Abstract
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.
Similar content being viewed by others
References
Blanch J, Walter T, Enge P (2007) Understanding PHMI for safety of life applications in GNSS. In: Proceedings of ION NTM 2007, San Diego, CA, January 22–24, pp 305–310
Blanch J, Walter T, Enge P (2012) Advanced RAIM user algorithm description: integrity support message processing, fault detection, exclusion, and protection level calculation. In: Proceedings of ION GNSS 2012, Nashville, Tennessee, September 17–21, pp 2828–2849
Blanch J, Walter T, Enge P (2015) Progress on working group-C activities on advanced RAIM. In: Proceedings of ION GNSS + 2015, Tampa, Florida, September 14–18, pp 629–638
Chen G, Hu Z, Wang G, Chen G, Liu Z, Zhao Q (2015) Assessment of BDS signal-in-space accuracy and standard positioning performance during 2013 and 2014. In: Proceedings of China satellite navigation conference (CSNC) 2015, Xian, China, Springer, Berlin, pp 437–453. doi:10.1007/978-3-662-46638-4_40
Cohenour C, van Graas F (2011) GPS orbit and clock error distributions. Navigation 58(1):17–28
CSNO (2013) BeiDou navigation satellite system open service performance standard, BeiDou OS SPS, 2013, China Satellite Navigation Office
CSNO (2016) BeiDou navigation satellite system signal in space interface control document, BeiDou SIS ICD, 2016, China Satellite Navigation Office
Dai X, Ge M, Lou Y, Shi C, Wickert J, Schuh H (2015) Estimating the yaw attitude of BDS IGSO and MEO satellites. J Geodesy 89(10):1005–1018. doi:10.1007/s00190-015-0829-x
Diaz SP, Meurer M, Rippl M, Belabbas B, Joerger M, Pervan B (2015) URA/SISA analysis for GPS-galileo ARAIM integrity support message. In: Proceedings of ION GNSS + 2015, Tampa, Florida, September 14–18, pp 735–745
DoD US (2008) Global positioning system standard positioning service performance standard, GPS SPS PS, September 2008, Department of Defense, US
Guo J (2014) The impacts of attitude, solar radiation and function model on precise orbit determination for GNSS satellites. PhD dissertation (in Chinese with English abstracts), Wuhan University, Wuhan, China
Guo J, Xu X, Zhao Q, Liu J (2016) Precise orbit determination for quad-constellation satellites at Wuhan University: strategy, result validation, and comparison. J Geodesy 90(2):143–159. doi:10.1007/s00190-015-0862-9
Heng L, Gao GX, Walter T, Enge P (2010) GPS ephemeris error screening and results for 2006–2009. In: Proceedings of ION ITM 2010, San Diego, CA, January 25–27, pp 1014–1022
Heng L, Gao GX, Walter T, Enge P (2011) Statistical characterization of GPS signal-in-space errors. In: Proceedings of ION ITM 2011, San Diego, CA, January 24–26, pp 312–319
Heng L, Gao GX, Walter T, Enge P (2012a) GLONASS signal-in-space anomalies since 2009. In: Proceedings of ION GNSS 2012, Nashville, Tennessee, September 17–21, pp 833–842
Heng L, Gao GX, Walter TF, Enge PK (2012b) GPS signal-in-space integrity performance evolution in the last decade: data mining 400,000,000 navigation messages from a global network of 400 receivers. IEEE Trans Aerosp Electron Syst 48(4):2932–2946
Heng L, Gao GX, Walter T, Enge P (2012b) Statistical characterization of GLONASS broadcast clock errors and signal-in-space errors. In: Proceedings of ION ITM 2012, Newport Beach, California, January 30-February 1, pp 1697–1707
Hu Z, Chen G, Zhang Q, Guo J, Su X (2013) An initial evaluation about BDS navigation message accuracy. In: Proceedings of China satellite navigation conference (CSNC) 2013, Wuhan, China, May 15–17, Springer, Berlin, pp 479–491
IGS/RTCM (2013) RINEX, the receiver independent exchange format, 3 April 2013, IGS RINEX WG and RTCM-SC104
Jefferson D, Bar-Sever Y (2000) Accuracy and consistency of broadcast GPS ephemeris data. In: Proceedings of ION GPS 2000, Salt Lake City, UT, September 19–22, pp 391–395
Kouba J (2009) A guide to using international GNSS service (IGS) products, http://acc.igs.org/UsingIGSProductsVer21.pdf
Martini I, Belabbas B, Perea S, Meurer M (2016) Model of signal in space biases in the integrity support message and advanced RAIM algorithm. In: Proceedings of ION ITM 2016, Monterey, California, January 25–28, pp 193–207
Montenbruck O, Steigenberger P, Hauschild A (2015) Broadcast versus precise ephemerides: a multi-GNSS perspective. GPS Solut 19(2):321–333. doi:10.1007/s10291-014-0390-8
Walter T, Blanch J (2015) Characterization of GPS clock and ephemeris errors to support ARAIM. In: Proceedings of ION 2015 Pacific PNT meeting, Honolulu, Hawaii, April 20–23, pp 920–931
Wu Y, Wang J, Jiang Y (2013) Advanced receiver autonomous integrity monitoring (ARAIM) schemes with GNSS time offset. Adv Space Res 52(1):52–61
Zhang Q, Sui L, Jia X (2014) SIS error statistical analysis of BeiDou satellite navigation system. Geo Inf Sci Wuhan Univ 39(3):217–274
Zhao Q, Guo J, Li M, Qu L, Hu Z, Shi C, Liu J (2013) Initial results of precise orbit and clock determination for COMPASS navigation satellite system. J Geod 87(5):475–486. doi:10.1007/s00190-013-0622-7
Zhou S, Hu X, Liu L, Guo R, Zhu L et al (2016) Applications of two-way satellite time and frequency transfer in the Bei Dounavigation satellite system. Sci China Phys Mech Astron 59:109511. doi:10.1007/s11433-016-0185-6
Acknowledgements
The authors gratefully acknowledge the support of the National Key R&D Program of China (No. 2016YFB0501803), the National Natural Science Foundation of China (No. 41304005, 91638203, 41774031), and LIESMARS Special Research Funding.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, Y., Liu, X., Liu, W. et al. Long-term behavior and statistical characterization of BeiDou signal-in-space errors. GPS Solut 21, 1907–1922 (2017). https://doi.org/10.1007/s10291-017-0663-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10291-017-0663-0