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VC-LAMBDA: a baseline vector constrained LAMBDA method for integer least-squares estimation

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Abstract

Global navigation satellite system (GNSS) ambiguity resolution is the key to realize high-precision navigation and positioning applications. For some dynamic application scenes such as moving-baseline-based positioning and attitude determination, the baseline information of GNSS antennas can be measured in advance; such a priori information can contribute to integer ambiguity resolution, especially when it is in weak GNSS models. In this research, a baseline vector constrained ambiguity resolution method (VC-LAMBDA) is demonstrated theoretically and verified experimentally. The objective function of VC-LAMBDA method is derived firstly, and then the corresponding search algorithm is designed, with an adaptive search space strategy adopted to speed up the search efficiency. The VC-LAMBDA method extends the scalar baseline length constrained LAMBDA method (C-LAMBDA) to the three-dimensional vector case, and simplifies the nonlinearly constrained integer least-squares (ILS) problem to a linearly constrained ILS problem. Two groups of real-measured data with one vehicle platform and one aircraft platform are tested to evaluate the practical performance of VC-LAMBDA, also compared with standard LAMBDA and C-LAMBDA methods. The two experiments show consistent results that VC-LAMBDA performs better than C-LMABDA method in ambiguity fixed success rate, robustness and time consumption, and both the two baseline constraint methods are significantly superior than standard LAMBDA method when it is in weak GNSS models.

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

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Acknowledgements

This study is supported by the National Key R&D Program of China (Grant No.2021YFC3000501), the National Postdoctoral Program for Innovative Talents, China (Grant No. BX20200249), the National Natural Science Foundation of China (Grant No. 41804020), the Hubei Technological Innovation Special Fund (Grant No. 2019AAA043), the Key Laboratory of Spatial Information and Geomatics (Guilin University of Technology) (No.19-185-10-10), and the China Postdoctoral Science Foundation (Grant No. 2020M682484).

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Authors and Affiliations

  1. GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan, 430079, Hubei, China

    Liye Ma & Yidong Lou

  2. School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan, 430079, Hubei, China

    Feng Zhu, Wanke Liu & Xiaohong Zhang

  3. Faculty of Geomatics, East China University of Technology, 418 Guanglan Road, Nanchang, 330013, Jiangxi, China

    Liguo Lu

  4. Guangxi Key Laboratory of Spatial Information and Geomatics, Guilin University of Technology, 12 Jiangan Road, Guilin, 541004, Guangxi, China

    Liguo Lu

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  1. Liye Ma
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  2. Feng Zhu
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  3. Wanke Liu
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  4. Liguo Lu
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  5. Yidong Lou
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  6. Xiaohong Zhang
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Contributions

FZ devised the main conceptual ideas. LYM and FZ performed the research, analyzed the data and wrote the paper. WKL and LGL provided guidance for the development of the algorithm. YDL and XHZ gave helpful discussion on shaping the analysis, result and manuscript.

Corresponding author

Correspondence to Feng Zhu.

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Ma, L., Zhu, F., Liu, W. et al. VC-LAMBDA: a baseline vector constrained LAMBDA method for integer least-squares estimation. J Geod 96, 59 (2022). https://doi.org/10.1007/s00190-022-01644-7

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