Skip to main content
SpringerLink
Log in

GNSS-RTK model: common-frequency versus mixed-frequency

  • Original Article
  • Published:
GPS Solutions Aims and scope Submit manuscript

Abstract

Global navigation satellite system real-time kinematic (RTK) normally takes advantage of a common-frequency (CF) model, in which, the frequency bands in use are assumed to be the same across all satellites visible to two receivers. This assumption discards satellites whose frequency bands differ from the majority of satellites, thereby weakening the CF model. In this contribution, we present a mixed-frequency (MF) RTK model that considers all satellites whose frequency bands may vary from each other. Due to the new rank deficiencies in the MF RTK model, the formulation of the MF RTK model needs to choose a set of unknown parameters as an S-basis based on the S-system theory. The formulated MF model is more generally applicable than the CF model, particularly for the BeiDou navigation satellite system (BDS) since its second-generation (BDS2) satellites broadcast B1I, B2I, and B3I signals and its third-generation (BDS3) satellites broadcast B1I, B3I, B1C, B2a, and B2b signals. To verify, we collected BDS data at a static station and a kinematic vehicle which are a zero-baseline and an approximate 10 km baseline, respectively, to test the MF model and compared it with three CF models employing BDS2 B1I + B2I + B3I (CF1), BDS3 B1I + B3I + B1C + B2a + B2b (CF2) and BDS B1I + B3I (CF3) observables. Both static and kinematic results show that the MF model outperforms the three CF models regarding the time-to-first-fix of integer ambiguity resolution and positioning accuracy. The MF model obtains the most accurate positioning; the fixed positioning errors (95% quantile) in the east, north, and up components are, in cm, 0.094, 0.081, and 0.230 in the static test and 5.49, 6.30, and 9.54 in the kinematic test, respectively. Compared with the CF model utilizing all BDS satellites (CF3), the MF model reduces the positioning error by 21.7%, 19.0%, and 11.5% in the east, north, and up components in the static test and 52.7%, 57.6%, and 58.4% in the kinematic test, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

References

  • Baarda W (1973) S-transformations and criterion matrices. In: Publications on Geodesy, 18, vol 5, no 1. Netherlands Geodetic Commission, Delft, The Netherlands

  • Gao R, Liu Z, Zhang B (2022) Ionosphere-weighted post-processing kinematic for airborne positioning with refined modeling of receiver phase biases and tropospheric zenith wet delays. GPS Solut 26(4):1–14

    Article  Google Scholar 

  • Guo F, Zhang X, Wang J, Ren X (2016) Modeling and assessment of triple-frequency BDS precise point positioning. J Geod 90(11):1223–1235

    Article  Google Scholar 

  • Hu C, Wang Q, Wu Z, Guo Z (2022) A mixed multi-frequency precise point positioning strategy based on the combination of BDS-3 and GNSS multi-frequency observations. Meas Sci Technol 34(2):025008

    Article  Google Scholar 

  • Li Y, Cai C (2022) A mixed single-and dual-frequency quad-constellation GNSS precise point positioning approach on Xiaomi Mi8 smartphones. J Navig 75(4):849–863

    Article  Google Scholar 

  • Li B, Chen G (2022) Improving the combined GNSS/INS positioning by using tightly integrated RTK. GPS Solut 26(4):1–14

    Article  Google Scholar 

  • Li X, Li X, Huang J, Shen Z, Wang B, Yuan Y, Zhang K (2021) Improving PPP–RTK in urban environment by tightly coupled integration of GNSS and INS. J Geod 95(12):1–18

    Article  Google Scholar 

  • Mi X, Zhang B, Odolinski R, Yuan Y (2020) On the temperature sensitivity of multi-GNSS intra-and inter-system biases and the impact on RTK positioning. GPS Solut 24(4):1–14

    Article  Google Scholar 

  • Montenbruck O, Schmid R, Mercier F, Steigenberger P, Noll C, Fatkulin R, Kogure S, Ganeshan A (2015) GNSS satellite geometry and attitude models. Adv Space Res 56(6):1015–1029

    Article  Google Scholar 

  • Montenbruck O et al (2017) The multi-GNSS experiment (MGEX) of the international GNSS service (IGS)–achievements, prospects and challenges. Adv Space Res 59(7):1671–1697

