Evaluation of the Time and Frequency Transfer Capabilities of a Network of Gnss Receivers Located in Timing Laboratories

In this paper, we investigate a possible network solution, similar to the IGS Analysis Center solutions, that can be easily managed by a network of timing institutes to solve for all the clock differences (in addition to other quantities) in a unique system to understand the feasibility and the advantages of this approach in time and frequency transfer. The investigation is based on a tool called magicGNSS, which is a Web application for GNSS data processing developed by GMV in Madrid, Spain. magicGNSS allows the users to perform a wide range of calculations and analyses related to GNSS, from the evaluation of performances at user level, to the computation of precise GNSS orbits and clocks, including the calculation of precise receiver coordinates. The time and frequency transfer capabilities of the network solution (named ODTS) are evaluated and compared to PPP solutions as well as to other time transfer results. The possibility to use magicGNSS as an almost near-real-time tool for the comparison of atomic clocks and time scales located in timing laboratories is also addressed. INTRODUCTION In time metrology, different techniques are used for time and frequency transfer, basically TWSTFT (Two-Way Satellite Time and Frequency Transfer), GPS CV (Common View), and GPS AV (All in View) [1]. In recent years, many national timing laboratories have collocated geodetic GPS receivers together with their traditional GPS/GLONASS CV/AV receivers and TWSTFT equipment. Time and frequency transfer using GPS code and carrier-phase is an important research activity for many institutions involved in time applications, basically due to the fact that carrier-phase measurements generated are two orders of magnitude more precise than the GPS code data. This was recognized when the International GNSS Service (IGS) and the Bureau International des Poids et Mesures (BIPM) formed a joint pilot study to analyze the IGS Analysis Centers clock solutions and recommend new means of combining them. In addition, the CCTF (Consultative Committee for Time and Frequency), in 2006, 41 st Annual Precise Time and Time Interval (PTTI) Meeting 560 passed a recommendation “Concerning the use of Global Navigation Satellite System (GNSS) carrier-phase techniques for time and frequency transfer in International Atomic Time (TAI).” Moreover, the BIPM in 2002 started a project named TAIP3 [2] to examine the use of code and phase measurements. Many of geodetic GNSS receivers hosted in national timing laboratories operate continuously within the International GNSS Service (IGS) and their data are regularly processed by IGS Analysis Centers. Participating stations must agree to adhere to certain strict standards and conventions that ensure the quality of the IGS Network. A number of products and tools have been developed in order to allow for highly precise time and frequency transfer without taking part in the IGS. One stand-alone GPS carrier-phase analysis technique is Precise Point Positioning (PPP), in which dual-frequency code and phase measures are used to compare the reference clock of a single receiver to a reference time scale. Several works [3-6] were carried out to evaluate the time and frequency transfer capabilities of PPP, leading the BIPM to start a pilot experiment that aims to evaluate the possibility of regularly computing some TAI links with the PPP algorithm to obtain an improved statistical uncertainty [7]. The PPP algorithm used for the BIPM pilot experiment was developed by the Natural Resources Canada (NRCan) [8]. MAGICGNSS magicGNSS is a web application for high-precision GNSS data processing. It allows the calculation of GPS satellite orbits and clocks, and also of station/receiver coordinates, tropospheric delay, and clocks. The user can upload his own station data (RINEX measurement files) and/or use data from a global network of pre-selected core stations from IGS. magicGNSS is available at http://magicgnss.gmv.com. A free account can be requested online. A *pro* account can also be requested with advanced features for professional applications. In Error! Reference source not found., the characteristics of the two magicGNSS account types (free and *pro*) are reported. Table 1. Characteristics of magicGNSS accounts. free *pro* Available algorithms PPP, ODTS, COMP Disk quota 1 Gb 10 Gb Core station data last 30 days from 2008/01/01 IGS products (1) last 30 days from 2000/05/03 Navigation messages (2) last 30 days from 2008/05/03 User station data in ODTS no yes Max. no. of stations in ODTS 36 60 Max. no. of stations in PPP 10 60 Max. data span in PPP 1 day 5 days Max. data span in ODTS 2 days 5 days Ftp upload no yes Deletion of user station data after 30 days never Usage of public station data PPP only PPP and ODTS Share your station data no yes Technical support by email limited next-day basis (1) Orbits and clocks needed for PPP and COMP (2) Needed for ODTS initialization 41 st Annual Precise Time and Time Interval (PTTI) Meeting 561 With magicGNSS, the user can analyze results in a convenient way through comprehensive PDF reports and organize the processing scenarios and history within his account in an easy way with a generous disk quota [9]. At present, magicGNSS supports GPS data, while GLONASS processing is planned for the end of 2009. One of the most interesting characteristics of magicGNSS is the easy way to use it. Inside the magicGNSS account, one has just to click on New to define a new scenario (network), then click on Save, and then click on Run to process the data and generate results. The algorithms that process station data to generate solutions in magicGNSS are called ODTS, which stands for Orbit Determination & Time Synchronization, and PPP. ODTS is a network solution requiring a set of stations distributed worldwide. PPP is a single-station solution (although several stations can be processed together for convenience). In ODTS and PPP, the stations must be static. The advantages of a network solution compared to PPP are that the estimates of each station can benefit from the measurements of all stations. This should be, in principle, more robust and precise. In addition, all clock differences are available in a single solution instead of asking for a time-consuming series of PPP single-station solutions. There are two types of station data within magicGNSS: core station data and user station data. For ODTS, the server maintains data from 36 IGS core stations distributed worldwide. Current core station data are available with a latency of typically 1 hour. The user (for *pro* account) can also