Evaluating two methods of estimating error variances using simulated data sets with known errors

In this paper we compare two different methods of estimating the error variances of two or more independent data sets. One method, called the three-cornered hat (3CH) method, requires three data sets. Another method, which we call the two-cornered hat (2CH) method, requires only two data sets. Both methods have been used in previous studies to estimate the error variances associated with a number of physical and geophysical data sets. A key assumption in both methods is that the errors of the data sets are not correlated, although some studies have considered the effect of the partial correlation of representativeness errors in two or more of the data sets.We compare the 3CH and 2CH methods using a simple model to simulate three and two data sets with various error correlations and biases. With this model, we know the exact error variances and covariances, which we use to assess the accuracy of the 3CH and 2CH estimates. We examine the sensitivity of the estimated error variances to the degree of error correlation between two of the data sets as well as the sample size. We find that the 3CH method is less sensitive to these factors than the 2CH method and hence is more accurate. We also find that biases in one of the data sets has a minimal effect on the 3CH method, but can produce large errors in the 2CH method.</p

Time activities at the BIPM

The generation and dissemination of International Atomic Time, TAI, and of Coordinated Universal Time, UTC, are explicitly mentioned in the list of the principal tasks of the BIPM, recalled in the Comptes Rendus of the 18th Conference Generale des Poids et Mesures, in 1987. These tasks are fulfilled by the BIPM Time Section, thanks to international cooperation with national timing centers, which maintain, under metrological conditions, the clocks used to generate TAI. Besides the current work of data collection and processing, research activities are carried out in order to adapt the computation of TAI to the most recent improvements occurring in the time and frequency domains. Studies concerning the application of general relativity and pulsar timing to time metrology are also actively pursued. This paper summarizes the work done in all these fields and outlines future projects

Relativity and the metrology of time

PhDThe motivation for this work is two-fold: the application of general relativity to the metrology of time on one hand (part II), and the use of the methods and technology of time metrology for tests of relativity on the other (part I). In Part I detailed theory for the treatment of the metrology of time in a relativistic context is developed. It provides mathematical expressions for application to the syntonisation and synchronisation of clocks and the realisation of the time coordinates of space-time reference systems. The theoretical expressions are developed to accuracies exceeding those of previous publications in order to accommodate any development in clock and time-transfer technology that can be expected in the near f uture. Part III presents two original experiments which test the theory of special relativity using state-of-the-art time metrology. The first experiment uses data from clock comparisons betweeng round clocks and clocks on board the Global Positioning System( GPS) satellites to test the second postulate of special relativity (the universality of the speed of fight). The experiment is sensitive to a possible anisotropy of the one-way speed of flight in any spatial direction, and on a non-laboratory scale (baselines; -> 20000 Ian) and provides the most stringent limits for the anisotropy published up to date. The second is a proposal for a test of special relativity using a spacecraft that carries an onboard atomic clock and uses a two way time transfer system. The potential accuracy of such a test is evaluated for the ESA/RSA ExTRAS (Experiment on Timing Ranging and Atmospheric Sounding)experiment which was planned for launch in 1997 but is now "on hold".Perren Fun

Coherent fibre-optic link: applications in Time and Frequency metrology, Geodesy, Radio Astronomy and Seismology

L'abstract è presente nell'allegato / the abstract is in the attachmen

The 26th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting

This document is a compilation of technical papers presented at the 26th Annual PTTI Applications and Planning Meeting. Papers are in the following categories: (1) Recent developments in rubidium, cesium, and hydrogen-based frequency standards, and in cryogenic and trapped-ion technology; (2) International and transnational applications of Precise Time and Time Interval technology with emphasis on satellite laser tracking, GLONASS timing, intercomparison of national time scales and international telecommunications; (3) Applications of Precise Time and Time Interval technology to the telecommunications, power distribution, platform positioning, and geophysical survey industries; (4) Applications of PTTI technology to evolving military communications and navigation systems; and (5) Dissemination of precise time and frequency by means of GPS, GLONASS, MILSTAR, LORAN, and synchronous communications satellites

Synchronising coherent networked radar using low-cost GPS-disciplined oscillators

