Error Propagation Properties of Recursive Least Squares Adaptation Algorithms

Abstract

The numerical properties of various implementations of the recursive least squares identification algorithm are of great importance for their con tinuous use in various adaptive schemes. Here we investiga te how an error that is introduced at an arbit rary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal t o the fo r gett ing factor. The same is true for fast lattice algorithms. The fast least squares al gorithm, sometimes known as the “fast Kalman algorithm” is however shown to be un stabl e with res pect to such errors.