Long-term behavior and statistical characterization of BeiDou signal-in-space errors

We derive orbit and clock errors for BeiDou satellites from March 1, 2013, to September 30, 2016 by comparing broadcast ephemerides with the precise ephemerides produced by Wuhan University. The broadcast ephemerides are pre-processed to filter out the “data-logging” errors, and a robust estimation is subsequently implemented for removing the time-varying common timescale bias between the broadcast and precise clocks. To obtain the nominal SISEs (Signal-In-Space Errors), the SIS (Signal-In-Space) outliers are excluded according to the standard of SIS integrity. The long-term satellite clock behavior reveals that for GEO, IGSO and MEO satellites, each category of satellites has its inter-category clock consistency, and the clocks of MEO as well as the clocks of IGSO satellites have better inter-category consistency than that of GEO satellites. Between different categories, GEO satellite clocks have been more divergent from IGSO satellite clocks since May 2014. The larger orbit errors, resulting in approximately 1–2 m orbit-only UREs (User Range Errors), periodically occur for all satellites every half year when the satellites are in eclipse period. For the GEO and IGSO satellites, several larger orbit errors may be caused by the effect of satellite maneuvering, resulting in 2–3 m orbit-only UREs. Most satellite clocks have a nonzero mean, and all MEO satellite clocks have a positive mean of approximately 1.0 m, whereas the IGSO satellite clocks have a negative mean at the same level. For the GEO satellites, the various means indicate that the clocks are divergent from one to another. The clock standard deviation of 1 m is achieved by all satellites except for C03. Near-zero means are obtained in along-track, cross-track and radial errors for the IGSO and MEO satellites but not for the GEO satellites. The average RMSs (Root Mean Square) of approximately 0.8, 1.7 and 2.0 m are obtained for the orbit-only UREs, global-average UREs and worst-UREs, respectively, for the constellation as a whole. The RMSs of clock errors for GEO, IGSO and MEO are 1.8, 1.4 and 1.3 m, respectively. Due to a nearly-static observation geometry, the GEO satellites always have the worst SISE performance, and as a result, they degrade the overall SISE statistical characterization. The analysis of URE and broadcast URA (User Range Accuracy) indicates that the broadcast URA of 2.0 m throughout is slightly optimistic. The unchanging URA of 2.0 m may not be able to describe adequately the accuracy of UREs. Instead, the upper-bound URA of 2.4 m is recommended to users. The cross-correlation analysis results show that there is a significant positive correlation between along-track errors and radial errors, whereas radial errors are not evidently correlated to clock errors as they are with GPS.