Normalised Givens rotations for recursive least squares processing

Abstract

An algorithm for recursive least squares optimisation based on the method of QR decomposition by Givens rotations is reformulated in terms of parameters whose magnitude is never greater than one. In view of the direct analogy to statistical normalisation, it is referred to as the normalised Givens rotation algorithm. An important consequence of the normalisation is that most of the resulting least squares computation may be carried out using fixed point arithmetic. This should enable the design of a much simpler application specific integrated circuit to implement the Givens rotation processor for adaptive filtering and beamforming.