A UNIFIED SQUARE-ROOT-FREE APPROACH FOR QRD-BASED RECURSIVE LEAST-SQUARES ESTIMATION

Abstract

Givens rotation is the most commonly used method in performing the QR decomposition (QRD) updating. The generic formula for these rotations requires explicit square-root (sqrt) computations which constitute a computational bottleneck and are quite undesirable from the practical VLSI circuit design point of view. So far, there has been more than ten known sqrt-free algorithms. In this correspondence, we provide a unified systematic approach for the sqrt-free Givens rotation. By properly choosing two parameters, mu and nu, all previously known sqrt-free, as well as new methods, are included in our unified approach. This unified treatment is also extended to the QRD-based recursive least squares (RLS) problem for optimum residual acquisition without sqrt operations.