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A continuous-time framework for least squares parameter estimation

Samer Riachy 1, 2, *
* Corresponding author
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : This paper proposes a continuous-time framework for the least-squares parameter estimation method through evolution equations. Nonlinear systems in the standard state space representation that are linear in the unknown, constant parameters are investigated. Two estimators are studied. The first one consists of a linear evolution equation while the second one consists of an impulsive linear evolution equation. The paper discusses some theoretical aspects related to the proposed estimators: uniqueness of a solution and an attractive equilibrium point which solves for the unknown parameters. A deterministic framework for the estimation under noisy measurements is proposed using a Sobolev space with negative index to model the noise. The noise can be of large magnitude. Concrete signals issued from an electronic device are used to discuss numerical aspects.
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https://hal.inria.fr/hal-01080376
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Submitted on : Wednesday, November 5, 2014 - 10:26:44 AM
Last modification on : Tuesday, September 29, 2020 - 12:24:10 PM
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Samer Riachy. A continuous-time framework for least squares parameter estimation. Automatica, Elsevier, 2014, pp.6. ⟨10.1016/j.automatica.2014.10.055⟩. ⟨hal-01080376⟩

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