Fast algorithms for least squares linear prediction based on orthogonal rotations

Cioffi (see Proc. International Conf. on ASSP, vol.503, p.1584, 1988) presented a fast Kalman algorithm that is based on the QR-decomposition (QRD) technique. The key to Cioffi´s algorithm is a connection between the solution to the linear prediction problem and the solution to an auxiliary problem (the so-called backward prediction problem). This is the same as the standard fast Kalman approach except that now this connection involves only orthogonal rotations. Cioffi´s original presentation is somewhat difficult to follow. The authors outline a much briefer and greatly simplified derivation of the new orthogonal fast Kalman algorithm. This is achieved by using a notation similar to that adopted in the literature in the context of the triangular recursive least squares processor. A new QRD-based least squares lattice algorithm for linear prediction follows quite readily given their simplified derivation of the fast Kalman algorithm