Parametric Estimation: Improvement Of The Rls Algorithm Using A Differential Approach
| Autor: | J.F. Roux, Denis Kouame, Abdeldjalil Ouahabi |
|---|---|
| Přispěvatelé: | Laboratoire Ultrasons Signaux et Instrumentation (LUSSI), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Traitement et Compréhension d’Images (IRIT-TCI), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université de Tours-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 1999 |
| Předmět: |
Mathematical optimization
0206 medical engineering 02 engineering and technology [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing Computer Science::Systems and Control unified operators Parametric estimation Diagonal matrix recursive least squares 0202 electrical engineering electronic engineering information engineering Electrical and Electronic Engineering Mathematics Differential method Recursive least squares filter Estimation theory Covariance matrix System identification 020206 networking & telecommunications 020601 biomedical engineering Computer Science::Other cost function Rate of convergence Computer Science::Sound Hardware and Architecture Mechanics of Materials Modeling and Simulation identification Algorithm ARMA Software |
| Zdroj: | Scopus-Elsevier International Journal of Modelling and Simulation International Journal of Modelling and Simulation, ACTA Press, 1999, 19 (1), pp.15--23. ⟨10.1080/02286203.1999.11760402⟩ |
| ISSN: | 1925-7082 0228-6203 |
| DOI: | 10.1080/02286203.1999.11760402 |
| Popis: | International audience; This paper describes a new computational method for recursive least squares (RLS) algorithm. It is well known that the initial values for computing RLS estimates should be chosen to guarantee the existence of the estimates at each step, that the initial covariance matrix may affect the convergence rate, and that a blow-up phenomenon (infinite increase of the covariance matrix) can appear. Much research has focused on each of these problems, but heavy computations and different specific design parameters result from the most common solutions. We propose an alternative simple algorithm that reaches a trade-off between the advantages of the well-known RLS algorithms and of the more complex computations. The proposed algorithm modifies the prior additional term used in the cost function. This modified term is updated during the recursion, in the context of a differential formalism. The aim of this formalism is, first, to provide valid computations and properties in both discrete and continuous time domains, and to yield the variations of the parameters at each step. Second, in the particular case of discrete time this formalism provides very good numerical properties. The methodology in developing this approach is quite different from the previous work on RLS estimation. We demonstrate that our algorithm, compared with RLS algorithm, leads to a higher convergence rate. It also offers a closer tracking of parameters in nonstationary case and satisfactory results in the presence of blow-up situations. This goal is achieved without significant additional computations, and the behaviour of the approach is illustrated through simulations. |
| Databáze: | OpenAIRE |
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