Error analysis for a class of numerical differentiator
نویسندگان
چکیده
Résumé Ce rapport est consacré aux estimations des dérivées. Contrairement à la procédure de régularisation de Tikhonov, nous utilisons un cadre algébrique récent qui conduit enfin à une projection dans la base de polynômes de Jacobi, afin d’estimer des dérivées des signaux bruités. Aucune information sur les propriétés statistiques du bruit est requise. Nous donnons quelques résultats concernant le choix des paramètres dans cette méthode de manière à minimiser l’erreur due au bruit et les erreurs d’approximation. De plus, deux nouveaux estimateurs centraux fondés sur telles techniques algébriques de la différenciation sont introduits. Une comparaison est faite entre ces estimations et quelques méthodes classiques de la différentiation numérique.
منابع مشابه
Time-varying high-gain observers for numerical differentiation
In this note, we propose high-gain numerical differentiators for estimating the higher derivatives of a given signal. We consider timevarying high-gain vectors converging exponentially to the high-gain vectors introduced by Esfandiari and Khalil in an earlier paper. The dynamics of these time-varying high-gain vectors can be chosen in order to achieve specific objectives, such as peaking attenu...
متن کاملTwo-step differentiator for delayed signal
Abstract: This paper presents a high-order differentiator for delayed measurement signal. The proposed differentiator not only can correct the delay in signal, but aslo can estimate the undelayed derivatives. The differentiator consists of two-step algorithms with the delayed time instant. Conditions are given ensuring convergence of the estimation error for the given delay in the signals. The ...
متن کاملSliding-mode observers for systems with unknown inputs: A high-gain approach
The problem of designing sliding-mode observers for systems with unknown inputs is considered when the so-called observer matching condition is not satisfied. This condition severely restricts the applicability of sliding-mode observers. To circumvent the observer matching condition, thereby broadening the class of systems for which sliding-mode observers can be constructed, a possible method i...
متن کاملFullband Higher Order Differentiators Based on LS Method
This paper deals with the Least Squares (LS) design of fullband higher order digital differentiators. The contribution extends a previous work on the problem presenting some new results (analytical, graphical and numerical) and conclusions. The design method for even and odd arbitrary k-th order differentiators based on the LS integral error criterion is considered. A few new closedform relat...
متن کاملAn application of Measurement error evaluation using latent class analysis
Latent class analysis (LCA) is a method of evaluating non sampling errors, especially measurement error in categorical data. Biemer (2011) introduced four latent class modeling approaches: probability model parameterization, log linear model, modified path model, and graphical model using path diagrams. These models are interchangeable. Latent class probability models express l...
متن کامل