Numerical properties of the linearly constrained QRD-RLS adaptive filter

Shepherd and McWhirter (1993) proposed a QRD-RLS algorithm for adaptive filtering with linear constraints. In this paper, the numerical properties of this algorithm are considered. In particular, it is shown that the computed weight vector satisfies a set of constraints which are perturbed from the original ones, the amount of perturbation being dependent on the wordlength. The linearly constrained FLS algorithm of Resende et al. (1996) is also studied. Simulation results show that this algorithm is numerically unstable, even in the absence of explosive divergence