## Abstract

We describe a method to assess the performance of the third-generation BeiDou navigation satellite system (BDS-3), in terms of satellite visibility and dilution of precision (DOP), on global and regional scales. Different from traditional methods, this method estimates the satellite visibility and DOP without requiring real or simulated ephemerides. Validated by the reference values derived from real ephemerides of GPS and GLONASS, the estimated number of visible satellites achieves an accuracy better than 0.15, and the estimated DOP values are lower than their reference values by less than 10% on average. Applying this method to BDS-3, with a 5° cutoff elevation angle, results show that the geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites of BDS-3 together contribute 3–6 visible satellites in the area of 60°S–60°N and 50°E–170°E. In this area, the number of visible BDS-3 satellites is 11–14, which is more than GPS and Galileo by 1–3, and GLONASS by 3–7. With better satellite visibility, the average BDS-3 horizontal, vertical, and time DOPs over this area are 0.74, 1.08, and 0.67, which are, respectively, 5%, 9%, and 3% lower than those of GPS and Galileo, 14%, 16%, and 21% lower than those of GLONASS, and 16%, 19% and 14% lower than those of the 24-MEO-only BDS-3.

### Similar content being viewed by others

## References

Bian S, Jin J, Fang Z (2005) The Beidou satellite positioning system and its positioning accuracy. Navigation 52(3):123–129

Cai C, He C, Santerre R, Pan L, Cui X, Zhu J (2016) A comparative analysis of measurement noise and multipath for four constellations: GPS, BeiDou, GLONASS and Galileo. Surv Rev 48(349):287–295

Cao Y, Hu X, Wu B, Zhou S, Liu L, Su R, Chang Z, He F, Zhou J (2012) The wide-area difference system for the regional satellite navigation system of COMPASS. Sci China Phys Mech 55(7):1307–1315

Chen J (2007) On precise orbit determination of low earth orbiters. Dissertation, Tongji University

Chen J, Chen Q, Wang B, Yang S, Zhang Y, Wang J (2017a) Analysis of inner-consistency of BDS broadcast ephemeris parameters and their performance improvement. In Proceedings of the ION Pacific PNT 2017 Conference, Honolulu, Hawaii, May 1–4, 2017

Chen J, Yang S, Zhou J, Cao Y, Zhang Y, Gong X, Wang J (2017b) A pseudo-range and phase combined SBAS differential correction model. Acta Geodaetica Cartogr Sin 46(5):537–546

Chiang K, Huang Y, Tsai M, Chen K (2010) The perspective from Asia concerning the impact of Compass/Beidou-2 on future GNSS. Surv Rev 42(315):3–19

CSNO (2012) Report on the development of BeiDou navigation satellite system (Version 2.1). China Satellite Navigation Office, Beijing

CSNO (2019) BeiDou navigation satellite system signal in space interface control document—open service signal B1I (Version 3.0). China Satellite Navigation office, Beijing

Eissfeller B, Ameres G, Kropp V, Sanroma D (2007) Performance of GPS, GLONASS and Galileo. In: Fritsch D (ed) Photogrammetric Week 07, Stuttgart, Germany, 3–7 September. 2007, Wichmann, Berlin Offenbach, pp 185–199

Gumilar I, Bramanto B, Kuntjoro W, Abidin H, Trihantoro N (2018) Contribution of BeiDou satellite system for long baseline GNSS measurement in Indonesia. In IOP Conference Series: Earth and Environmental Science 149(1):012070

Hauschild A, Montenbruck O, Sleewaegen J, Huisman L, Teunissen P (2012) Characterization of compass M-1 signals. GPS Solut 16(1):117–126

Hofmann-Wellenhof B, Lichtenegger H, Wasle E (2007) GNSS–global navigation satellite systems: GPS, GLONASS, Galileo, and more. Springer, Berlin

Kihara M, Okada T (1984) A satellite selection method and accuracy for the global positioning system. Navigation 31(1):8–20

Lou Y, Li X, Zheng F, Liu Y, Guo H (2018) Assessment and impact on BDS positioning performance analysis of recent BDS IGSO-6 satellite. J Navig 71(3):729–748

Meng X, Roberts G, Dodson A, Cosser E, Barnes J, Rizos C (2004) Impact of GPS satellite and pseudolite geometry on structural deformation monitoring: analytical and empirical studies. J Geod 77(12):809–822

Montenbruck O, Steigenberger P (2013) The BeiDou navigation message. J Glob Position Syst 12(1):1–12

Montenbruck O, Hauschild A, Steigenberger P, Hugentobler U, Teunissen P, Nakamura S (2013) Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system. GPS Solut 17(2):211–222

Parkinson B (1996) GPS error analysis. In: Parkinson B, Enge P, Axelrad P, Spilker J (eds) Global positioning system: theory and applications, vol I. American Institute of Aeronautics and Astronautics, Inc., Cambridge, Massachusetts, pp 469–484

Spilker J (1996) Satellite constellation and geometric dilution of precision. In: Parkinson B, Enge P, Axelrad P, Spilker J (eds) Global positioning system: theory and applications, Volume I. American Institute of Aeronautics and Astronautics, Inc., Cambridge, Massachusetts, pp 177–208

