# Broadcast Ephemeris with Centimetric Accuracy: Test Results for GPS, Galileo, Beidou and Glonass
## 6 Results for Volume Calculations  
In the previous sections, we presented results based on limited data, in order to privilege the detail of the analysis more than the volume calculations on a larger number of days and satellites. In this section, we apply the same approach systematically to a larger body of data. We concentrate on the full month of January 2020.  
In the Appendix A, Tables A1-A4 contain the Helmert parameters and their standard deviations for GPS, Glonass, Galileo and Beidou, respectively, averaged over one month. The Helmert parameters were estimated by modeling the differences between the ECEF coordinates computed with the broadcast ephemeris and those available in the SP3 file of CNES, on a satellite-by-satellite basis. For BeiDou, the CODE SP3 ephemeris were used. Then the 31 daily values were averaged. For GPS, BeiDou and Glonass, the mean of each of the seven parameters is zero within one standard deviation, implying that on average the broadcast and SP3 reference frames are aligned. For Galileo, the only parameters which are nonzero within one standard deviation are Rx and Rx. In general, the broadcast and SP3 frames are aligned. However, individual values (e.g., Rx of G01 or G11) can be large enough to generate significant departures of the broadcast predictions relative to the reference SP3 positions. Consequently, it is advisable, for maximum accuracy, to make available the Helmert parameters in conjunction with the corrections to the broadcast ephemeris, for each satellite and day.  
We now turn to evaluate the effectiveness of our proposed approach to account for unmodeled reference frame adjustments and orbit effects in the broadcast ephemeris on all the satellites and days of January 2020. To this purpose, we have the average spectra of the pre-fit and post-fit residuals for each constellation. Figures 15-18 show the results for GPS, Glonass, Galileo and Beidou (IGSO and MEO), respectively. The spectra are computed in the Radial, Tangential and Across track triad. The upper plot shows the spectrum of the pre-fit residuals, i.e., the differences between broadcast and SP3 coordinates prior to the adjustment. The lower plot shows the spectra of the post-fit residuals, i.e., after the fit. The plots clearly show that the pre-fit spectra are dominated by low frequency signals (periods larger than 6 h, or frequency less than 0.05 mHz) with amplitudes of the order of 1 m. The lower plots show that the parameter adjustment proposed in this paper effectively removes the low frequency signals, so that the spectra of the differences between the positions computed with the corrected broadcast model and the SP3 positions are very nearly flat. The scales of the y axis are different. In particular for Galileo, it is worth noting that the proposed algorithm removes from the original broadcast ephemeris most of the unmodeled perturbations, whereas for Glonass we observe a lower efficiency.  
Figure 16: Spectrum of the pre-fit (top) and post-fit (bottom) residuals of the coordinates of the Glonass satellites relative to the CNES precise ephemeris, projected on the radial, tangential and across track basis. Average values for January 2020.  
Figure 15: Spectrum of the pre-fit (top) and post-fit (bottom) residuals of the coordinates of the GPS satellites relative to the CNES precise ephemeris, projected on the radial, tangential and across track basis. Average values for January 2020.