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

Nonlinear Transformation of Differential Equations into Phase Space

Time-frequency representations transform a one-dimensional function into a two-dimensional function in the phase-space of time and frequency. The transformation to accomplish is a nonlinear transformation and there are an infinite number of such transformations. We obtain the governing differential equation for any two-dimensional bilinear phase-space function for the case when the governing equation for the time function is an ordinary differential equation with constant coefficients. This connects the dynamical features of the problem directly to the phase-space function and it has a number of advantages

Approximation of the Wigner Distribution for Dynamical Systems Governed by Differential Equations

A conceptually new approximation method to study the time-frequency properties of dynamical systems characterized by linear ordinary differential equations is presented. We bypass solving the differential equation governing the motion by writing the exact Wigner distribution corresponding to the solution of the differential equation. The resulting equation is a partial differential equation in time and frequency. We then show how it lends itself to effective approximation methods because in the time frequency plane there is a high degree of localization of the signal. Numerical examples are given and compared to exact solutions

identifying nonstationary clock noises in navigation systems

The stability of the atomic clocks on board the satellites of a navigation system should remain constant with time. In reality there are numerous physical phenomena that make the behavior of the clocks a function of time, and for this reason we have recently introduced the dynamic Allan variance (DAVAR), a measure of the time-varying stability of an atomic clock. In this paper we discuss the dynamic Allan variance for phase and frequency jumps, two common nonstationarities of atomic clocks. The analysis of both numerical simulations and experimental data proves that the dynamic Allan variance is an effective way of characterizing nonstationary behaviors of atomic clocks

Time-Evolution of the Power Spectrum of the Black Hole X-ray Nova XTE J1550-564

We have studied the time evolution of the power spectrum of XTE J1550-564, using X-ray luminosity time series data obtained by the Rossi X-Ray Timing Explorer satellite. A number of important practical fundamental issues arise in the analysis of these data, including dealing with time-tagged event data, removal of noise from a highly non-stationary signal, and comparison of different time-frequency distributions. We present two new methods to understand the time frequency variations, and compare them to the dynamic power spectrum of Homan et al. All of the approaches provide evidence that the QPO frequency varies in a systematic way during the time evolution of the signal.Comment: 4 pages, 3 figures; 2001 IEEE - EURASIP Workshop on Nonlinear Signal and Image Processing (June 3-6, 2001), and to appear in the proceeding

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)

Instantaneous spectrum estimation of event-based densities

We present a method for obtaining a time-varying spectrum that is particularly suited when the data are in event-based form. This form arises in many areas of science and engineering, and especially in astronomy, where one has photon counting detectors. The method presented consists of three procedures. First, estimating the density using the kernel method; second, highpass filtering the manifestly positive density; finally, obtaining the time-frequency distribution with a modified Welch′s method. For the sake of validation event-based data are generated from a given distribution and the proposed method is used to construct the time-frequency spectrum and is compared to the original density. The results demonstrate the effectiveness of the method

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