Numerically stable fast transversal filters for recursive least squares adaptive filtering

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, 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, it is shown 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 a complexity of 8N multiplications and additions per time recursion. The results are presented for the complex multichannel joint-process filtering problem