On-the-fly ambiguity resolution involving only carrier phase measurements for stand-alone ground-based positioning systems


Despite the wide use of the global navigation satellite system (GNSS), its performance can be severely degraded due to blockage and vulnerability to interference. Stand-alone ground-based positioning systems can provide positioning services in the absence of GNSS signals and have tremendous application potential. For precise point positioning in ground-based systems, ambiguity resolution (AR) is a key issue. On-the-fly (OTF) AR methods are desirable for reasons of convenience. The existing methods usually linearize a nonlinear problem approximately by a series expansion that is based on an initial position estimation obtained by code measurements or measuring instruments. However, if the initial position estimation contains relatively large errors, the convergence of existing methods cannot be ensured. We present a new OTF-AR method based on the double difference square (DDS) observation model for ground-based precise point positioning, which involves only carrier phase measurements. The initial solution obtained from the DDS model is sufficiently accurate to obtain a float solution by linearization, and this step only requires the frequency synchronization of base stations. Further, if the clock differences of the base stations are accurately calibrated, a fixed solution can be obtained by employing the LAMBDA algorithm. Numerical simulations and a real-world experiment are conducted to validate the proposed method. Both the simulations and the experimental results show that the proposed method can achieve high-accuracy positioning. These results enable precise point positioning to be applied in situations where no reliable code measurements or other measuring instruments are available for stand-alone ground-based positioning systems.

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  1. Amt JH (2006) Methods for aiding height determination in pseudolite-based reference systems using batch least-squares estimation. Master Thesis. Air Force Institute of Technology, Ohio

    Google Scholar 

  2. Barnes J, Rizos C, Wang J, Small D, Voigt G, Gambale N, Locata (2003) A new positioning technology for high precision indoor and outdoor positioning. In: Proceedings of 2003 international symposium on GPS/GNSS, pp 9–18

  3. Bertsch J, Choudhury M, Rizos C, Kahle H (2009) On-the-fly ambiguity resolution for Locata. In: International symposium on GPS/GNSS, Gold Coast, pp 1–3

  4. Cobb HS (1997) GPS pseudolites: theory, design, and applications. Doctor Thesis. Stanford University, Stanford

    Google Scholar 

  5. Dai L, Wang J, Tsujii T, Rizos C (2001) Pseudolite applications in positioning and navigation: modelling and geometric analysis. In: International symposium on kinematic systems in geodesy, geomatics and navigation (KIS2001), Banff, pp 482–489

  6. Ge M, Gendt G, Rothacher M, Shi C, Liu J (2008) Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations. J Geodesy 82(7):389–399. https://doi.org/10.1007/s00190-007-0187-4

    Article  Google Scholar 

  7. Gourevitch S, van Diggelen F, Qin X, Kuhl M (1995) Ashtech RTZ, real-time kinematic GPS with OTF initialization. In: ION GPS 1995. Institute of Navigation, Palm Springs, pp 167–170

  8. Guo X, Zhou Y, Wang J, Liu K, Liu C (2018) Precise point positioning for ground-based navigation systems without accurate time synchronization. GPS Solut 22(2):34. https://doi.org/10.1007/s10291-018-0697-y

    Article  Google Scholar 

  9. Hofmann-Wellenhof B, Remondi BW (1988) The antenna exchange: one aspect of high-precision GPS kinematic survey. In: GPS-techniques applied to geodesy and surveying. Springer, pp 259–277

  10. Jiang W, Li Y, Rizos C (2013) On-the-fly Locata/inertial navigation system integration for precise maritime application. Meas Sci Technol 24(10):105104

    Article  Google Scholar 

  11. Jiang W, Li Y, Rizos C (2014) On-the-fly indoor positioning and attitude determination using terrestrial ranging signals. In: ION GNSS 2014. Institute of Navigation, Tampa, pp 3222–3230

  12. 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

    Article  Google Scholar 

  13. Kee C, Jun H, Yun D (2003) Indoor navigation system using asynchronous pseudolites. J Navig 56(3):443–455. https://doi.org/10.1017/S0373463303002467

    Article  Google Scholar 

  14. Kiran S, Bartone CG (2004) Flight-test results of an integrated wideband-only airport pseudolite for the category IV/III local area augmentation system. IEEE Trans Aerospace Electron Syst 40(2):734–741

    Article  Google Scholar 

  15. Lee HK, Wang J, Rizos C (2005) An integer ambiguity resolution procedure for GPS/pseudolite/INS integration. J Geodesy 79(4–5):242–255. https://doi.org/10.1007/s00190-005-0466-x

    Article  Google Scholar 

  16. Lee HK, Soon B, Barnes J, Wang JL, Rizos C (2008) Experimental analysis of GPS/Pseudolite/INS integration for aircraft precision approach and landing. J Navig 61(2):257–270. https://doi.org/10.1017/S037346330700464x

    Article  Google Scholar 

  17. Lee T, Kim C, Jeon S, Jeon S, Kim G, Kee C (2010) Pedestrian indoor navigation algorithm based on the pseudolite and low-cost IMU with magnetometers including in-flight calibration. In: ION ITM 2010. Institute of Navigation, San Diego, pp 230–235

  18. Montillet JP, Roberts GW, Hancock C, Meng X, Ogundipe O, Barnes J (2009) Deploying a Locata network to enable precise positioning in urban canyons. J Geodesy 83(2):91–103. https://doi.org/10.1007/s00190-008-0236-7

    Article  Google Scholar 

  19. Montillet JP, Bonenberg LK, Hancock CM, Roberts GW (2014) On the improvements of the single point positioning accuracy with Locata technology. GPS Solut 18(2):273–282. https://doi.org/10.1007/s10291-013-0328-6

    Article  Google Scholar 

  20. Teunissen PJ (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodesy 70(1–2):65–82

    Article  Google Scholar 

  21. Wang J (2002) Pseudolite applications in positioning and navigation: progress and problems. J Glob Position Syst 1(1):48–56

    Article  Google Scholar 

  22. Wang T, Yao Z, Lu M (2018) On-the-fly ambiguity resolution based on double-differential square observation sensors. Sensors 18(8):2495. https://doi.org/10.3390/s18082495

    Article  Google Scholar 

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This work is supported by National Natural Science Foundation of China (NSFC), under Grant 61771272.

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Correspondence to Zheng Yao.

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Wang, T., Yao, Z. & Lu, M. On-the-fly ambiguity resolution involving only carrier phase measurements for stand-alone ground-based positioning systems. GPS Solut 23, 36 (2019). https://doi.org/10.1007/s10291-019-0825-3

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  • Ambiguity resolution
  • Ground-based positioning system
  • Precise point positioning