A METHOD FOR RECURSIVE LEAST-SQUARES FILTERING BASED UPON AN INVERSE QR DECOMPOSITION

A new computationally efficient algorithm for recursive least squares filtering is derived, which is based upon an inverse QR decomposition. The method solves directly for the time-recursive least squares filter vector, while avoiding the highly serial backsubstitution step required in previously derived direct QR approaches. Furthermore, the method employs orthogonal rotation operations to recursively update the filter, and thus preserves the inherent stability properties of QR approaches to recursive least squares filtering. The results of simulations over extremely long data sets are also presented, which suggest stability of the new time-recursive algorithm. Finally, parallel implementation of the resulting method is briefly discussed, and computational wavefronts are displayed.