Infoscience

Thesis

La détection de périodicités cachées

This thesis is a small part of the preparation of the launch of the Gaia mission, a satellite of the European Space Agency (ESA). One of the goals of the mission is to perform a classification among variable stars considering different attributes. Periodic behavior in the observed light curve is such an attribute. It is of importance to determine these hidden cycles with as high an accuracy as possible. A key difficulty is connected to the fact that observations are taken at irregularly distributed time points. Classical methods of frequency analysis do not work in this situation. In a first step, we made a catalogue of potential solutions and applied them to real and simulated data. The performances have been compared in order to select the best method. In a second step, we considered the asymptotic performance of estimators based on regression methods. We derived the asymptotic distribution under the hypothesis that the observation model contains a periodic signal with period P0 > 0, continuous and square integrable on [0; P0), with Gaussian correlated errors. The irregular sampling has to satisfy the asymptotic property that the whole interval [0, P0) can be observed. We have also considered the special case of a periodic signal with period P0 > 0, piecewise constant on [0; P0) and the asymptotic distribution of the estimator. If an irregular sampling scheme does not satisfy the asymptotic property that the signal can be fully observed, the period can still be estimated reliably. We determined the asymptotic distribution of an estimator in a particular situation and under the assumption that the observation model contains a periodic signal with period P0 > 0, continuous and square integrable on [0; P0), and is observed with additive errors that are independent and identically distributed.

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