A unified square-root-free approach for QRD-based recursive-least-squares estimation

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, p and v, all previously known sqrt-free, as well as new methods, are included in our unified approach. This unified treatment is also extended to the QRDbased recursive least squares (RLS) problem for optimum residual acquisition without sqrt operations.