Linear combination optimization model of BeiDou triple-frequency integral coefficient carrier phase observation

MENG Fanjun1 LI Shujun1 PAN Zongpeng2 LI Zhongpan2 SUN Yicheng

(1.Department of Military Oceanography and Hydrography & Cartography, PLA Dalian Naval Academy, Dalian, Liaoning Province, China 116018)
(2.Institute of Surveying and Mapping, Information Engineering University, Zhengzhou, Henan Province, China 450001)
【Knowledge Link】scale factor

【Abstract】According to the application requirements of BeiDou triple-frequency observation, the linear combination observation model was established. Based on the error analysis of the model, a spatial analysis of the real coefficient ionosphere-free combination, troposphere-free combination, and minimum noise combination weakening or eliminating errors was conducted from a geometric perspective. Then, the relationship between the ionosphere-free plane, the troposphere-free plane, and the minimum noise line was more intuitively described. Upon this basis, the linear combination of the BeiDou integral coefficient was derived, and the combination of long wavelengths, weak ionospheric delay and weak observation noise was analyzed. Moreover, the number of lanes, the ionospheric delay coefficient and the noise amplification factor were used as the judgment indicators for the linear combination of the optimal triple-frequency integral coefficient. Finally, several sets of the linear combination of the optimal triple-frequency integral coefficient with different characteristics represented by (−1, −5, 6), (0, −1, 1), and (1, 4, −5) were obtained, and the sum of the coefficients of the optimized liner combination model of triple-frequency integral coefficient was generally S = 0 or S = ±1.

【Keywords】 BeiDou triple-frequency observation; integral coefficient; linear combination; ionosphere-free; troposphere-free; the minimum noise; long wavelength;


【Funds】 National Natural Science Foundation of China (41571441)

Download this article

(Translated by FAN JC)


    [1] YANG Yuanxi. Progress, contribution and challenges of Compass/BeiDou satellite navigation system [J]. Acta Geodaetica et Cartographica Sinica, 2010, 39 (1): 1–6 (in Chinese).

    [2] LI Jinlong, YANG Yuanxi, HE Haibo, et al. Optima carrier-phase combinations for triple-frequency GNSS derived from an analytical method [J]. Acta Geodaetica et Cartographica Sinica, 2012, 41 (6): 797–803 (in Chinese).

    [3] GNSS & LBS Association of China. China satellite navigation and location service industry development white paper [R]. [S. l.]: [s. n.], 2018 (in Chinese).

    [4] RICHERT T. The impact of future global navigation satellite systems on precise carrier phase positioning [D]. Calgary: University of Calgary, 2005.

    [5] RICHERT T, EI-SHEIMY N. Optimal linear combinations of triple frequency carrier phase data from future global navigation systems [J]. GPS Solutions, 2007, 11 (1): 11–19.

    [6] COCARD M, BOURGON S, KAMALI O, et al. A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS [J]. Journal of Geodesy, 2008, 82 (9): 555–564.

    [7] HUANG Lingyong, SONG Lijie, WANG Yan, et al. BeiDou triple-frequency geometry-free phase combination for cycle-slip detection and correction [J]. Acta Geodaetica et Cartographica Sinica, 2012, 41 (5): 763–768 (in Chinese).

    [8] LI Jinlong, YANGYuanxi, XU Junyi, et al. Real-time cycle-slip detection and repair based on code-phase combinations for GNSS triple frequency un-differenced observations [J]. Acta Geodaetica et Cartographica Sinica, 2011, 40 (6): 717–722, 729 (in Chinese).

    [9] ZHANG Xiaohong, HE Xiyang. BDS triple-frequency carrier-phase linear combination models and their characteristics [J]. Science China (Earth Sciences), 2015, 58 (6): 896–905.

    [10] YAN Huaicheng, HAN Baomin, ZHANG Jiaxin. Research on triple-frequency carrier-phase observation linear combination of BeiDou satellite navigation system [J]. Chinese Space Science and Technology, 2017, 37 (1): 104–110 (in Chinese).

    [11] WANG Huarun, CHAI Hongzhou, XIE Kai. Study of cycle-slip detection using BDS triple frequency geometry-free and ionosphere-free combination [J]. Journal of Geodesy and Geodynamics, 2015, 35 (3): 406–411 (in Chinese).

    [12] WANG Shengzhao. Study on the ambiguity resolution methods based on Compass triple frequency data [D]. Xuzhou: China University of Mining and Technology, 2015 (in Chinese).

    [13] XIE Kai. Research on ambiguity resolution based on Compass triple-frequency data [D]. Zhengzhou: Information Engineering University, 2014 (in Chinese).

    [14] YU Xingwang. Multi-frequency GNSS precise positioning theory and method research [D]. Wuhan: Wuhan University, 2011 (in Chinese).

    [15] TANG Weiming, DENG Chenlong, SHI Chuang, et al. Triple-frequency carrier ambiguity resolution for BeiDou navigation satellite system [J]. GPS Solutions, 2014, 18 (3): 335–344.

This Article


CN: 11-4415/P

Vol 44, No. 08, Pages 1-5+60

August 2019


Article Outline



  • 0 Introduction
  • 1 BeiDou triple-frequency combination observation model
  • 2 Linear combination of triple-frequency real coefficient that reduces error
  • 3 Linear combination of the optimal triple-frequency integral coefficient
  • 4 Conclusion
  • References