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Improvement of the fast recursive least-squares algorithms via normalization: A comparative study

This paper deals with the derivation and the properties of fast optimal least-squares algorithms, and particularly with their normalization. It is shown how the well-known fast Kalman algorithm, written in the most general form, can be normalized through a purely algebraic point of view, leading to the normalized least-squares transversal filter derived by Cioffi, Kailath, and Lev-Ari from the geometric approach. An improved form of the algorithm is presented. The different algorithms have been compared from a practical point of view as regards their convergence, initialization procedures, complexity, and numerical properties. Normalized transversal algorithms are shown to be interesting because of their nice structured form, simplicity of conception, and improved good numerical behavior.