Article

Parameter identification for nonlinear systems: Guaranteed confidence regions through LSCR

Università degli Studi di Brescia, Brescia, Lombardy, Italy
Automatica (Impact Factor: 3.02). 08/2007; 43(8):1418-1425. DOI: 10.1016/j.automatica.2007.01.016
Source: DBLP

ABSTRACT

In this paper we consider the problem of constructing confidence regions for the parameters of nonlinear dynamical systems. The proposed method uses higher order statistics and extends the LSCR (leave-out sign-dominant correlation regions) algorithm for linear systems introduced in Campi and Weyer (2005, Guaranteed non-asymptotic confidence regions in system identification. Automatica 41(10), 1751-1764. Extended version available athttp://www.ing.unibs.it/∼campi� ). The confidence regions contain the true parameter value with a guaranteed probability for any finite number of data points. Moreover, the confidence regions shrink around the true parameter value as the number of data points increases. The usefulness of the proposed approach is illustrated on some simple examples. 2007 Elsevier Ltd. All rights reserved.

Full-text preview

Available from: unibs.it
  • Source
    • "There is a growing interest for developing methods that do not rely on the central limit theorem or on Gaussian assumptions about the noise ([3], [4], [5], [6], [7]). The 16 th IFAC Symposium on System Identification had a plenary session dedicated to this topic [2]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: Hypothesis testing methods that do not rely on exact distribution assumptions have been emerging lately. The method of sign-perturbed sums (SPS) is capable of characterizing confidence regions with exact confidence levels for linear regression and linear dynamical systems parameter estimation problems if the noise distribution is symmetric. This paper describes a general family of hypothesis testing methods that have an exact user chosen confidence level based on finite sample count and without relying on an assumed noise distribution. It is shown that the SPS method belongs to this family and we provide another hypothesis test for the case where the symmetry assumption is replaced with exchangeability. In the case of linear regression problems it is shown that the confidence regions are connected, bounded and possibly non-convex sets in both cases. To highlight the importance of understanding the structure of confidence regions corresponding to such hypothesis tests it is shown that confidence sets for linear dynamical systems parameter estimates generated using the SPS method can have non-connected parts, which have far reaching consequences.
    Full-text · Article · Nov 2014 · Automatica
  • Source
    • "This is especially important if one wants to estimate physically meaningful parameters of some knowledge-based model in physics, chemistry, biology , etc., or if decisions have to be taken on the basis of the numerical values of the model parameters to tune controllers or to detect faults, for instance. A key issue is drawing conclusions that are as little prejudiced as possible, and the approach recently proposed by Campi et al. for this purpose [1] [2] [3] is particularly attractive, as it makes it possible to obtain exact, non-asymptotic confidence regions under relatively mild assumptions on the noise distribution. A difficulty with this approach, however, is the numerical characterization of these confidence regions. "
    [Show abstract] [Hide abstract]
    ABSTRACT: In parameter estimation, it is often desirable to supplement the estimates with an assessment of their quality. A new family of methods proposed by Campi et al. for this purpose is particularly attractive, as it makes it possible to obtain exact, non-asymptotic confidence regions under mild assumptions on the noise distribution. A bottleneck of this approach, however, is the numerical characterization of these confidence regions. So far, it has been carried out by gridding, which provides no guarantee as to its results and is only applicable to low dimensional spaces. This paper shows how interval analysis can contribute to removing this bottleneck.
    Full-text · Article · Nov 2013 · Automatica
  • Source
    • "Cette hypothèse donne un sensà la notion de vraie valeur pour le vecteur des paramètres. Dans [1] [2] [3], deux nouvelles approches nommées LSCR et SPS sont introduites pour obtenir une caractérisation exacte de 1. Ce travail a ´ eté en partie financé par l'ANR CPP. l'incertitude paramétrique dans des conditions non-asymptotiques . "

    Full-text · Article · Sep 2013
Show more