Advertisement

GPS Solutions

, 23:79 | Cite as

Performance analysis of indoor pseudolite positioning based on the unscented Kalman filter

  • Xin Li
  • Peng ZhangEmail author
  • Guanwen Huang
  • Qin Zhang
  • Jiming Guo
  • Yinzhi Zhao
  • Qingzhi Zhao
Original Article
  • 178 Downloads

Abstract

The indoor pseudolite (PL) code-based solution is not sufficiently precise, and conducting prolonged static carrier phase observations is impractical due to the static PL geometric distribution. Thus, a high-precision indoor PL positioning, which is generally based on the known point initialization (KPI) method and adopts the extended Kalman filter (EKF), is used to obtain the PL float ambiguity solution. However, the first-order linear truncation error of the EKF cannot be neglected because the indoor space is small, and its performance is quite dependent on the accuracy of the initial coordinates in the KPI. In this study, a well-suited nonlinear parameter estimation method, which is expected to have high precision and low dependence on the initial coordinate values, namely the unscented Kalman filter (UKF), is introduced and applied in PL positioning. Based on the relative positioning model and the KPI method, the positioning performance of the EKF and UKF under code-based differential pseudolite (DPL) positioning and phase-based real-time kinematic (RTK) positioning modes is compared and analyzed. Numerical results indicate that the computational efficiencies of the EKF and UKF are of the same level, though the former is slightly superior to the latter. In terms of the DPL positioning results, the precision of the UKF is higher with a decimeter-level improvement compared with that of the EKF. The dependence on the accuracy of the initial coordinates of UKF is reduced to some extent, which makes it a convenient technique, especially in the PL ambiguity resolution of the RTK positioning with fast convergence speed. The UKF outperforms the EKF and is more practicable in indoor PL positioning. The UKF can also achieve a decimeter-level positioning precision in DPL and a centimeter-level positioning precision in RTK.

Keywords

Indoor pseudolite (PL) Known point initialization (KPI) Unscented Kalman filter (UKF) Differential pseudolite (DPL) positioning Real-time kinematic (RTK) positioning 

Abbreviations

AR

Ambiguity resolution

DD

Double differenced

DGPS

Differential GPS positioning

DPL

Differential pseudolite

EKF

Extended Kalman filter

GDOP

Geometric dilution of precision

GNSS

Global navigation satellite system

GPS

Global positioning system

ICB

Initial coordinate bias

KPI

Known point initialization

PNC

Process noise of coordinates

PL

Pseudolite

PL-AR

Pseudolite ambiguity resolution

RTK

Real-time kinematic positioning

SD

Single differenced

SPP

Single point positioning

STD

Standard deviation

UKF

Unscented Kalman filter

USRP

Universal software radio peripheral

Notes

Acknowledgements

This work was supported by the China Postdoctoral Science Foundation (No. 2018M633441); the Fundamental Research Funds for the Central Universities, Chang’an University, 2018 (No. 300102268102); and the Programs of the National Natural Science Foundation of China (41790445, 41774025, 41604001, and 41731066).

