A Minimal, Givens Rotation Based Frls Lattice Algorithm

We propose a new Givens rotation based least-squares lattice algorithm. Based on spherical trigonometry principles, this algorithm turns out to be a normalized version of the fast QRD-based least-squares lattice filter, introduced independently by Ling and Proudler et al. In constrast to those algorithms, the storage requirements of the new algorithm are minimal (in the system theory sense). From this, we show that the new algorithm satisfies the backward consistency property, and hence enjoys stable error propagation. 1 INTRODUCTION Yule's PARCOR identity was recently shown to coincide with the cosine law of spherical trigonometry. This observation establishes a connection between FRLS adaptive filtering and spherical trigonometry [1], [2], because the prewindowed fully-normalized FRLS lattice algorithm of Lee et al. [3] consists of three particular applications of Yule's PARCOR Identity. Let us briefly recall this algorithm for convenience of the reader. Let n n,t and h n,t be the ..