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

Generating a real-time time scale making full use of the available frequency standards

We propose a time-scale algorithm for the automated generation of a real-time time scale, making full use of the frequency standards available in a typical time laboratory. The time-scale algorithm is made by a pre-processing stage, a steering algorithm, and a post-processing stage. In particular, in this work we propose a set of three different steering algorithms, running in parallel and eventually producing a unique steering correction to be applied to a master clock. Each algorithm is based on a different steering reference, namely, a primary frequency standard, an ensemble clock, and the Coordinated Universal Time (UTC), or its rapid version, UTCr. Pre- and post-processing stages help to provide robustness and to cope with data gaps. The proposed algorithms have been extensively and successfully tested off-line, on real data from the time laboratory of the Italian National Institute of Metrological Research (INRiM), where an on-line test has also been performed in the period May-October 2019. Then, since the mid of January 2020, the time-scale algorithm has been applied for the generation of the Italian legal time scale, UTC(IT). We show here the results of the off-line tests and of the 5-month on-line test. The proposed strategy can be used wherever a stable, accurate, and robust time reference is needed, e.g. for a local realization of UTC in a laboratory k, UTC(k), or for generating the reference system time of a global navigation satellite system (GNSS)

Rubidium clock lamplight variations and long-term frequency instability: First analyses of multiyear GPS data

In the rubidium atomic frequency standard (RAFS), an rf-discharge lamp produces the device's atomic signal. As a consequence of the light-shift effect, variations in the lamplight's intensity result in variations in the RAFS' output frequency. While the basic physics of the light-shift is reasonably well understood, its operational implications for global navigation satellite system (GNSS) performance is only beginning to be fully appreciated. Here, we describe first results examining decade-long histories of on-orbit GPS RAFS lamplight variations and GPS RAFS frequency variations. Our preliminary analyses have focused on one space vehicle's RAFS, and our conclusions are tempered by that present limitation. Nevertheless, our analyses suggest that a RAFS' long-term frequency stability (i.e., τ 106 sec) is likely lower-bounded by the lamp's intensity fluctuations. Moreover, considering the light-shift coefficient for this one particular RAFS over 12 years, we find that the data do not support Camparo's hypothesis regarding RAFS frequency aging and a time-varying light-shift coefficient

The Allan variance in the presence of a compound Poisson process modelling clock frequency jumps

Atomic clocks can be affected by frequency jumps occurring at random times and with a random amplitude. The frequency jumps degrade the clock stability and this is captured by the Allan variance. In this work we assume that the random jumps can be modelled by a compound Poisson process, independent of the other stochastic and deterministic processes affecting the clock stability. Then, we derive the analytical expression of the Allan variance of a jumping clock. We find that the analytical Allan variance does not depend on the actual shape of the jumps amplitude distribution, but only on its first and second moments, and its final form is the same as for a clock with a random walk of frequency and a frequency drift. We conclude that the Allan variance cannot distinguish between a compound Poisson process and a Wiener process, hence it may not be sufficient to correctly identify the fundamental noise processes affecting a clock. The result is general and applicable to any oscillator, whose frequency is affected by a jump process with the described statistics

The J2 relativistic periodic component of GNSS satellite clocks

The frequency of space atomic clocks on board the satellites of global navigation satellite systems, as observed from the ground, shows different types of periodic variations, among which the J2 relativistic component due to the Earth oblateness. This component is often so small to be masked by the clock noise, but nonetheless it affects the stability of the clock’s frequency. Here, after reviewing the theory of the J2 relativistic effect, we carefully analyze GPS clocks’ data looking for the J2 periodic component. Moreover, we study its effect on the clock’s Allan deviation, showing how it deforms the shape of the bump visible at an averaging time of about one half of the satellites’ orbital period, due to periodic frequency variations of other origin

A recursive clock anomalies detector with double exponential smoothing

A recursive clock anomalies detectro based on double exponential smoothing able to detect frequency jumps, frequency drift changes and variance changes, with possible applications in GNSS. Test on real and simulated data

Atomic clocks and the continuous-time random-walk

Atomic clocks play a fundamental role in many fields, most notably they generate Universal Coordinated Time and are at the heart of all global navigation satellite systems. Notwithstanding their excellent timekeeping performance, their output frequency does vary: it can display deterministic frequency drift; diverse continuous noise processes result in nonstationary clock noise (e.g., random-walk frequency noise, modelled as a Wiener process), and the clock frequency may display sudden changes (i.e., “jumps”). Typically, the clock’s frequency instability is evaluated by the Allan or Hadamard variances, whose functional forms can identify the different operative noise processes. Here, we show that the Allan and Hadamard variances of a particular continuous-time random-walk, the compound Poisson process, have the same functional form as for a Wiener process with drift. The compound Poisson process, introduced as a model for observed frequency jumps, is an alternative to the Wiener process for modelling random walk frequency noise. This alternate model fits well the behavior of the rubidium clocks flying on GPS Block-IIR satellites. Further, starting from jump statistics, the model can be improved by considering a more general form of continuous-time random-walk, and this could bring new insights into the physics of atomic clocks