A computation of the sliding window recursive QR decomposition

A set of recursions for sequential updating of QR based algorithms in finite (or sliding) windows using orthonormal Givens plane rotations is presented. These recursions can be used for (1) sliding window spatial QR-RLS adaptive filtering including implicit error computation and/or (2) sliding window tracking of orthonormal database for array processing applications. The proposed sliding window QR algorithms have approximately twice the computational complexity when compared with the classical exponentially weighted growing window QR algorithms. They are based on very elementary computation structures which are familiar from the well-known Gentleman and Kung array.<>