    Article  Google Scholar 

  • Odolinski R, Teunissen PJ (2016) Single-frequency, dual-GNSS versus dual-frequency, single-GNSS: a low-cost and high-grade receivers GPS-BDS RTK analysis. J Geod 90(11):1255–1278

    Article  Google Scholar 

  • Odolinski R, Teunissen PJ (2017) Low-cost, high-precision, single-frequency GPS–BDS RTK positioning. GPS Solut 21(3):1315–1330

    Article  Google Scholar 

  • Odolinski R, Odijk D, Teunissen PJ (2014a) Combined GPS and BeiDou instantaneous RTK positioning: combined GPS and BeiDou RTK. Navigation 61(2):135–148

    Article  Google Scholar 

  • Odolinski R, Teunissen P, Odijk D (2014b) combined GPS+ BDS+ Galileo+ QZSS for long baseline RTK positioning. In: Proceeding of the ION GNSS 2014b. Institute of Navigation, Tampa, Florida, USA, September 8–12, pp 2326–2340

  • Shi J, Ouyang C, Huang Y, Peng W (2020) Assessment of BDS-3 global positioning service: ephemeris, SPP, PPP, RTK, and new signal. GPS Solut 24(3):1–14

    Article  Google Scholar 

  • Teunissen P (1985) Generalized inverses, adjustment, the datum problem and S-transformations. In: Grafarend EW, Sanso F (eds) Optimization of geodetic networks. Springer, Berlin

    Google Scholar 

  • Teunissen P (1990) Quality control in integrated navigation systems. IEEE Aerosp Electron Syst Mag 5(7):35–41

    Article  Google Scholar 

  • Teunissen PJG (1998) Success probability of integer GPS ambiguity rounding and bootstrapping. J Geod 72:606–612

    Article  Google Scholar 

  • Teunissen PJ (1999) An optimality property of the integer least-squares estimator. J Geod 73:587–593

    Article  Google Scholar 

  • Teunissen PJ, Montenbruck O (2017) Springer handbook of global navigation satellite systems, vol 10. Springer

    Book  Google Scholar 

  • Verhagen S, Teunissen PJ (2013) The ratio test for future GNSS ambiguity resolution. GPS Solut 17(4):535–548

    Article  Google Scholar 

  • Yang Y, Mao Y, Sun B (2020) Basic performance and future developments of BeiDou global navigation satellite system. Satell Navig 1(1):1–8

    Article  Google Scholar 

  • Zha J, Zhang B, Liu T, Hou P (2021) Ionosphere-weighted undifferenced and uncombined PPP-RTK: theoretical models and experimental results. GPS Solut 25(4):1–12

    Article  Google Scholar 

  • Zhang B, Teunissen PJ, Odijk D (2011) A novel un-differenced PPP-RTK concept. J Navig 64(S1):S180–S191

    Article  Google Scholar 

  • Zhang X, Wu M, Liu W, Li X, Lu C, Wickert J (2017) Initial assessment of the COMPASS/BeiDou-3: new-generation navigation signals. J Geod 91(10):1225–1240

    Article  Google Scholar 

  • Zhang B, Hou P, Zha J, Liu T (2022) PPP–RTK functional models formulated with undifferenced and uncombined GNSS observations. Satell Navig 3(1):3

    Article  Google Scholar 

Download references

Acknowledgements

This work was funded by the National Natural Science Foundation of China (Grant No. 42022025). The corresponding author is supported by the CAS Pioneer Hundred Talents Program.

Author information

Authors and Affiliations

  1. State Key Laboratory of Geodesy and Earth’s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan, China

    Cheng Ke, Pengyu Hou & Baocheng Zhang

  2. College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China

    Cheng Ke & Pengyu Hou

  3. (German) International Science and Technology Cooperative Offshore Center for Geodesy Frontier Technology, Wuhan, China

    Baocheng Zhang

Authors
  1. Cheng Ke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pengyu Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Baocheng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

CK processed the data and analyzed the results. CK and PH wrote the manuscript. BZ proposed the method, designed the research, and wrote the manuscript.

Corresponding author

Correspondence to Baocheng Zhang.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ke, C., Hou, P. & Zhang, B. GNSS-RTK model: common-frequency versus mixed-frequency. GPS Solut 27, 128 (2023). https://doi.org/10.1007/s10291-023-01465-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10291-023-01465-x

Keywords

Search

Navigation