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The paper provides a new algorithm to recursively update the parameter vector of a linear predictor. The proposed method is based on modified Cholesky (LD) factorisation of an augmented correlation matrix. In essence the algorithm suggested is a modified version of the method presented by Ljung and Soderstrom, with distinct advantages. Although computationally the burden of both methods is the same, the proposed algorithm has been mathematically restructured in such a way that a computational step is eliminated. This results in considerable simplifications when implementing the suggested algorithm in a systolic array configuration, since the problem reduces to the processing of a single matrix structure.