Error propagation analysis of fast recursive least squares algorithms

In this paper, we present new versions of numerically stable fast recursive least squares (NS-FRLS) algorithms. These new versions are 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 these versions is presented by formulating new conditions on the forgetting factor. An advanced comparative method is used to study the efficiency of these new versions relatively to RLS algorithm by calculating their squared norm gains ratio (SNGR). The simulation over a very long duration for a stationary signal did not reveal any tendency to divergence.

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