# Broadcast Ephemeris with Centimetric Accuracy: Test Results for GPS, Galileo, Beidou and Glonass
## 1 Introduction
In this comparison a crucial role is played by the Center of Mass (CoM) to Antenna Phase Center (APC) correction (CoM is the reference point for SP3 orbits and APC is the reference point for Broadcast Ephemeris). These range from 0.04 m (GPS IIR-B/M) to 2.5 m (Glonass M) and can be modeled as a boresight bias or as a small-scale factor (up to \(8\times 10^{-8}\)) [23]. As we shall see in detail in the next sections, for each SV, the differences between \(XYZ\)(BRDM) and \(XYZT\)(SP3), the ECEF coordinates and satellite time correction computed from the broadcast message and the precise SP3 data file, show clear systematics and discontinuities at the crossover between two contiguous ephemeris blocks. It is then natural to ask if the broadcast parameters can be adjusted, for example in a least square sense, to minimize such discrepancies. As it will be shown in a number of examples, there are indications that the differences between broadcast and SP3 ephemeris and clock can be brought down to the centimeter level by appropriate tuning of the broadcast parameters complemented by additional reference frame parameters, depending on the type of navigation message (GPS-like or Glonass-like). The approach is then applied to process one month of data using all the available satellites. The average spectra of the Broadcast to SP3 differences in the spatial coordinates clearly indicate that the proposed approach remove the spectral features at low frequencies caused by the inaccuracies of the broadcast model. The spectra of the post-fit residuals are shown to be very nearly flat and with features of at most few centimeters. This paper is organized as follows. Section 2 addresses the mathematical model of the least squares adjustment and discusses the results for GPS, Galileo and Beidou in IGSO and MEO orbits. We concentrate on specific examples, in order to do a detailed analysis. Hence, we consider one satellite per constellation and one day, both chosen arbitrarily. Section 3 addresses the improvement of the Glonass navigation message using SP3 orbits and clocks. Then, specific issues are addressed: comparison between high rate clock products of IGS/MGEX and the polynomial model (Section 4), and possible improvements in the message content for increased accuracy (Section 5). In Section 6, we apply the approach described above to volume computations involving one month of data and all the satellites of the four constellations. We show that the seven Helmert parameters averaged over the 30 days and all the satellites of each constellations average to zero, within one standard deviation, with the only exceptions of the rotations Rx and Rz of Galileo slightly above the one sigma threshold. This suggests that, on average, the GNSS-specific reference frame is aligned to the ITRF2014, but that for centimetric accuracy the seven Helmert parameters appropriate to the day and satellite should be used. Then we compare spectra of the pre-fit and post-fit residuals of the Broadcast-SP3 position differences averaged over one month and all satellites of a given constellation. We show that the former has significant power (1 m typically) at low frequencies (<1 cycle/6 h), whereas the latter has a spectrum very close to flat. This supports the idea that the proposed approach has effectively accounted for most of the signal, at the centimetric level. We remark in the Conclusions that if the broadcast ephemeris, when appropriately tuned, is capable of centimetric accuracy, then there are some important consequences. One is that the broadcast format, which is optimized in bandwidth requirements, could be used in real time for precision applications, taking advantage of the existing RTCM messages. Another inference is that ephemeris and clocks in the broadcast format could be used in place of the same data in the SP3 format, at least for MEO satellites.