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 interpretation of the system matrix-and uses the fact that the latter quantities can be computed via a lattice structure. Backward consistency and backward stability become guaranteed under simple numerical conventions. In contrast with the known a posteriori QR-LSL algorithm, the new algorithm present; fewer numerical complexity, and backward consistency is guaranteed without the constraint of passive rotations in the recursive lattice section. Furthermore, reordering of some operations results in a version with identical numerical behavior and inherent parallelism that can be exploited for fast implementations. Both a priori and a posteriori QR-LSL algorithms are compared by means of simulations. For small mantissa wordlengths and forgetting factors λ not too close to 1, the proposed algorithm performs better due to dispensing with passive rotations. For forgetting factors very close to one and small wordlengths, both algorithms are sensitive to the accuracy of some well-identified computations