# Broadcast Ephemeris with Centimetric Accuracy: Test Results for GPS, Galileo, Beidou and Glonass
## 4 Polynomial Clock Model vs. IGS/MGEX High Rate Clocks  
The clock polynomials we have computed for GPS, Galileo, Beidou and Glonass fit with centimetric rms the clock values tabulated at 15 min intervals in the SP3 files. For most applications, the polynomial clock corrections are used to interpolate the values at rates of the order of 1 Hertz or higher. In [2], it is pointed out that noise in rubidium, cesium and hydrogen maser clocks is characterized by a random walk phase modulation. For lag times of up to 10 s, the Allan variance is between \(10^{-11}\) and \(10^{-12}\) for the Cesium or Rubidium clocks. For Galileo's Passive Hydrogen Maser, the frequency stability is somewhat smaller than \(10^{-12}\)[18, 19, 24, 25, 26]. This means that two consecutive, non-overlapping time segments of 100 s nominal length will have a 1 sigma difference of 1 ns to 0.1 ns for a two-sample Allan stability of \(10^{-11}\) and \(10^{-12}\) respectively. It follows that our clock polynomials need to be tested against high rate clock estimates. The IGS/MGEX makes available such files with sampling rate of 30 s. In the rest of this section, we will therefore compute differences in the clock corrections, between our polynomial values based upon 15 min sampling and high rate IGS clocks based on 30 s sampling.  
Figure 13 gives a comparative example of IGS/MGEX high rate clocks (30 s sampling) and the predictions of our polynomials based on best fit to 15 min data ([[http://ftp.aiub.unibe.ch/CODE_MGEX/CODE/2020/COM20864.CLK.Z](http://ftp.aiub.unibe.ch/CODE_MGEX/CODE/2020/COM20864.CLK.Z)]([http://ftp.aiub.unibe.ch/CODE_MGEX/CODE/2020/COM20864.CLK.Z](http://ftp.aiub.unibe.ch/CODE_MGEX/CODE/2020/COM20864.CLK.Z)) for Beidou and [[https://cddis.nasa.gov/archive/gnss/products/mgex/2086/GRGOMGXFIN_20200020000_01D_30S_CLK.gz](https://cddis.nasa.gov/archive/gnss/products/mgex/2086/GRGOMGXFIN_20200020000_01D_30S_CLK.gz)]([https://cddis.nasa.gov/archive/gnss/products/mgex/2086/GRGOMGXFIN_20200020000_01D_30S_CLK.gz](https://cddis.nasa.gov/archive/gnss/products/mgex/2086/GRGOMGXFIN_20200020000_01D_30S_CLK.gz)) for GPS, Glonass and Galileo, accessed on 10 October 2021). Figure 13 indicates that the rms discrepancy is smaller than 0.1 ns for GPS, Galileo and Beidou, while for Glonass we have a factor 10 worse rms. Several departures from random noise are well visible, suggesting that our clock polynomials smooth the high frequency part of the noise. The differences are on average of up to few equivalent cm or less. This implies that an overall figure of merit for our improved broadcast model of a few cm is the accuracy level we can expect, even at high sampling rates. These rms estimates are within the consistencies among the various MGEX solutions for clocks and orbits, as discussed in [16].  
Figure 12: Corrections to the broadcast (**a**) clock, (**b**) positions, (**c**) velocities, and (**d**) lunisolar accelerations for R0I using CNES precise orbits as reference. The vector of state (3 clock parameters + 9 orbit parameters) is estimated at intervals of 1 h. Rate of clock drift (a\({}_{2}\)) was computed but is not shown.  
Figure 13: _Cont._