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Acknowledgements BeiDou-3 signals. Journal of Geodesy, 94(1), 14.
The numerical calculations in this paper was done on the supercomputing Guo, J., Li, X., Li, Z., Hu, L., Yang, G., Zhao, C., et al. (2018). Multi-GNSS precise
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Authors’ contributions Horn, B. (1987). Closed-form solution of absolute orientation using unit quater-
XL conceived the idea and revised the paper; XW analyzed the data and wrote nions. Journal of the Optical Society of America A, 4(4), 629–642.
the paper; JL and SL assisted in data acquisition and article revision; XL and HL Huber, P. (1964). Robust estimation of a location parameter. Annals of Math-
helped with the writing. All authors read and approved the fnal manuscript. ematical Statistics, 35(2), 73–101.
Lepetit, V., Moreno-Noguer, F., & Fua, P. (2009). Epnp: an accurate o(n) solu-
Funding tion to the pnp problem. International Journal of Computer Vision, 81(2),
This study is fnancially supported by the National Natural Science Foundation 155–166.
of China (Grant No. 41774030, Grant 41974027), the Hubei Province Natural Leutenegger, S., Lynen, S., Bosse, M., Siegwart, R., & Furgale, P. (2015). Keyframe-
Science Foundation of China (Grant No. 2018CFA081), the National Youth based visual-inertial odometry using nonlinear optimization. The Interna-
Thousand Talents Program, the frontier project of basic application from tional Journal of Robotics Research, 34(3), 314–334.
Wuhan science and technology bureau (Grant No. 2019010701011395), and Li, M. & Mourikis, A. I. (2012). Improving the accuracy of EKF-based visual-
the Sino-German mobility programme (Grant No. M-0054). inertial odometry. In Proceedings of the IEEE international conference on
robotics and automation (pp. 828–835).
Availability of data and materials Li, T., Zhang, H., Gao, Z., Niu, X., & El-Sheimy, N. (2019b). Tight fusion of a
The datasets used and analysed in this study are available from the corre- monocular camera, MEMS-IMU, and single-frequency multi-GNSS RTK for
sponding author on reasonable request. precise navigation in GNSS-challenged environments. Remote Sensing,
11(6), 610.
Competing interests Li, X., Li, X., Liu, G., Feng, G., Yuan, Y., Zhang, K., et al. (2019a). Triple-frequency
The authors declare that they have no competing interests. PPP ambiguity resolution with multi-constellation GNSS: BDS and Galileo.
Jouranl of Geodesy, 93(8), 1105–1122.
Received: 17 July 2020 Accepted: 1 December 2020 Li, X., Li, X., Liu, G., Xie, W., & Feng, G. (2020a). The phase and code biases of
Galileo and BDS-3 BOC signals: efect on ambiguity resolution and pre-
cise positioning. Journal of Geodesy, 94(1), 9.
Li, X., Liu, G., Li, X., Zhou, F., Feng, G., Yuan, Y., et al. (2020b). Galileo PPP rapid
ambiguity resolution with fve-frequency observations. GPS Solutions,
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