Analysis of Fast Recursive Least Squares Algorithms for Adaptive Filtering

In this paper, we present new version of numerically stable fast recursive least squares (NS-FRLS) algorithm. This new version is obtained by using some redundant formulae of the fast recursive least squares (FRLS) algorithms. Numerical stabilization is achieved by using a propagation model of first order of the numerical errors. A theoretical justification for this version is presented by formulating new conditions on the forgetting factor. An advanced comparative method is used to study the efficiency of this new version relatively to RLS algorithm by calculating their normalized square norm gain error (NGE). We provide a theoretical justification for this version by formulating new conditions on forgetting factor. It will be followed by an analytical analyze of the convergence of this version and we show, both theoretically and experimentally, their robustness. The simulation over a very long duration for a stationary signal did not reveal any tendency to divergence. Key-Words: Fast RLS, Estimation, Adaptive Filtering, Propagation of Errors, Numerical Stability.