Generalized square-root adaptive algorithms

We extend the QR-based recursive least squares algorithms to a more general square-root formulation, which involves array transforms using orthogonal and possibly non-orthogonal transforms e.g. Gauss transform. The adaptive algorithms, thus obtained, have better numerical properties than the traditional pseudo-inverse-based algorithms. This new update scheme covers an extended set of algorithms; it connects the recursive least squares to gradient based algorithms. Moreover, we show that the previously derived block diagonal QR based algorithms belongs to this general square-root class