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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)
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)
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 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)
The Allan variance was introduced 50 years ago for analyzing the stability of frequency standards. In addition to its metrological interest, it may be also considered as an estimator of the large trends of the power spectral density (PSD) of frequency deviation. For instance, the Allan variance is able to discriminate different types of noise characterized(More)
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)
We analyze the Allan variance estimator as the combination of discrete-time linear filters. We apply this analysis to the different variants of the Allan variance: the overlapping Allan variance, the modified Allan variance, the Hadamard variance and the overlapping Hadamard variance. Based upon this analysis, we present a new method to compute a new(More)
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