A unified treatment of fast algorithms for identification†

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Abstract
We propose a unified description of several so-called fast, algorithms. The projection operator technique is used to derive least-squares ladder (or lattice) algorithms in the filter and the predictor forms. This technique, usually associated with orthogonal projection operations, is extended to oblique projections. The first application is an easy derivation of the ‘ exact ’ instrumental variable ladder algorithm which, to our knowledge, has not previously been described in the literature. A second application is a new derivation, based on the operator technique, of an algorithm for the fast calculation of gain matrices for recursive estimation schemes.

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