Patrizia Tavella

The clock model and its relationship with the Allan and related variances

The clock errors are modeled by stochastic differential equations (SDE) and the relationships between the diffusion coefficients used in SDE and the Allan variance, a typical tool used to estimate clock noise, are derived. This relationship is fundamental when a mathematical clock model is used, for example in Kalman filter, noise estimation, and clock prediction activities.

Comparative Study of Time Scale Algorithms

The statistical generation of an accurate, stable and reliable time scale from a clock ensemble calls for an efficient algorithm. Here we present a comparative study which points out conceptual differences and similarities between two different types of time scale algorithm used worldwide: 1. ALGOS (BIPM), which produces, bimonthly, the international reference TAI (temps atomique international) at the Bureau International des Poids et Mesures (Sevres, France), and 2. AT1 (NIST), from which is obtained, in real-time, the AT1 time scale at the National Institute of Standards and Technology (Boulder, Colorado, USA). These two algorithms rely basically upon weighted averages of clock readings, but the weight determination and the frequency prediction are of different types because they are adapted to different needs and to the peculiarities of the available time measurements.

The dynamic Allan variance

We present and discuss the dynamic Allan variance, a measure of the time-varying stability of an atomic clock. First, the dynamic Allan variance is mathematically defined, then its behavior is extensively tested on simulated and experimental data. The results prove the validity and the effectiveness of the proposed new tool.

Detection of Anomalies in the Behavior of Atomic Clocks

In this paper, the problem of identifying variations in the nature of atomic clock noise is addressed. Two methods are proposed. One method is based on a generalized likelihood ratio test (GLRT), and the other is based on the dynamic Allan variance (DAVAR), which is a representation of the instantaneous clock stability that is able to point out possible nonstationary behaviors. Both methods efficiently track variations in the experimental clock data and, thus, appear as suitable tools for the detection of atomic clock anomalies

Experimental assessment of the time transfer capability of precise point positioning (PPP)

In recent years, many national timing laboratories have installed geodetic global positioning system (GPS) receivers together with their traditional GPS/GLONASS common view (CV) receivers and two way satellite time and frequency transfer (TWSTFT) equipment. A method called precise point positioning (PPP) is in use in the geodetic community allowing precise recovery of geodetic GPS receiver position, clock phase and tropospheric delay by taking advantage of the International GNSS Service (IGS) precise products. Natural Resources Canada (NRCan) has developed software implementing the PPP and a previous assessment of the PPP as a promising time transfer method was carried out at Istituto Elettrotecnico Nazionale (IEN) in 2003. This paper reports on a more systematic work performed at IEN and NRCan to further characterize the PPP method for time transfer application, involving data from nine national timing laboratories. Dual-frequency GPS observations (pseudorange and carrier phase) over the last ninety days of year 2004 were processed using the NRCan PPP software to recover receiver clock estimates at five minute intervals, using the IGS final satellite orbit and clock products. The quality of these solutions is evaluated mainly in terms of short-term noise. In addition, the time and frequency transfer capability of the PPP method were assessed with respect to independent techniques, such as TWSTFT, over a number of European and Transatlantic baselines

The characterization of clock behavior with the dynamic Allan variance

We introduce the dynamic Allan variance, a quantity that characterizes the variation in time of the stability of an atomic clock. We connect the dynamic Allan variance to the Wigner spectrum, a time-frequency representation that can reveal the time-varying frequencies generally present in the clock error noise under nonstationary conditions. We also propose a practical implementation of the dynamic Allan variance for quasi-stationary clock noises, and we show numerical results that prove the validity of our approach, both on simulated and real data.

Application of the Dynamic Allan Variance for the Characterization of Space Clock Behavior

Due to their stability atomic clocks represent the core of navigation systems such as GPS and the future European Galileo system. To identify possible anomalies, it is fundamental to detect when the clock stability varies with time. The dynamic Allan variance (DAVAR) makes this monitoring process possible. We extend the DAVAR to the case of a time series with missing data, and we analyze the presence of periodic behaviors, two common phenomena in space clocks.

Detection and identification of atomic clock anomalies

When an anomaly occurs in an atomic clock, its stability and frequency spectrum change with time. The variation with time of the stability can be evaluated with the dynamic Allan variance. The variation with time of the frequency spectrum can be described with the spectrogram, a time–frequency distribution. We develop a method that uses the dynamic Allan variance and the spectrogram to detect and to identify the typical anomalies of an atomic clock. We apply the method to simulated data.

The In-Orbit performances of GIOVE clocks

The Galileo In-Orbit Validation Element (GIOVE) is an experiment led by the European Space Agency (ESA) aimed at supporting the on-going implementation of Galileo, the European global navigation satellite system (GNSS). Among the objectives of the GIOVE Mission are the validation and characterization of the on-board clock technologies. The current baseline technologies for on-board clocks are the rubidium atomic frequency standard (RAFS) and the passive hydrogen maser (PHM). Both technologies have been validated and qualified on ground and are now being further validated in a representative in-orbit environment aboard 2 spacecrafts, GIOVE-A and GIOVE-B. This paper presents the results obtained in the frame of the GIOVE experimentation. The behavior and performances of the clock technologies on board both spacecrafts has been investigated and analyzed in terms of operation, frequency stability, and clock prediction error after more than 3 years of operation for GIOVE-A and almost one year for GIOVE-B. In addition, relativistic frequency shifts of GIOVE spacecrafts have been investigated.

The Evaluation of Uncertainties in [UTC-UTC(k)]

This work presents a study of the determination of uncertainties in [UTC − UTC(k)] needed for publication in the Bureau Inernational des Poids et Mesuress (BIPMs) Circular T and the Key Comparison Database, as required by the Mutual Recognition Arrangement. In the first part of the paper, an analytical solution based on the law of the propagation of uncertainty is derived. In the second part, the solution is verified numerically using the software used by the BIPM for the generation of UTC.