A HYBRID LEAST-SQUARES QR-LATTICE ALGORITHM USING A-PRIORI ERRORS

This paper presents a new minimal and backward stable QR-LSL algorithm obtained through the proper interpretation of the system matrix that describes the adaptation and filtering operations of QR-RLS algorithms . The new algorithm is based on a priori prediction errors normalized by the a posteriori prediction error energy-as suggested by the interp retation of the system matrix-and uses the fact that the latter quanti ties can be computed via a lattice structure, Backward consistency and backward stability become guaranteed under simple numerical conventio ns. In contrast with the known a posteriori QR-LSL algorithm, the new algorithm presents lower numerical complexity, and backward consistenc y is guaranteed without the constraint of passive rotations in the rec ursive lattice section, Furthermore, reordering of some operations res ults in a version with identical numerical behavior and inherent paral lelism that can be exploited for fast implementations. Both a priori a nd a posteriori QR-LSL algorithms are compared by means of simulations , For small mantissa wordlengths and forgetting factors lambda not too close to 1, the proposed algorithm performs better due to dispensing with passive rotations. For forgetting factors very close to one and s mall wordlengths, both algorithms are sensitive to the accuracy of som e well-identified computations.