Abstract
Global navigation satellite systems (GNSS) are acting as an indispensable tool for geodetic research and global monitoring of the Earth, and they have been rapidly developed over the past few years with abundant GNSS networks, modern constellations, and significant improvement in mathematic models of data processing. However, due to the increasing number of satellites and stations, the computational efficiency becomes a key issue and it could hamper the further development of GNSS applications. In this contribution, this problem is overcome from the aspects of both dense linear algebra algorithms and GNSS processing strategy. First, in order to fully explore the power of modern microprocessors, the square root information filter solution based on the blocked QR factorization employing as many matrix–matrix operations as possible is introduced. In addition, the algorithm complexity of GNSS data processing is further decreased by centralizing the carrier-phase observations and ambiguity parameters, as well as performing the real-time ambiguity resolution and elimination. Based on the QR factorization of the simulated matrix, we can conclude that compared to unblocked QR factorization, the blocked QR factorization can greatly improve processing efficiency with a magnitude of nearly two orders on a personal computer with four 3.30 GHz cores. Then, with 82 globally distributed stations, the processing efficiency is further validated in multi-GNSS (GPS/BDS/Galileo) satellite clock estimation. The results suggest that it will take about 31.38 s per epoch for the unblocked method. While, without any loss of accuracy, it only takes 0.50 and 0.31 s for our new algorithm per epoch for float and fixed clock solutions, respectively.
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Acknowledgements
This study is partially supported by the National Key Research and Development Plan (No. 2016YFB0501802), the National Natural Science Foundation of China (41374034 and 41504028), and the Natural Science Foundation of Hubei (2015CFB326). And the thanks are also given to IGS and CMONOC for providing data.
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Appendix
Appendix
According to Eqs. (5) to (10) in Sect. 2.1, Tables 6 and 7 give the details of algorithm complexity of each step involved in filter and prediction, respectively. It is noted that we do not distinguish different operators (e.g., addition, subtraction, multiplication, division), in other words, they are all treated as one arithmetic operation in the following analysis. Here again, \(n=n_y +n_p \) is the number of parameters, m represents the number of observations plus parameters; \(r=\frac{n_y}{n_p}\) is the ratio of the parameter number of ambiguities to other unknowns.
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Gong, X., Gu, S., Lou, Y. et al. An efficient solution of real-time data processing for multi-GNSS network. J Geod 92, 797–809 (2018). https://doi.org/10.1007/s00190-017-1095-x
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DOI: https://doi.org/10.1007/s00190-017-1095-x