Journal of Geodesy

, Volume 93, Issue 10, pp 1867–1880 | Cite as

Combined difference square observation-based ambiguity determination for ground-based positioning system

  • Tengfei Wang
  • Zheng YaoEmail author
  • Mingquan Lu
Original Article


In the absence of a global navigation satellite system, a ground-based positioning system can provide stand-alone positioning service and has advantages in layout flexibility of terrestrial base stations that broadcast ranging signals. To realize precise point positioning (PPP) in ground-based positioning systems, the carrier phase ambiguity must be determined for the receiver. On-the-fly (OTF) ambiguity determination methods are desirable for their convenience in practice. In most existing OTF methods based on the initial position estimate obtained from code measurements or other measuring instruments, the nonlinear term representing true distances are linearized by a series expansion. However, due to the severe nonlinear effects, if the accuracy of the initial position estimate is relatively poor, such linearization will result in large errors and convergence difficulties. Moreover, the more accurate initial estimate a method requires, the more inconvenient it will be. To avoid the dependence on the initial estimate, we proposed a combined difference square (CDS) observation and it provides a framework to eliminate the nonlinear terms in the difference square observations by linear combination. Based on this, a rotational-symmetry CDS (RS-CDS) observation-based ambiguity determination method is proposed, which needs no a priori information or reliable code measurements and is especially suitable for dynamic applications. In addition, it does not require accurate time synchronization of base stations, making the deployment of the overall system easier. The numerical simulations show that geometry diversity effectively improves the performance of ambiguity determination. Two real-world experiments indicate that the proposed method enables PPP for ground-based positioning systems without accurate time synchronization.


Ambiguity determination Ground-based positioning system Precise point positioning 



This work is supported by National Natural Science Foundation of China (NSFC), under Grant 61771272. The datasets of the two experiments are available from the corresponding author on reasonable request.


  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 TechnologyGoogle Scholar
  2. Barnes J, Rizos C, Wang J, Small D, Voigt G, Gambale N (2003) Locata: A new positioning technology for high precision indoor and outdoor positioning. In: ION GPS/GNSS, pp 1119–1128Google Scholar
  3. Bertsch J, Choudhury M, Rizos C, Kahle H (2009) On-the-fly ambiguity resolution for Locata. In: International symposium on GPS/GNSS, pp 1–3Google Scholar
  4. Beser J, Parkinson BW (1982) The application of NAVSTAR differential GPS in the civilian community. Navigation 29:107–136CrossRefGoogle Scholar
  5. Cobb HS (1997) GPS pseudolites: theory, design, and applications. Doctor thesis, Stanford UniversityGoogle Scholar
  6. 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 & navigation (KIS2001), pp 482–489Google Scholar
  7. 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. CrossRefGoogle Scholar
  8. 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. CrossRefGoogle Scholar
  9. Jiang W, Li Y, Rizos C (2015) Locata-based precise point positioning for kinematic maritime applications. GPS Solut 19(1):117–128. CrossRefGoogle Scholar
  10. Kee C, Jun H, Yun D (2003) Indoor navigation system using asynchronous pseudolites. J Navig 56(3):443–455. CrossRefGoogle Scholar
  11. Khan FA, Rizos C, Dempster AG (2010) Locata performance evaluation in the presence of wide- and narrow-band interference. J Navig 63(3):527–543. CrossRefGoogle Scholar
  12. 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 Aerosp Electron Syst 40(2):734–741CrossRefGoogle Scholar
  13. Lee HK, Wang J, Rizos C, Park W (2003) Carrier phase processing issues for high accuracy integrated GPS/pseudolite/INS systems. In: Proceedings of 11th IAIN world congress, Berlin, Germany, paper 252Google Scholar
  14. Lee HK, Wang J, Rizos C (2005) An integer ambiguity resolution procedure for GPS/pseudolite/INS integration. J Geodesy 79(4–5):242–255. CrossRefGoogle Scholar
  15. 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. CrossRefGoogle Scholar
  16. Lombardi M (2002) Fundamentals of time and frequency. Book section 17, CRC Press. Google Scholar
  17. 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. CrossRefGoogle Scholar
  18. 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. CrossRefGoogle Scholar
  19. Niwa H, Kodaka K, Sakamoto Y, Otake M, Kawaguchi S, Fujii K, Kanemori Y, Sugano S (2008) GPS-based indoor positioning system with multi-channel pseudolite. In: 2008 IEEE international conference on robotics and automation, IEEE, New York, USA, pp 905–910Google Scholar
  20. Teunissen PJ, Odijk D (1997) Ambiguity dilution of precision: definition, properties and application. In: Proceedings of ION GPS 1997, Kansas City, MO, USA, pp 891–899Google Scholar
  21. Wang J (2002) Pseudolite applications in positioning and navigation: progress and problems. J Glob Position Syst 1(1):48–56CrossRefGoogle Scholar
  22. Wang T, Yao Z, Lu M (2018) On-the-fly ambiguity resolution based on double-differential square observation. Sensors 18(8):2495. CrossRefGoogle Scholar
  23. Wang T, Yao Z, Lu M (2019) On-the-fly ambiguity resolution involving only carrier phase measurements for stand-alone ground-based positioning systems. GPS Solut 23(2):36. CrossRefGoogle Scholar
  24. Yang L, Li Y, Jiang W, Rizos C (2015) Locata network design and reliability analysis for harbour positioning. J Navig 68(2):238–252. CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Electronic EngineeringTsinghua UniversityBeijingChina

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