# Broadcast Ephemeris with Centimetric Accuracy: Test Results for GPS, Galileo, Beidou and Glonass
## 1 Introduction
Likewise, the receiver clock will have to be synchronized to the time scales of different GNSSs, which are not aligned to each other to sufficient accuracy [4]. Recognizing the several issues related to the simultaneous use of data from several GNSSs, the International GNSS Service (IGS) of the International Association of Geodesy (IAG) has promoted the MGEX (Multiple GNSS Experiment [5; 9; 10]). As part of the MGEX activities, several Analysis Centers make available Precise Ephemeris files where ECEF coordinates and satellite clock offsets are computed using a fiducial network of several hundreds of stations with nearly global coverage and a common time scale. These ephemeris files in the conventional SP3 format contain directly the ECEF coordinates and satellite clock offsets relative to a common time scale at, normally, 15-min intervals. The orbit calculation follows international conventions on the coordinates of the stations, origin orientation and scale of the Terrestrial Reference System (currently ITRF2014 or equivalently IGb14; IGS14 during the dates of the study) [11], antenna models [12], Earth Rotation Parameters, Earth and Ocean Tides, atmospheric loading and gravity field coefficients. The solution includes modelling the SV attitude for Solar Radiation Pressure [13], the ionospheric delay, the tropospheric refraction and the receiver antenna model, for example. These precise ephemeris files are consequently considered the most accurate and rigorous representation of the instantaneous position of the Center of Mass (CoM) of each SV in an equally well-defined Terrestrial Reference Frame [14; 15]. Several Analysis Centers deliver precise multiGNSS precise ephemeris files. The mutual consistency among the different solutions is discussed by [16] who estimated in a few cm to several decimeters, depending on the GNSS, the differences of the orbit/clock products of the Analysis Center. The impact of MGEX products provided by different IGS ACs on post-processing PPP performance in terms of accuracy, availability and consistency is discussed in [17]. According to [18] orbit comparisons among the MGEX Analysis Centers show agreements of about 0.1-0.25 m for Galileo, 0.1-0.2 m for Beidou MEOs (Medium Earth Orbit), 0.2-0.3 m for Beidou IGSOs (Inclined Geosynchronous Orbit) and 0.2-0.4 m for QZSS. Clock comparisons of individual ACs have a consistency of 0.2-0.4 ns for Galileo, 0.2-0.3 ns for Beidou IGSOs, 0.15-0.2 ns for Beidou MEOs, 0.5-0.8 ns for Beidou GEOs (Geostationary Orbit) and 0.4-0.8 ns for QZSS. The satellite clock corrections sampled at 15 min may lose accuracy when interpolated at a higher rate, due to the stability characteristics of the on-board atomic clocks [19]. The Allan variance of the Cesium and Rubidium frequency standards is known to increase at shorter sampling times due to flicker noise more than Galileo's Passive Hydrogen Maser. Consequently, for those applications (e.g., PPP Precise Point Positioning) which require the satellite clock offset to be computed at a much higher rate (1-10 Hz) than one sample every 15 min, it is necessary to have epoch estimates rather than interpolations. For this purpose, MGEX issues specific clock files with 30 s sampling. Comparisons between ECEF coordinates and clock offsets computed with merged Broadcast Ephemeris files (BRDM) and SP3 values taken as reference have been the subject of several investigations. The authors of [20; 21] proposed the concept of SISRE (Signal in Space Range Error), a statistical characterization of the uncertainty of the modeled pseudorange due to errors in the broadcast orbit and clock. Comparing the Broadcast and precise (IGS) data, they demonstrated SISREs ranging of 0.2 m (Galileo), 0.6 m (GPS), 1 m (Beidou) and 2 m (Glonass) over a 12-month period in 2017. In [22], Galileo's potential for highest accuracy in positioning is confirmed.