A mathematical model for the atomic clock error in case of jumps

We extend the mathematical model based on stochastic differential equations describing the error gained by an atomic clock to the cases of anomalous behavior including jumps and an increase of instability. We prove an exact iterative solution that can be useful for clock simulation, prediction, and interpretation, as well as for the understanding of the impact of clock error in the overall system in which clocks may be inserted as, for example, the Global Satellite Navigation Systems

Time metrology in Global Navigation Satellite Systems

Precise timekeeping is at the basis of any Global Navigation Satellite System. In this thesis, after an extensive introduction on time and frequency metrology, some of the basic time-related aspects of navigation systems are discussed, and new ideas and solutions are presented. In the first part of the work, the most relevant innovative contributions are related to the mathematical clock model and to the stability analysis of atomic clocks affected by frequency jumps, as well as to the development of a new averaging algorithm for the generation of a robust time scale from an ensemble of atomic clocks. In the second part, devoted to the role of timekeeping in satellite navigation systems, the innovative contributions are mainly about: a revision of the relativistic corrections; the development and testing of a new composite clock, which could be used as a system time scale for the Galileo system; a study on the impact of the light-shift effect on the timing performance of GPS rubidium clocks; the development of a new recursive clock anomalies detector, as well as a discussion about the possible implementations of a clock anomalies detector and a compensation system for on-board applications

Is the physics within the Solar system really understood?

A collection is made of presently unexplained phenomena within our Solar system and in the universe. These phenomena are (i) the Pioneer anomaly, (ii) the flyby anomaly, (iii) the increase of the Astronomical Unit, (iv) the quadrupole and octupole anomaly, and (v) Dark Energy and (vi) Dark Matter. A new data analysis of the complete set of Pioneer data is announced in order to search for systematic effects or to confirm the unexplained acceleration. We also review the mysterious flyby anomaly where the velocities of spacecraft after Earth swing--bys are larger than expected. We emphasize the scientific aspects of this anomaly and propose systematic and continuous observations and studies at the occasion of future flybys. Further anomalies within the Solar system are the increase of the Astronomical Unit and the quadrupole and octupole anomaly. We briefly mention Dark Matter and Dark Energy since in some cases a relation between them and the Solar system anomalies have been speculated.Comment: 22 pages, 3 figures, submitted for the proceedings of the 359th WE-Heraeus Seminar on "Lasers, Clocks, and Drag-Free: Technologies for Future Exploration in Space and Tests of Gravity

Characterizing changes in the noise statistics of GNSS space clocks with the dynamic Allan variance

The dynamic Allan variance (DAVAR) is a tool for the characterization of precise clocks. Monitoring anomalies of precise clocks is essential, especially when they are employed onboard the satellites of a global navigation satellite system (GNSS). When an anomaly occurs, the DAVAR changes with time, its shape depending on the type of anomaly occurred. We obtain the analytic DAVAR for a change of variance in the clock noise, an anomaly with critical effects on the clock performances. This result is helpful when the clock health is monitored by observing the DAVAR

An Efficient and Configurable Preprocessing Algorithm to Improve Stability Analysis

partially_open6The Allan variance (AVAR) is widely used to measure the stability of experimental time series. Specifically, the AVAR is commonly used in space applications, such as for monitoring the clocks of the Global Navigation Satellite Systems (GNSSs). In these applications the experimental data present some peculiar aspects which are not generally encountered when the measurements are carried out in a laboratory. Space clocks data can in fact present outliers, jumps and missing values which corrupt the clock characterization. Therefore, an efficient preprocessing is fundamental to ensure a proper data analysis and to improve the stability estimation performed with the AVAR or other similar variances. In this work we propose a preprocessing algorithm and its implementation in a robust software code (in MATLAB® language) able to deal with time series of experimental data affected by nonstationarities and missing data; our method is properly detecting and removing anomalous behaviors, hence making the subsequent stability analysis more reliable.openSesia, Ilaria; Cantoni, Elena; Cernigliaro, Alice; Signorile, Giovanna; Fantino, Gianluca; Tavella, PatriziaSesia, Ilaria; Cantoni, Elena; Cernigliaro, Alice; Signorile, Giovanna; Fantino, Gianluca; Tavella, Patrizi

Progress in Atomic Fountains at LNE-SYRTE

We give an overview of the work done with the Laboratoire National de M\'etrologie et d'Essais-Syst\`emes de R\'ef\'erence Temps-Espace (LNE-SYRTE) fountain ensemble during the last five years. After a description of the clock ensemble, comprising three fountains, FO1, FO2, and FOM, and the newest developments, we review recent studies of several systematic frequency shifts. This includes the distributed cavity phase shift, which we evaluate for the FO1 and FOM fountains, applying the techniques of our recent work on FO2. We also report calculations of the microwave lensing frequency shift for the three fountains, review the status of the blackbody radiation shift, and summarize recent experimental work to control microwave leakage and spurious phase perturbations. We give current accuracy budgets. We also describe several applications in time and frequency metrology: fountain comparisons, calibrations of the international atomic time, secondary representation of the SI second based on the 87Rb hyperfine frequency, absolute measurements of optical frequencies, tests of the T2L2 satellite laser link, and review fundamental physics applications of the LNE-SYRTE fountain ensemble. Finally, we give a summary of the tests of the PHARAO cold atom space clock performed using the FOM transportable fountain.Comment: 19 pages, 12 figures, 5 tables, 126 reference