Solution to the Weight Extraction Problem in Fast QR-Decomposition RLS Algorithms

Fast QR decomposition RLS (FQRD-RLS) algorithms are well known for their good numerical properties and low computational complexity. However the FQRD-RLS algorithms do not provide access to the filter weights, and so far their use has been limited to problems seeking an estimate of the output error signal. In this paper we present a novel technique to obtain the filter weights of the FQRD-RLS algorithm at any time instant. As a consequence, we extend the range of applications to include problems where explicit knowledge of the filter weights is required. The proposed weight extraction technique is tested in a system identification setup. The results verify our claim that the extracted coefficients of the FQRD-RLS algorithm are identical to those obtained by any RLS algorithm such as the inverse QRD-RLS algorithm