A modified QRD for smoothing and a QRD-LSL smoothing algorithm

term in (A.12) be negligible compared with (35), we must further require that (T =B 2)e 0 =B approaches zero. This rather unusual requirement simply assures that the modeling errors (bias squared) be negligible compared with the error variance. The derivation of the bound in (30) follows similarly by slightly modifying the definition of D D D: REFERENCES [1] S. Bellini and F. Rocca, " Asymptotically efficient blind deconvolution, " High order contrasts for self-adaptive source separation, " Int. J. Adaptive Contr. Signal Process., to be published. [12] D. T. Pham, " Blind separation of instantaneous mixture of sources via an independent component analysis, " IEEE Trans. Abstract—This paper introduces a modified QR-decomposition (QRD) that extends the method of QRD to a more general case to solve the least-squares lattice smoothing problems. We show that the conventional QRD is a special form of the modified QRD that occurs when no future data values are used. Within the framework of the modified QRD procedure, an order-recursive QRD-based least-squares lattice (QRD-LSL) smoothing algorithm is formulated. The algorithm combines all the desirable features of the standard QRD-LSL filtering algorithm with a more accurate smoothing process. The results of some computer simulations of a channel equalizer are also presented.