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In Global Navigation Satellite Systems, the on-board time has to be modelized and predicted in order to broadcast the time parameters to final users. As a consequence, the time prediction performance of the on-board clocks has to be characterized. In order to estimate the time uncertainty of the on-board oscillator, a linear or parabolic fit is performed… (More)

- David A Howe, Ron L Beard, Charles A Greenhall, François Vernotte, William J Riley, Trudi K Peppler
- IEEE transactions on ultrasonics, ferroelectrics…
- 2005

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)

- F. Vernotte, G. Zalamansky, E. Lantz
- 1998

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 cutoff frequency. The effects of spectral aliasing for the white-phase noise… (More)

- F. Vernotte, G. Zalamansky, E. Lantz
- 1998

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 cutoff 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)

- François Vernotte
- IEEE transactions on ultrasonics, ferroelectrics…
- 2002

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)

- François Vernotte, Éric Lantz
- IEEE transactions on ultrasonics, ferroelectrics…
- 2012

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)

- P. Allison, J. Bellido, +11 authors F. Vernotte

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)

- F Vernotte, G Zalamansky
- IEEE transactions on ultrasonics, ferroelectrics…
- 1999

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)

- Francois Vernotte, Michel Lenczner, Pierre-Yves Bourgeois, Enrico Rubiola
- IEEE transactions on ultrasonics, ferroelectrics…
- 2016

This paper introduces the parabolic variance (PVAR), a wavelet variance similar to the Allan variance (AVAR), based on the linear regression (LR) of phase data. The companion article arXiv:1506.05009 [physics.ins-det] details the Ω frequency counter, which implements the LR estimate. The PVAR combines the advantages of AVAR and modified AVAR (MVAR). PVAR is… (More)

- Eric Lantz, Francois Vernotte
- IEEE Signal Processing Magazine
- 2013

What 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)