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Mutual Benefits of Timekeeping and Positioning

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Mutual Benefits of Timekeeping and Positioning Tavella and Petit Satell Navig (2020) 1:10 https://doi.org/10.1186/s43020-020-00012-0 Satellite Navigation https://satellite-navigation.springeropen.com/ REVIEW Open Access Precise time scales and navigation systems: mutual benefts of timekeeping and positioning Patrizia Tavella* and Gérard Petit Abstract The relationship and the mutual benefts of timekeeping and Global Navigation Satellite Systems (GNSS) are reviewed, showing how each feld has been enriched and will continue to progress, based on the progress of the other feld. The role of GNSSs in the calculation of Coordinated Universal Time (UTC), as well as the capacity of GNSSs to provide UTC time dissemination services are described, leading now to a time transfer accuracy of the order of 1–2 ns. In addi- tion, the fundamental role of atomic clocks in the GNSS positioning is illustrated. The paper presents a review of the current use of GNSS in the international timekeeping system, as well as illustrating the role of GNSS in disseminating time, and use the time and frequency metrology as fundamentals in the navigation service. Keywords: Atomic clock, Time scale, Time measurement, Navigation, Timekeeping, UTC Introduction information. Tis is accomplished by a precise connec- Navigation and timekeeping have always been strongly tion between the GNSS control centre and some of the related. Te current GNSSs are based on a strict time- national laboratories that participate to UTC and realize keeping system and the core measure, the pseudo-range, their real-time local approximation of UTC. is actually a time measurement. To this aim, very good Tese features are reviewed in this paper ofering an clocks are installed on board GNSS satellites, as well as in overview of the mutual advantages between navigation the ground stations and control centres. and time keeping, particularly the cross-fertilization that National and international timekeeping relies on has always been achieved in these two felds. GNSS. In fact, the international reference time, Coordi- nated Universal Time (UTC), is obtained from the aver- Clocks and time metrology in GNSS age of about 450 atomic clocks maintained in about 80 In modern GNSS, the position of the user is estimated as national laboratories worldwide, and the clocks of the the intersection of three or more spheres whose centre diferent laboratories are generally compared by means of is the known position of a satellite and whose radius is GNSS. given by the velocity of light multiplied by the travel time In this case, instead of using GNSS to estimate posi- of the satellite signal, knowing when it started and meas- tion, the time transfer users mostly use the timing infor- uring, by the local receiver, when it arrived. mation provided by GNSSs and, in some cases, they don’t Since the light velocity is a very large number, it is suf- solve for their position as it is already known with suf- fcient to allow an error of 1 ns (10−9 s) to obtain at least fcient accuracy. 30 cm of error in the estimated position. A time error of Moreover, the current GNSS not only ofer positioning one nanosecond between a space-based to ground clock services, but also timing services as they broadcast suit- is difcult to achieve; an error of 100 ns is more common, able information on UTC and the user can obtain timing which would give a positioning error of 30 metres. Tis gives an understanding of why time metrology is vitally *Correspondence: [email protected] important in navigation. Bureau International des Poids et Mesures, Pavillon de Breteuil, With reference to Fig. 1, we see that all the segments 92312 Sèvres Cedex, France of a GNSS are equipped with clocks, with diferent © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Tavella and Petit Satell Navig (2020) 1:10 Page 2 of 12 Fig. 1 The typical GNSS structure and the presence of clocks purposes. Te more stable, reliable, and space-qualifed Bureau International des Poids et Mesures (BIPM) [https atomic clocks have the aim of keeping time onboard sat- ://www.bipm.org/en/bipm/tai/]. ellites and to generate the navigation signal. If we write the typical pseudo-range equation, we can On the ground, the network of monitoring stations, immediately see how time metrology is imbedded in the as well as the control centres, need stable and accurate navigation solution (see for example Tavella 2017). x clocks to generate the system reference time, to measure If we indicate by rec the receiver’s unknown 3-dimen- x the satellite pseudo-ranges, and to ensure the orbit and sional position, similarly sat indicates the 3-dimensional clock estimation and prediction. satellite position. If tsat is the epoch at which the signal User receivers are equipped with clocks, to measure leaves the satellite, and trec is the epoch at which it arrives the time of arrival of the satellite signals. Te receiver at the receiver, the distance between satellite and receiver clock, not necessarily an atomic clock, has an unknown is indicated by Eq. (1) ofset which needs to be estimated in the whole naviga- Dsat = c[(t − t )] =|x − x | tion solution, adding a fourth unknown to the estimation rec rec sat sat rec (1) problem, besides to three space positioning coordinates. where c is the velocity of light. Te satellite position In principle, this is sufcient to estimate the user’s posi- and epoch of transmission are known, as transmit- tion, but to ofer an additional timing service, the GNSSs ted by the same satellite in the navigation message, are in some way connected to time laboratories that the epoch of reception is measured, therefore the realize local approximations of Coordinated Universal x unknowns are the 3-dimensional space coordinate sat Time (UTC), the ultimate reference time realized by the Tavella and Petit Satell Navig (2020) 1:10 Page 3 of 12 and by measuring three satellites the system could be (a) GPS time is a paper time scale estimated with a resolved. Tis is true in principle but what happens if Kalman flter and steered versus UTC(USNO), a user’s measurement is actually a pseudo distance, or (b) Galileo System Time is a weighted average of pseudo range, which contains other unwanted contri- the ground clocks steered versus UTC, butions. A complete equation could be 2. Te ofset (tsat − tref ) is estimated by the algorithm Psat = c[(t − t )] =|x − x | rec rec sat sat rec that processes the same pseudorange measures and + c(trec − tref ) − (tsat − tref ) + Irec + Tr + εrec estimating orbits and clocks (Kalman flter in case of (2) GPS, batch least square in case of Galileo, …) (t − t ) where we fnd more terms. Firstly, the fact that the sys- 3. Te real time ofset sat ref transmitted to the tem and the receiver clocks are not perfectly synchro- user is actually a prediction based on previous meas- nized should be taken into account, they may have an ures, the prediction method depends on the type of ofset with is indicated with respect to a certain com- clocks, the latency, and the requested uncertainty. mon reference time indicated by tref . Te receiver clock ofset is actually introduced as a fourth unknown of the Te information on the satellite position and the system for which we are asking for a fourth satellite to be onboard clock are communicated to the satellite by the measured. ground control segment and they are estimated with pre- Te ofset (tsat − tref ) between the satellite and the vious pseudo-range measures obtained by the network reference time takes into account the fact that the clock of ground monitoring stations. What is uploaded to the onboard can have an ofset and this ofset is to be com- satellite can only be a prediction to be transmitted in the municated to the user to be taken into account in the navigation message to the users. Te predicted satellite navigation solution. Te terms Irec, Tr, and εrec are taken clock ofsets (and orbits) need to be valid for a certain into account additional delays due to the ionosphere, the period in the future, until the satellite is again in view of troposphere and the receiver hardware. the uploading station to receive fresh estimates. If we concentrate only on the timing contribution, from Clock measurement, estimation and prediction, as the (Eq. 2), we see some important issues: defnition of the reference time and its steering versus UTC are the typical activities of a timekeeping labora- tory. Te clocks and the requirements may be diferent, 1. Te reference time tref is the navigation system Refer- ence Time to be defned from the ensemble of space/ but very similar issues are faced. For a general descrip- ground clocks, similarly to any national reference tion of GNSS many books and papers are available, for time scale.
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