Francois Vernotte

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The prediction of very-long-term time stability is a key issue in various fields, such as time keeping, obviously, but also navigation and spatial applications. This is usually performed by extrapolating the measurement data obtained by estimators such as the Allan variance, modified Allan variance, Hadamard variance, etc. This extrapolation may be assessed(More)
It is well-known that low frequency noises (flicker FM and random walk FM) are not stationary; it is not possible to define either the mean value or the (true) variance. Therefore, the use of a stationary approach yields convergence problems unless a low cut-off frequency is introduced, the physical meaning of which is not clear. As an example, in the case(More)
The noise levels given by spectral analysis are relevant parameters for the characterization of the time-domain stability of oscillators. The estimation of the noise levels of a sampled signal may be achieved with variances even if the sampling frequency is far lower than the high cut-off frequency. The effects of spectral aliasing for the white-phase noise(More)
We describe a method based on the total deviation approach whereby we improve the confidence of the estimation of the Hadamard deviation that is used primarily in global positioning system (GPS) operations. The Hadamard-total deviation described in this paper provides a significant improvement in confidence indicated by an increase of 1.3 to 3.4 times the(More)
We showed in Part I of this paper [1] that the estimation of the white-phase noise level of a sampled signal may be achieved with variances even if the sampling frequency is far lower than the high cut-off frequency. In Part II, the effects of spectral aliasing for the different types of noise are reviewed. The responses of the Allan variance and the(More)
This article presents the project of creating a composite clock, the advances in its realization and the technical choices. The goal is to generate an output signal which combines the advantages of each clock, the long-term stability for the cesium clock, the mid-term stability for the hydrogen maser clock, and the short-term stability for the(More)
The power spectral density of frequency fluctuations of an oscillator is generally modeled as a sum of power laws with integer exponents (from -2 to +2). However, a power law with a fractional exponent may exist. We propose a method for measuring the level of such a noise process and determining the probability density of the exponent. This yields a(More)
Reconstruction of cosmic ray arrival directions for Surface Detectors (SD) and Fluorescence Detectors (FD) of the Pierre Auger Observatory requires accurate timing (25 nanoseconds or better) between measurements at individual detectors and instrument triggers. Timing systems for both SD and FD are based on Motorola Oncore UT+ GPS receivers installed into(More)
hat is the best estimator for assessing a parameter of a probability distribution from a small number of measurements? Is the same answer valid for a location parameter like the mean as for a scale parameter like the variance? It is sometimes argued that it is better to use a biased estimator with low dispersion than an unbiased estimator with a higher(More)
The traditional GPS common view technique, using C/A code receivers, is the main time transfer method used by various timing laboratories over the world. Moreover, this method is used to realize the TAI (Temps Atomique International) and the TA (F) (Temps Atomique Français). Clock offsets between laboratory clocks are determined according to a fixed(More)