This text evaluates the feasibility of synchronising coherent, pulsed-Doppler, networked, radars with carrier frequencies of a few gigahertz and moderate bandwidths of tens of megahertz across short baselines of a few kilometres using low-cost quartz GPSDOs based on one-way GPS time transfer. It further assesses the use of line-of-sight (LOS) phase compensation, where the direct sidelobe breakthrough is used as the phase reference, to improve the GPS-disciplined oscillator (GPSDO) synchronised bistatic Doppler performance. Coherent bistatic, multistatic, and networked radars require accurate time, frequency, and phase synchronisation. Global positioning system (GPS) synchronisation is precise, low-cost, passive and covert, and appears well-suited to synchronise networked radar. However, very few published examples exist. An imperfectly synchronised bistatic transmitter-receiver is modelled. Measures and plots are developed enabling the rapid selection of appropriate synchronisation technologies. Three low-cost, open, versatile, and extensible, quartz-based GPSDOs are designed and calibrated at zero-baselines. These GPSDOs are uniquely capable of acquiring phase-lock four times faster than conventional phase-locked loops (PLLs) and a new time synchronisation mechanism enables low-jitter sub-10 ns oneway GPS time synchronisation. In collaboration with University College London, UK, the 2.4 GHz coherent pulsed-Doppler networked radar, called NetRAD, is synchronised using the University of Cape Town developed GPSDOs. This resulted in the first published example of pulsed-Doppler phase synchronisation using GPS. A tri-static experiment is set up in Simon’s Bay, South Africa, with a maximum baseline of 2.3 km. The Roman Rock lighthouse was used as a static target to simultaneously assess the range, frequency, phase, and Doppler performance of the monostatic, bistatic, and LOS phase corrected bistatic returns. The real-world results compare well to that predicted by the earlier developed bistatic model and zero-baseline calibrations. GPS timing limits the radar bandwidth to less than 37.5 MHz when it is required to synchronise to within the range resolution. Low-cost quartz GPSDOs offer adequate frequency synchronisation to ensure a target radial velocity accuracy of better than 1 km/h and frequency drift of less than the Doppler resolution over integration periods of one second or less. LOS phase compensation, when used in combination with low-cost GPSDOs, results in near monostatic pulsed-Doppler performance with a subclutter visibility improvement of about 30 dB

Frequency Combs For Precision Optical Metrology

Redefinition of the SI second to an optical transition could improve the realization of the second by two orders of magnitude, from 16-digits to 18-digits of resolution. These levels of resolution provide improved timing signals that could be used to increase the location accuracy of navigation systems, enable tests of fundamental physics and provide measurements of the geoid at the one centimeter scale.Recently, a roadmap for an optical redefinition of the second was outlined by a working group of time and frequency metrologists from around the world. Achieving the milestones outlined on this roadmap would ensure continuity with the current SI second, and demonstrate the maturity and reliability of optical atomic clock technology as the basis for the unit of the second. Optical frequency combs can be used to coherently link frequencies across the optical and microwave domains. This is important to achieve the milestones for an optical SI second as they require comparisons of optical atomic clocks of different atomic species as well as comparisons against the current microwave cesium primary standard. Frequency combs are a critical component for optical timekeeping as they provide a means to generate microwave timing signals from optical atomic clocks. In this thesis I will describe the architecture and characterization of a single branch Er:Fiber optical frequency comb. This comb has demonstrated levels of performance that can support both current and next generation optical atomic clocks.Progress on the roadmap toward an optical redefinition of the second that is being made with the Boulder atomic clock network, and both absolute frequency measurements and clock ratio measurements from this work will be presented. I will describe the characterization of the network and its subcomponents to ensure that it can support the performance of state-of-the-art optical clocks and cavities. This thesis will conclude with an overview of an optical timescale, and the requirements for the optical frequency comb systems used to generate microwave timing signals from this timescale.</p

Undifferenced and uncombined GNSS time and frequency transfer with integer ambiguity resolution

Precise point positioning (PPP) has been a competitive global navigation satellite system (GNSS) technique for time and frequency transfer. However, the classical PPP is usually based on the ionosphere-free combination of dual-frequency observations, which has limited flexibility in the multi-frequency scenario. More importantly, the unknown integer ambiguities are not restored to the integer nature, making the advantage of high-precision carrier phase observations underutilized. In this contribution, using the undifferenced and uncombined (UDUC) observations, we derive the time and frequency transfer model suitable for multi-constellation and multi-frequency scenarios. Notably, in short- and medium-baseline time and frequency transfer, the ionosphere-fixed and ionosphere-weighted UDUC models are derived, respectively, by making full use of the single-differenced (SD) ionospheric constraints. The proposed model can be applied to short-, medium- and long-baseline time and frequency transfer. The ambiguities are solved in a double-differenced (DD) form and can thus be restored to integers. To verify the feasibility of the model, GPS data from several time laboratories were collected, and the performance of the time and frequency transfer were analyzed with different baseline lengths. The results showed that the ionosphere-fixed and ionosphere-weighted UDUC models with integer ambiguity resolution could improve the frequency stability by 25–60% and 9–30% at an averaging time of several tens of seconds to 1 day for short- and medium-baseline, respectively. Concerning the long-baseline, the UDUC model is 10–25% more stable than PPP for averaging time below a few thousands second and over 1 day