The FTE manifold and its role in the numerical behavior of fast transversal filter RLS algorithm

Some preliminary results are presented on a novel approach to the analysis of the propagation of round-off errors in the fast transversal filter (FTF) recursive least squares (RLS) algorithm. This approach is based on the concept of backward consistency which can be applied to any recursive algorithm, e.g. to the class of Kalman filtering algorithms. The backward consistency concept is applied to the FTF algorithm. This application leads to the introduction of the FTF state variables that are backwardly consistent. In other words, each point on the FTF manifold represents a value for the FTF state variables that corresponds exactly to the solution of a prewindowed shift-invariant least-squares (LS) problem. The advantage of this approach is that the error propagation on the FTF manifold corresponds exactly (without averaging or even linearization) to the propagation of a perturbation on the input data in the LS problem. The dynamics of this perturbation are analyzed