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.<
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