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

The generic formula for the Givens rotation, the most commonly used method for QR-decomposition (QRD) updating, requires explicit square-root (sqrt) computations, which constitute a computational bottleneck. A unified systematic approach for sqrt-free Givens rotations is provided. By properly choosing two parameters, all previously known, as well as new, sqrt-free methods are included in the unified approach. This unified treatment is also extended to the QRD-based recursive-least-squares (RLS) problem for optimum residual acquisition without sqrt operations