After implementing Galileo processing capabilities in my PPP software, the next step towards GNSS modernization was the inclusion of BeiDou satellites. The active constellation of BeiDou-2 satellites currently consists of 6 geostationary (GEO), 5 inclined geosynchronous orbit (IGSO) and 4 medium earth orbit (MEO) satellites. Until 2020, when 27 MEO satellites should be in orbit, BeiDou will be more of a regional system covering mainly Asia and Australia. While the implementation of Galileo was rather straightforward, including BeiDou turned out to be more of a challenge.
The first (minor) issue encountered originated in the RINEX files, where the signals L1I and C1I were being tracked. My initial implementation followed the RINEX 3.03 format definition which specifies that BeiDou signals would be labeled as either C2x (B1), C7x (B2) or C6x (B3). However, a footnote in the RINEX document did mention the following: “When reading a RINEX 3.02 file, both C1x and C2x coding should be accepted and treated as C2x in RINEX 3.03.”
Once this issue resolved, I was able to compute a PPP solution, albeit not a great one… I had to read a few papers on BeiDou before realizing that the phase center offsets (PCO) provided in the IGS ANTEX file are actually not the ones used by several analysis centers. The GFZ products that I am using in this study use phase center offsets estimated by ESA and published in an IGS Workshop poster (Dilssner et al. 2014). I thus had to create my own ANTEX file using the values provided in this publication. This poster refers to BeiDou satellites as IGSO-1 to IGSO-5 and MEO-3 to MEO-6. This labeling of satellites does not match any information in the ANTEX files but the correspondence with the PRN number could be made using the IGS MGEX webpage.
After using the proper PCO values, the PPP solution greatly improved, although the carrier-phase residuals were still larger than expected. The problem, this time, was an improper satellite attitude determination. As specified in the paper by Montenbruck et al. (2015), geostationary satellites use an orbit-normal mode with a fixed yaw-angle of zero degrees, as opposed to the yaw-steering mode used by GPS, GLONASS and Galileo. The BeiDou MEO satellites also use this orbit-normal mode when the angle between the Sun and the orbital plane (“beta”) is smaller than approximately 4 degrees (see the interesting work by Dai et al. (2015) for more details on the transition periods).
While the carrier-phase residuals now had a reasonable RMS value, the code residuals were still quite large, even at high elevation angles. This issue could be mitigated by applying the calibration values proposed by Wanninger and Beer (2015) to account for satellite-induced code pseudorange variations.
To test this initial implementation, I processed 24 hours of data from station CUT0, located at Curtin University in Australia, collected on 02 Jan 2016 following the PPP methodology in kinematic mode. I assigned the same weight to all GNSS, and obtained the following RMS errors for different GNSS configurations:
|Solution||Latitude (mm)||Longitude (mm)||Height (mm)|
|G + R||8.2||7.1||18.1|
|G + R + E||7.9||6.4||17.7|
|G + R + E + C||7.0||5.1||15.5|
Even though the results for the GPS-only solution were not great to start with (did I introduce a new bug?), a reduction in the RMS of each component can be observed with additional constellations. In the quad-constellation solution, up to 34 satellites were used simultaneously in the solution. I then selected a 45-min period with good satellite coverage (from 01:00 to 01:45 GPST) to analyze the convergence period of the different solutions:
It is interesting to note that simply adding GLONASS to GPS already provides a significant reduction in convergence time, although tracking more than 30 satellites certainly brings additional benefits to the solution. When the full constellations of triple-frequency satellites will be available for all systems, combined with ambiguity resolution capabilities, PPP convergence will most likely be a thing of the past.
Dai X, Ge M, Lou Y, Shi C, Wickert J, Schuh H (2015) Estimating the yaw-attitude of BDS IGSO and MEO satellites. J Geod 89(10):1005-1018. doi:10.1007/s00190-015-0829-x
Dilssner F, Springer T, Schönemann E, Enderle W (2014) Estimation of satellite antenna phase center corrections for BeiDou. IGS Workshop, Pasadena, California, USA
Montenbruck O, Schmid R, Mercier F, Steigenberger P, Noll C, Fatkulin R, Kogure S, Ganeshan A S (2015) GNSS satellite geometry and attitude models. Advances in Space Research 56(6):1015-1029. doi:10.1016/j.asr.2015.06.019
Wanninger W, Beer S (2015) BeiDou satellite-induced code pseudorange variations: diagnosis and therapy. GPS Solut 19(4):639-648. doi: 10.1007/s10291-014-0423-3