upload his own station data (RINEX files) via the Web or ftp. Batch upload and automation are possible using ftp. Normal or compressed data files can be uploaded, and if the RINEX file does not have P1, the C1 code will automatically be converted to P1 using the CC2NONCC tool from IGS. Station data uploaded and shared by other users can also be processed. The GPS operators inform the users about events affecting satellite availability by publishing messages named NANUs. magicGNSS automatically downloads NANUs as they are issued and extracts the relevant information so that only healthy satellites will be considered in the data processing. An additional module, called COMP, allows comparing magicGNSS products with IGS and among themselves. Error! Reference source not found. shows the products generated by magicGNSS. Table 2. magicGNSS products. Product ODTS PPP Format Accuracy (RMS) Report ✓ ✓ pdf N/A Satellite orbits ✓ ✕ sp3 ~2/6/4 cm Satellite clocks ✓ ✕ clk ~0.10 ns Station clocks ✓ ✓ clk ~0.10 ns Station tropo ✓ ✓ txt ~5 mm (zenith) Station coords ✓ ✓ snx <1 cm (*) In the Radial/Along/Normal directions DATA PROCESSING AND PRODUCTS The basic ODTS and PPP input measurements are pseudorange (code) and phase L1-L2 dual-frequency iono-free combinations. On L1, the P1 code is used in order to be consistent with IGS. The raw input code and phase measurements are decimated and used internally by ODTS and PPP at a typical rate of 5 minutes (down to 30 sec can be used in PPP). The code measurements are smoothed using the phase with a Hatch filter, thus reducing the code error from the meter lever to typically 25 cm. ODTS and PPP are based on a batch least-squares algorithm that minimizes measurement residuals solving for orbits, satellite and station clock offsets, phase ambiguities, and station tropospheric zenith delays. In the case of PPP, satellite orbits and clocks are not solved for, but fixed to IGS products (ultra-rapid, rapid, or final). For this reason PPP is not a totally independent technique, unlike ODTS that, autonomously, provides all products. 41 st Annual Precise Time and Time Interval (PTTI) Meeting 562 Clocks are calculated as snapshot values, i.e., as instantaneous values at the measurement time epoch, without correlation to previous estimates. Clocks are estimated with a rate that typically is five minutes, conversely to the receivers measurements that are generated every second and, then, decimated to 30 seconds. In ODTS, satellite and station clock offsets are estimated with respect to a reference clock provided by one of the stations and chosen by the user (taking into account that the overall clock stability could be affected by the stability of the chosen reference clock). In PPP, the station clock is referred to the IGS Time scale (IGST), as derived from the satellite clocks in the IGS products. From subsequent subtraction, the differences between station clocks can be inferred. The satellite and Earth dynamics are based on high-fidelity models that follow IERS recommendations issued in 2003, trying to implement the partial updates that are published periodically, with some delay and only if they’re relevant for magicGNSS application (it’s not guaranteed that all updates have been considered). Modelled effects include a full Earth gravity model, Sun, Moon, and planetary attractions, solid Earth tides, ocean loading, and solar radiation pressure (SRP), including eclipses. Radiation force discontinuities during eclipse entry/exit are smoothed in order to improve orbit accuracy. The satellite attitude is modelled as a generic nadir-pointing yaw-steering law applicable to all GNSS satellites. In ODTS, the orbit fit is based on the estimation of the initial state vector (position and velocity) and eight empirical SRP parameters. Earth Rotation Parameters (ERPs) are automatically downloaded from the IERS server, but they can also be estimated by ODTS itself. The tropospheric correction is based on the estimation of a zenith delay per station (a constant value every hour), using a mapping function to account for the satellite-station signal elevation. Small effects such as relativity and carrier-phase wind-up are also modelled. For the core stations, a priori station coordinate values come from ITRF or IGS solutions, and they can be refined within the ODTS process. For user stations, the precise coordinates from PPP can be used as input values for ODTS. Satellite and station antenna offsets and phase center variations are taken into account; the latest ANTEX file from IGS is always used. DESCRIPTION OF THE ODTS ALGORITHM The ODTS processing can be summarized as follows: 1. Given a satellite position and velocity at a certain starting epoch, an orbit can be produced on the basis of dynamic information, by numerical integration of the equations of motion of the satellite over a certain period. Furthermore, the partial derivatives of the satellite position with respect to the estimated dynamical parameters are produced. 2. For the epochs within that period at which tracking data are available, a tracking observation can be reconstructed numerically, using the known station position, the satellite position coming from the integrated orbit, and precise models for the effects affecting the tracking signal propagation. Also, the partial derivatives of the reconstructed measurements with respect to the estimated parameters are produced. 3. The measurement residuals (difference between the pre-processed tracking observations and the associated calculated observations) are computed. 4. The sum of the squares of all available residuals is minimized by estimating corrections to the various model parameters in a least-squares sense. To accomplish that, the computation of the partial derivatives of the expected measurements with respect to the estimated parameters is needed. The process described is iterated until one of the following criteria is met: 41 st Annual Precise Time and Time Interval (PTTI) Meeting 563 the number of iterations exceeds a certain threshold defined by configuration; the RMS of the weighted measurement residuals is below a certain threshold defined by configuration; the difference between two consecutive solutions is below a certain margin established by configuration. The next sections describe those steps in detail. ORBIT COMPUTATION The orbit propagation consists of computing the satellite state vector for a whole integration arc, given an initial state vector at the epoch t0 and a model of forces acting on the satellite. The solution of the problem is achieved by integrating the equations of motion, which can be expressed in matrix form as follows: 0 0 ) ( ) , ( y t y y t f dt y d     