Identification of continuous-time errors-in-variables models

Abstract

A novel direct approach for identifying continuous-time linear dynamic errors-in-variables models is presented in this paper. The effects of the noise on the state-variable filter outputs are analyzed. Subsequently, a few algorithms to obtain consistent continuous-time parameter estimates in the errors-invariables framework are derived. It is also possible to design search-free algorithms within our framework. The algorithms can be used for nonuniformly sampled data. The asymptotic distributions of the estimates are derived. The performances of the proposed algorithms are illustrated with some numerical simulation examples.

Identification of nonlinear dynamic models of electrostatically actuated MEMS

“…In this paper, a method of bias estimation is proposed and described in paragraph 3.5. Several others methods can be found for example in (Mahata and Garnier (2006);Young (1970); Söderström and Mahata (2002); Welsh et al (2007); Mahata and Garnier (2005)). …”

“…(17) Such a transformation is indeed often used to mitigate the problem of ill-conditioning of the computation of derivatives from sampled noisy data (Young (1965b); Mahata and Garnier (2006)) (see paragraph 3.4).…”

“…The knowledge-model (3,4,5) has the particularity to be linear with respect to parameters I, µ 0 , K, and functions k and v. To take advantage to this linearity, an identification method based on the minimization of the equation error (Mahata and Garnier (2006); Garnier and Wang (2008)) will be used. To apply such a method, the model has first to be transformed by means of suitable global operations, in such a way that the new equivalent model formulation is specifically adapted to the identification problem, thanks to the following essential properties: first, the linearity with respect to the parameters to be identified is preserved, and second, the continuous dependence on noise measurements is restored, this last property being impossible to get in the initial form of the model because of the presence of derivative operators.…”

“…Different kind of filters can be considered (Young (1965a); Saha et al (1982); Sagara and Zhao (1990); Jemni and Trigeassou (1996)). In this paper, a state variable filter (Young (1965b); Mahata and Garnier (2006); Garnier and Wang (2008)), namely (in this case) a second order filter (because the maximal degree of derivatives involved in model (17) is two) obtained by composition of identical first order filters, is used: …”

Unifying some higher-order statistic-based methods for errors-in-variables model identification

“…(Mahata and Garnier 2006, Mahata 2007, Diversi et al 2007, Hong et al 2007, Pintelon and Schoukens 2007, Thil et al 2007, Söderström 2008, Thil et al 2008b), and a survey paper gathering most of the known developments has been recently published (Söderström 2007). …”