References

  1. Bonenberg LK (2014) Closely-coupled integration of Locata and GPS for engineering applications. Ph.D. Dissertation, University of NottinghamGoogle Scholar
  2. Cobb HS (1997) GPS pseudolites: Theory, design, and applications. Ph.D. Dissertation, Stanford UniversityGoogle Scholar
  3. Dai L, Wang J, Rizos C, Han S (2002) Pseudo-satellite applications in deformation monitoring. GPS Solut 5(3):80–87.  https://doi.org/10.1007/PL00012902 CrossRefGoogle Scholar
  4. Du X, Liu L, Wang K (2012) GPS positioning algorithm based on UKF. J Astronaut 32(4):1059–1062Google Scholar
  5. Jiang W, Li Y, Rizos C (2015) Locata-based precise point positioning for kinematic maritime applications. GPS Solut 19(1):117–128.  https://doi.org/10.1007/s10291-014-0373-9 CrossRefGoogle Scholar
  6. Juang J-C (2004) Seamless handover of combined GPS/pseudolite navigation. In: Proceedings ION GNSS 2004, Institute of Navigation, Long Beach, CA, Sept 21–24, pp 2059–2065Google Scholar
  7. Julier SJ, Uhlmann JK, Durrant-Whyte H F (1995) A new approach for filtering nonlinear system. In: Proceeding of the American control conference, Seattle, Washington, USA, June 21–23, pp 1628–1632Google Scholar
  8. Julier SJ, Uhlmann JK, Durrant-Whyte HF (2000) A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Autom Control 45(3):477–482CrossRefGoogle Scholar
  9. Jwo DJ, Lai CN (2008) Unscented Kalman filter with nonlinear dynamic process modeling for GPS navigation. GPS Solut 12(4):249–260.  https://doi.org/10.1007/s10291-007-0081-9 CrossRefGoogle Scholar
  10. LeMaster EA, Rock SM (1999) Self-calibration of pseudolite arrays using self-differencing transceivers. In: Proceedings ION GPS 1999, Institute of Navigation, Nashville, USA, Sept 13–17, pp 1549–1558Google Scholar
  11. Li T, Wang J, Huang J (2012) Analysis of ambiguity resolution in precise pseudolite positioning. In: Proceedings of the 2012 international conference on indoor positioning and indoor navigation, Sydney, Australia, Nov 13–15.  https://doi.org/10.1109/ipin.2012.6418924
  12. Li X, Zhang P, Guo J, Wang J, Qiu W (2017) A new method for single-epoch ambiguity resolution with indoor pseudolite positioning. Sensors 17(4):921.  https://doi.org/10.3390/s17040921 CrossRefGoogle Scholar
  13. O’Keefe K, Sharma J, Cannon ME, Lachapelle G (1999) Pseudolite-based inverted GPS concept for local area positioning. In: Proceedings ION GPS 1999, Institute of Navigation, Nashville, USA, Sept 13–17, pp 1523–1530Google Scholar
  14. Remondi BW (1991) Pseudo-kinematic GPS results using the ambiguity function method. Navigation 38(1):17–36.  https://doi.org/10.1002/j.2161-4296.1991.tb01712.x CrossRefGoogle Scholar
  15. Rizos C, Roberts G, Barnes J, Gambale N (2010) Experimental results of Locata: a high accuracy indoor positioning system. In: Proceedings of the 2010 international conference on indoor positioning and indoor Navigation, Zurich, Switzerland, Sept 15–17.  https://doi.org/10.1109/ipin.2010.5647717
  16. Sorenson HW (1985) Kalman filtering: Theory and application. In: Sorenson Harold W (ed) IEEE Press selected reprint series. IEEE Press, New YorkGoogle Scholar
  17. Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1):65–82.  https://doi.org/10.1007/BF00863419 CrossRefGoogle Scholar
  18. Wan X, Zhan X, Du G (2012) Carrier phase method for indoor pseudolite positioning system. Appl Mech Mater 130(37):2064–2067.  https://doi.org/10.4028/www.scientific.net/AMM.130-134.2064 CrossRefGoogle Scholar
  19. Wang J (2002) Pseudolite applications in positioning and navigation: progress and problems. J Global Positioning Syst 1(1):48–56CrossRefGoogle Scholar
  20. Wang J, Tsujii T, Rizos C, Dai L, Moore M (2000) Integrating GPS and Pseudolite Signals for position and attitude determination: theoretical analysis and experiment results. In: Proceedings ION GPS 2000, Institute of Navigation, Salt Lake City, USA, Sept 19–22, pp 2252–2262Google Scholar
  21. Wang Z, He Y, Han J (2009) Simultaneous locating and calibrating pseudolite navigation system for autonomous mobile robots. In Proceeding of the 5th IEEE international workshop on intelligent data acquisition and advanced computing systems, Rende, Italy, Sep 21–23, pp 519–524Google Scholar
  22. Xiong K, Zhang H, Chan C (2006) Performance evaluation of UKF-based nonlinear filtering. Automatica 42(2):261–270CrossRefGoogle Scholar
  23. Yang C, Shi W, Chen W (2018) Correlational inference-based adaptive unscented Kalman filter with application in GNSS/IMU-integrated navigation. GPS Solut 22:100.  https://doi.org/10.1007/s10291-018-0766-2 CrossRefGoogle Scholar
  24. Yuan G, Gan X, Li Z (2007) Analyze and research the integrated navigation technique for GPS and pseudolite. In: Proceeding of the 2nd international conference on space information technology, Wu Han, China, 10–11 Nov.  https://doi.org/10.1117/12.775071
  25. Zhao Y, Zhang P, Guo J, Li X, Wang J, Yang F, Wang X (2018) A new method of high-precision positioning for an indoor pseudolite without using the known point initialization. Sensors 18(6):1977.  https://doi.org/10.3390/s18061977 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xin Li
    • 1
  • Peng Zhang
    • 2
    Email author
  • Guanwen Huang
    • 1
  • Qin Zhang
    • 1
  • Jiming Guo
    • 2
  • Yinzhi Zhao
    • 2
  • Qingzhi Zhao
    • 3
  1. 1.College of Geology Engineering and GeomaticsChang’an UniversityXi’anChina
  2. 2.School of Geodesy and GeomaticsWuhan UniversityWuhanChina
  3. 3.College of GeomaticsXi’an University of Science and TechnologyXi’anChina

Personalised recommendations