Numerically stable fast recursive least-squares transversal filters

The problem of numerical stability of fast recursive least-squares transversal filter (FTF) algorithms is addressed. The prewindowing case with exponential weighting is considered. A framework for the analysis of the error propagation in these algorithms is developed. Within this framework, it is shown that the computationally most efficient 7N form (dealt with by G. Carayanmis et al. (1983) and by J.M. Cioffi (1984)) is exponentially unstable. By introducing redundancy in this algorithm, feedback of numerical errors becomes possible. This leads to a numerically stable FTF algorithm with complexity 9N. The results are presented for the complex multichannel joint-process filtering problem