# Broadcast Ephemeris with Centimetric Accuracy: Test Results for GPS, Galileo, Beidou and Glonass
## 7 Discussion  
The sample of data we have tested suggests that the GPS-like (Keplerian orbit plus perturbations) navigation message can be tuned to a precise ephemeris and clock with an rms spread ranging from 1.4 cm (Galileo) to 5.2 cm (GPS), provided that the corrections to  
Figure 17: Spectrum of the pre-fit (top) and post-fit (bottom) residuals of the coordinates of the Galileo satellites relative to the CNES precise ephemeris, projected on the radial, tangential and across track basis. Average values for January 2020. Figure 18: Spectrum of the pre-fit (top) and post-fit (bottom) residuals of the coordinates of the Beidou satellites (IGSO and MEO) relative to the CODE precise ephemeris, projected on the radial, tangential and across track basis. Average values for January 2020.  
the broadcast parameters are complemented by daily adjustments in origin and orientation of the reference frame parameters. These adjustments are negligibly small for Galileo but can be of several tens of cm for GPS and Beidou. For an IGSO orbit like Beidou C07, the translation parameters are undefined due to lack of geometry. It may be expected that similar results can be obtained for Japan's QZSS which are also in a IGSO orbit, and for India's NAVIC/IRNSS. The validity time of the ephemeris is two hours. For GPS, we tested a fit interval of 4 h. In such a case, the post-fit residuals indicate the presence of an oscillation of an approximately 4-h period, which is the signal expected to be caused primarily by the third zonal (\(I_{3}\)) of the Earth's gravity field. Including this perturbation in the navigation message would help in increasing the validity time and have a more random spread of the post-fit residuals. The inference is that the format of the broadcast ephemeris adopted by GPS, Galileo, Beidou, and possibly NAVIC/IRNSS and QZSS, can represent the SV position to very high accuracy, comparable with that of the precise ephemeris. Comparison of power spectra of the Broadcast-SP3 residuals before and after the adjustment computed for all the satellites and one month support this hypothesis. Satellites in the GEO orbit have not been tested because a reference precise ephemeris is at this time unavailable. For the clock corrections, a similar reasoning applies. The three-parameter model can likewise be tuned on precise clock corrections at 15 min sampling. It is to be noted, however, that flicker noise at sampling rates of up to 100 s can increase considerably the Allan variance for Cesium or Rubidium clocks. For the Galileo's Passive Hydrogen Maser this is also true but not so marked as for Cesium or Rubidium clocks. Therefore, the effective validity of the polynomial clock model at sampling rates of the order of 1 Hz needs to be tested with IGS's high rate clocks. One of the most important challenges in satellite navigation precise positioning is to be able to broadcast corrections to the navigation message so that the user has positions and clocks of the used GNSS's of sufficient accuracy to apply for example a PPP (Precision Point Positioning) algorithm. Currently, the International GNSS Service (IGS) agency and various analysis centers (ACs) provide users with ultra-rapid precise satellite orbit and clock products for GPS and Glonass with 6-h updates and a 3-h latency (igs.org/acc/gps-only/#ultra-rapid, accessed on 10 October 2021). Corresponding products for Galileo and Beidou are discussed by [30]. The accuracy of the predicted orbits is not good enough for high-precision PPP [25]. A widely used approach to generate high accuracy orbits and clocks usable in Real Time PPP is the SSR (State Space Representation).