-85-K-0550.