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A Precise Weighting Approach with Application to Combined L1/B1 GPS/BeiDou Positioning

Published online by Cambridge University Press:  17 June 2014

Changsheng Cai ,
Lin Pan  and
Yang Gao
Changsheng Cai
Affiliation:
(School of Geosciences and Info-Physics, Central South University, Changsha, China)
Lin Pan
Affiliation:
(School of Geosciences and Info-Physics, Central South University, Changsha, China)
Yang Gao*
Affiliation:
(School of Geomatics, Liaoning Technical University, Fuxin, China) (Department of Geomatics Engineering, University of Calgary, Calgary, Alberta, Canada)
*
(E-mail: ygao@ucalgary.ca)
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Abstract

The BeiDou system has been providing a regional navigation service since 27 December 2012. The Global Navigation Satellite System (GNSS) user community will benefit from combined Global Positioning System (GPS)/BeiDou positioning due to improved positioning accuracy, reliability and availability. But to achieve the best positioning solutions, precise weights of the GPS and BeiDou observations are important since this involves the processing of measurements from two different satellite systems with different quality. Currently, a priori variances are typically used to determine the weights of different types of observations. However, such an approach may not be precise since many un-modelled errors are not accounted for. The Helmert variance component estimation method is more appropriate in this case to determine the weights of GPS and BeiDou observations. This requires high redundant observations in order to obtain reliable solutions, which will be a concern in the case of insufficient numbers of visible satellites. To address this issue, a weighting approach is proposed by a combination of the Helmert method and a moving-window average filter. In this approach, the filter is applied to combine all epoch-by-epoch weight estimates within a time window. As a result, more precise and reliable weights for GPS and BeiDou observations can be obtained at every epoch. Both static and kinematic tests in open sky and under tree environments are conducted to assess the performance of the new weighting approach. The results indicate significantly improved positioning accuracy.

Keywords

GPSBeiDouPrecise weightingCombined GPS/BeiDou positioning
Type
Research Article
Information
The Journal of Navigation , Volume 67 , Issue 5 , September 2014 , pp. 911 - 925
Copyright
Copyright © The Royal Institute of Navigation 2014 

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References

REFERENCES

Brunner, F.K., Hartinger, H. and Troyer, L. (1999). GPS signal diffraction modelling: the stochastic SIGMA-Δ model. Journal of Geodesy, 73(5), 259–267.CrossRefGoogle Scholar
CSNO (2012). BeiDou navigation satellite system signal in space interface control document (open service signal B1I), China Satellite Navigation Office, Version 1.0, December 2012.Google Scholar
Euler, H.J. and Goad, C.C. (1991). On optimal filtering of GPS dual frequency observations without using orbit information. Bulletin Géodésique, 65, 130–143.Google Scholar
Gao, Y. (2004). P3 user manual (version 1.0), University of Calgary, Canada. <http://people.ucalgary.ca/~ygao/images/P3%20manual.pdf>..>Google Scholar
Gerdan, G.P. (1995). A comparison of four methods of weighting double difference pseudorange measurements. The Australian Surveyor, 40(4), 60–66, doi: 10.1080/00050334.1995.10558564.CrossRefGoogle Scholar
Hartinger, H. and Brunner, F.K. (1999). Variances of GPS phase observations: The SIGMA-ε model. GPS Solutions, 2(4), 35–43.Google Scholar
Helmert, F.R. (1907). Die Ausgleichungsrechnung nach der Methode der kleinsten Quadrate, Zweite Auflage, Teubner, Lepzig.Google Scholar
IS-GPS-200F (2011). Global positioning system directorate systems engineering and integration interface specification, September 21, 2011.Google Scholar
Kizilsu, G. and Sahin, M. (2000). SLR precision analysis for LAGEOS I and II. Earth Planes Space, 52(10), 789–794.CrossRefGoogle Scholar
Klobuchar, J. (1987). Ionospheric time-delay algorithms for single-frequency GPS users. IEEE Transactions on Aerospace and Electronic Systems, AES-23(3), 325–331.Google Scholar
Koch, K.R. (1986). Maximum likelihood estimate of variance components. Bulletin Geodesique, 60, 329–338.Google Scholar
Kouba, J. and Héroux, P. (2001). GPS precise point positioning using IGS orbit products. GPS Solutions, 5(2), 12–28, doi:10.1007/PL00012883.Google Scholar
Kusche, J. (2003). A Monte-Carlo technique for weight estimation in satellite geodesy. Journal of Geodesy, 76(11), 641–652, doi: 10.1007/s00190-002-0302-5.Google Scholar
Saastamoinen, J. (1973). Contribution to the theory of atmospheric refraction. Bulletin Géodésique, 107, 13–34.Google Scholar
Shen, Y., Li, B. and Xu, G. (2009). Simplified equivalent multiple baseline solutions with elevation-dependent weights. GPS Solutions, 13(3), 165–171.Google Scholar
Shi, C., Zhao, Q., Hu, Z. and Liu, J. (2012). Precise relative positioning using real tracking data from COMPASS GEO and IGSO satellites. GPS Solutions, 17(1), 103–119, doi: 10.1007/s10291-012-0264-x.Google Scholar
Wang, J.G., Gopaul, N. and Scherzinger, B. (2009). Simplified algorithms of variance component estimation for static and kinematic GPS single point positioning. Journal of Global Positioning Systems, 8(1), 43–52.Google Scholar
Wieser, A. and Brunner, F.K. (2000). An extended weight model for GPS phase observations. Earth Planets Space, 52(10), 777–782.Google Scholar
Zumberge, J.F., Heflin, M.B., Jefferson, D.C., Watkins, M.M. and Webb, F.H. (1997). Precise point positioning for the efficient and robust analysis of GPS data from large networks. Journal of Geophysical Research, 102(B3), 5005–5017, doi: 10.1029/96JB03860.Google Scholar