Analyse non standard du bruit

TL;DR

This paper introduces a new mathematical framework based on nonstandard analysis for non-asymptotic noise estimation in sensors, eliminating the need for statistical noise analysis and enabling applications to various noise types.

Contribution

It develops a nonstandard formalization of oscillating functions to create innovative noise estimation techniques that are non-asymptotic and do not rely on statistical assumptions.

Findings

Framework applicable to multiplicative noises

Effective for estimating window lengths

Handles burst errors efficiently

Abstract

Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin, an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical analysis of the noises corrupting any sensor. Various applications are deduced for multiplicative noises, for the length of the parametric estimation windows, and for burst errors.