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Comparative analysis regarding numerical concerns for recursive least squares lattice (RLSL) algorithms

Much interest has been devoted to the numerical behavior of the Recursive Least Squares Lattice (RLSL) algorithms. Two types of updating schemes that are equivalent in exact arithmetic have been proposed previously: the direct and the indirect versions of the RLSL algorithm. However, the numerical behavior of these algorithms is quite different, the direct updating scheme being the more robust of the two. We provide the results from an arithmetic error analysis that uses first order approximation techniques to give arithmetic error effects which propagate in both time and order for two fast adaptive RLSL algorithms.