Wang J, Iz H, Lu C (2002) Dependency of GPS positioning precision on station location. GPS Solut 6(1–2):91–95

Wang G, de Jong K, Zhao Q, Hu Z, Guo J (2015) Multipath analysis of code measurements for BeiDou geostationary satellites. GPS Solut 19(1):129–139

Wanninger L, Beer S (2015) BeiDou satellite-induced code pseudorange variations: diagnosis and therapy. GPS Solut 19(4):639–648

Xiao W, Liu W, Sun G (2016) Modernization milestone: BeiDou M2-S initial signal analysis. GPS Solut 20(1):125–133

Yahya M, Kamarudin M (2008) Analysis of GPS visibility and satellite-receiver geometry over different latitudinal regions. In International Symposium on Geoinformation (ISG 2008): Kuala Lumpur, Malaysia, pp 13–15

Yang Y (2010) Progress, contribution and challenges of Compass/Beidou satellite navigation system. Acta Geodaetica Cartogr Sin 39(1):1–6

Yang Y, Xu J (2016) Navigation performance of BeiDou in polar area. Geomat Inf Sci Wuhan Univ 41(1):15–20

Yang Y, Li J, Xu J, Tang J, Guo H, He H (2011) Contribution of the compass satellite navigation system to global PNT users. Chinese Sci Bull 56(26):2813–2819

Yang Y, Li J, Wang A, Xu J, He H, Guo H, Shen J, Dai X (2014) Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system. Sci China Earth Sci 57(1):144–152

Yang Y, Tang J, Montenbruck O (2017) Chinese navigation satellite systems. In: Teunissen P, Montenbruck O (eds) Springer handbook of global navigation satellite systems. Springer International Publishing, Cham, pp 273–304

Zhang Y, Chen J, Zhou J, Yang S, Wang B, Chen Q, Gong X (2016) Analysis and application of BDS broadcast ephemeris bias. Acta Geodaetica Cartogr Sin 45(S2):64–71

Zhang X, Wu M, Liu W, Li X, Yu S, Lu C, Wickert J (2017) Initial assessment of the COMPASS/BeiDou-3: New-generation navigation signals. J Geod 91(10):1225–1240

Zhang R, Tu R, Liu J, Hong J, Fan L, Zhang P, Lu X (2018) Impact of BDS-3 experimental satellites to BDS-2: service area, precise products, precise positioning. Adv Space Res 62(4):829–844

## Acknowledgements

This study is supported by National Natural Science Foundation of China (41604017 and 41674029). We would like to express our gratitude to editor Alfred Leick and anonymous reviewers for their constructive comments and suggestions. We thank MGEX and GFZ for providing multi-GNSS orbit products.

## Author information

### Authors and Affiliations

### Corresponding author

## Additional information

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Appendix 1: retrieval of 0.5° × 0.5° grid cells along the figure-8-shape track of BDS-3 IGSO satellites

### Appendix 1: retrieval of 0.5° × 0.5° grid cells along the figure-8-shape track of BDS-3 IGSO satellites

We define a \(\eta {\text{-}}\xi\) coordinate system on the circular orbit plane of a BDS-3 IGSO satellite, with the \(\eta {\text{-}}\)axis pointing to the ascending node and the \(\xi {\text{-}}\)axis pointing to the satellite on the argument of latitude of 90°. The satellite positions on the circular orbit with an interval of 0.25° are

where *R* is the distance between the satellite and the earth center (42,157 km). Their corresponding ECEF Cartesian coordinates are

where \({R_3}( - {\Omega _i})\) and \({R_1}( - {i_{{\text{orb}}}})\) are rotation matrices

where \({i_{{\text{orb}}}}\) is the orbit inclination (55°) and \({\Omega _i}\) is the right ascension of ascending node. Let the satellite be right above the intersection point of subsatellite track (0°, 118°E) at time \({t_0}=0\), and the 1440 satellite positions be corresponding to the positions at time \({t_i}=i\Delta t{\text{ (}}i=1,2,...,1440)\), where\(\Delta t=T/1440\) with \(T=86164\)s (orbit period). Then the \({\Omega _i}\) can be written as

where \(\omega\) is the angular velocity of the satellite.

From the Cartesian coordinates \(({X_i},{Y_i},{Z_i})\), the geocentric latitude\({\varphi _i}\) and longitude \({\lambda _i}\) of the satellite can calculated as

We divide the spherical orbit surface (with the radius of *R*) into 0.5°×0.5° grid cells by geocentric latitude and longitude and use the satellite positions \(({\varphi _i},{\lambda _i})\) \({\text{(}}i=1,2,...,1440)\) to determine which grid cells are on the figure-8-shape satellite track. The sampling interval of 0.25° for calculating the satellite positions ensures that all the 0.5° × 0.5° grid cells on the track are retrieved.

## Rights and permissions

## About this article

### Cite this article

Wang, M., Wang, J., Dong, D. *et al.* Performance of BDS-3: satellite visibility and dilution of precision.
*GPS Solut* **23**, 56 (2019). https://doi.org/10.1007/s10291-019-0847-x

Received:

Accepted:

Published:

DOI: https://doi.org/10.1007/s10291-019-0847-x