Metrology and statistics: from clocks to millisecond pulsars

Time is the physical quantity that is measured with the greatest precision, far ahead of all the others. Recent advances in atomic clocks have made it possible to achieve relative stabilities of the order of a few 10⁻¹⁸, thus corresponding to an uncertainty of about one second in the age of the Universe. However, it is not because these uncertainties become ridiculously small that they should be neglected, quite the contrary. The aim of this work is to contribute to improving the determination of these uncertainties. It is divided in two parts and concerns the fine characterization and improvement of a set of estimation methods.

The first part of the present work consists in describing a procedure to determine the jumps which can affect the time links used in the Coordinated Universal Time (UTC), calculated by the BIPM. This tool, based on a Kalman filter, should correctly determine the date of the steps and their magnitude, mainly for time steps, and give a warning to the BIPM Time Department about this unexpected problem. This warning will help to understand the nature of the steps which, in some cases, can affect the behavior of UTC. A critical example is the receiver calibration causing a step in time links and potentially impacting UTC behavior. To ensure the long-term stability of UTC, it is crucial to verify the data and identify problems.

The second part of the work mainly concerns a detailed analysis of frequency instabilities in terms of Bayesian statistics. In particular the objective is to obtain reliable confidence intervals around the measurements of the power spectrum of red noise processes at the lowest frequencies, e.g. the observation of millisecond pulsars in radio astronomy. Thus it is only possible to average on simultaneous observation of multiple instruments. We compare 95 % upper limit of the red noise parameter using the spectrum average and cross-spectrum. Checked by massive Monte Carlo simulations, the cross-spectrum estimator leads to the variance-Gamma distribution with two instruments and a generalization to n instruments based on the Fourier transform of characteristic functions is provided.

atomic clocks, bayesian statistics, confidence interval, cross-spectrum, metrology, phase jump, probability density function, spectrum average, time-frequency analysis, time stability

Full document (EN) : TEL-04083649