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Connecting integer ambiguities to avoid reinitialization and keep VRS seamless switching for virtual grid-based NRTK

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Abstract

Virtual grid technology-based network real-time kinematic (NRTK) is the key to wide-area high-accuracy positioning and navigation. In long-distance kinematic positioning applications, the virtual reference station (VRS) closest to the rover is selected, which brings about frequent switching in VRSs. Due to inconsistent ambiguities between the previous and the current VRSs, the between-station differenced carrier phase ambiguities of the rover, and the current VRS are regarded as cycle slips, leading to the reinitialization of ambiguities and therefore result in damaging positioning accuracy and continuity of the rover. An integer ambiguity connection method (IAC) is proposed to avoid reinitialization in VRS switching, which is able to maintain high-accuracy, continuous, and high-availability positioning performance. In this method, the between-station differenced ambiguities of the original and the new VRSs are fixed with asynchronous RTK and then transmitted to the rover; in this way, the rover can directly build the between-station differenced ambiguities with the new VRS to realize seamless switching. The performance evaluation is first conducted for the IAC method with simulation experiments using virtual grid-based NRTK (VGB-NRTK) service. Then, two sets of multiple-switching ship-borne experiments were carried out, and the data were processed with IAC method by post-processed kinematic. The results show that when VRS switches, integer ambiguities are reinitialized and fixed again after several epochs with the traditional strategy, while they can be kept continuously with the IAC method.

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The data used in this manuscript are available from the corresponding author upon request.

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Acknowledgements

The research was supported by the National Key Research and Development Program of China (Grant No. 2020YFB0505803), the National Natural Science Foundation of China (Grant No. 42104021), the Science and Technology Major Project of Hubei Province (Grant No. 2021AAA010), the Special Fund of Hubei Luojia Laboratory (Grant No. 220100005), the Wuhan Science and Technology Project (Grant No. 2020010601012185), and the Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University (Grant No. 20-02-01).

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Authors and Affiliations

  1. School of Geodesy and Geomatics, Hubei Luojia Laboratory, Wuhan University, 129 Luoyu Road, Wuhan, 430079, Hubei, China

    Feng Zhu, Xi Chen, Wanke Liu, Yingzhe Wang & Xiaohong Zhang

  2. Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, 129 Luoyu Road, Wuhan, 430079, Hubei, China

    Feng Zhu

  3. Chinese Antarctic Center of Surveying and Mapping, Wuhan University, 129 Luoyu Road, Wuhan, 430079, Hubei, China

    Xiaohong Zhang

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  1. Feng Zhu
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  2. Xi Chen
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  3. Wanke Liu
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  4. Yingzhe Wang
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  5. Xiaohong Zhang
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Contributions

All authors contributed to the study concept and design. FZ devised the main conceptual ideas. FZ, XC and YZW performed the research, analyzed the data, and wrote the paper. XHZ and WKL gave helpful discussions on shaping the analysis and result of the manuscript.

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Correspondence to Wanke Liu.

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Appendix: Results of traversing VRSs in directions B and C

Appendix: Results of traversing VRSs in directions B and C

When traversing the VRSs in direction B, 307 VRSs were observed. The ambiguity resolution status of the VRSs is shown in Figs. 17 and 18. PAR succeeded on all the VRSs within ten epochs, with a maximum of three epochs and an average of 1.36 epochs. There are 119 pairs of VRSs whose single-differenced ambiguities are not equal to zero. The average SAFR of all the VRSs is given in Table 10, from which it can be seen GPS is the lowest at 88.8%, followed by Galileo at 94.0%, and BDS is the highest at 94.4%.

Fig. 17
figure 17

Distribution of VRSs in direction B with SAFRs for Fre. 1 (left), Fre. 2 (middle), and Fre. 3 (right) of GPS (top), GAL (middle), and BDS (bottom). Different colors on the grid points correspond to different satellite ambiguity fixing rates, which are provided in Table 2

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Fig. 18
figure 18

Distribution of VRSs in direction B with the SAFR for multi-system (top) and multifrequency (bottom). Different colors on the grid points correspond to different satellite ambiguity fixing rates, which are provided in Table 2

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Table 10 Statistics of the average SAFR of all the VRSs in direction B
Full size table

When traversing the VRSs in direction C, 311 VRSs were observed. The ambiguity resolution status of the VRSs is illustrated in Figs. 19 and 20. PAR succeeded on all the VRSs within 10 s, with an average of 1.36 epochs and a maximum of three epochs. There are 157 pairs of VRSs whose single-differenced ambiguities are not the same. Table 11 shows the averaged SAFR for all the VRSs. For the averaged SAFR, GPS is the lowest at 87.1%, followed by Galileo at 91.9% and BDS has the highest SAFR at 93.6%.

Fig. 19
figure 19

Distribution of VRSs in direction C with SAFRs for Fre. 1 (left), Fre. 2 (middle), and Fre. 3 (right) of GPS (top), GAL (middle), and BDS (bottom). Different colors on the grid points correspond to different satellite ambiguity fixing rates, which are provided in Table 2

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Fig. 20
figure 20

Distribution of VRSs in direction C with the SAFR for multi-system (top) and multifrequency (bottom). Different colors on the grid points correspond to different satellite ambiguity fixing rates, which are provided in Table 2

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Table 11 Statistics of the averaged SAFR for all the VRSs in direction C
Full size table

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Zhu, F., Chen, X., Liu, W. et al. Connecting integer ambiguities to avoid reinitialization and keep VRS seamless switching for virtual grid-based NRTK. GPS Solut 27, 133 (2023). https://doi.org/10.1007/s10291-023-01471-z

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