MODULAR AND NUMERICALLY STABLE FAST TRANSVERSAL FILTERS FOR MULTICHANNEL AND MULTIEXPERIMENT RLS

In this paper, we present scalar implementations of multichannel and m ultiexperiment fast recursive least squares algorithms in transversal filter form (the so-called FTF algorithms). The point is that by proce ssing the different channels and/or experiments sequentially, i.e., on e at a time, the multichannel and/or multiexperiment algorithm gets de composed into a set of intertwined single-channel single-experiment al gorithms. For multichannel algorithms, the general case of possibly di fferent filter orders in different channels is handled. Geometrically, this modular decomposition approach corresponds to a Gram-Schmidt ort hogonalization of multiple error vectors. Algebraically, this techniqu e corresponds to matrix triangularization of error covariance matrices and converts matrix operations into a regular set of scalar operation s. Modular algorithm structures that are amenable to VLSI implementati on on arrays of parallel processors naturally follow from our approach . Numerically, the resulting algorithm benefits from the advantages of triangularization techniques in block processing, which are a well-kn own part of Kalman filtering expertise. Furthermore, recently introduc ed stabilization techniques for proper control of the propagation of n umerical errors in the update recursions of FTF algorithms are also in corporated.