Skip to main content
Log in

A constrained LAMBDA method for GPS attitude determination

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

Abstract

An improved method to obtain fixed integer ambiguity in GPS attitude determination is presented. Known conditions are utilized as constraints to acquire attitude information when the float solution and its variance–covariance matrix are not accurate enough. The searching ellipsoidal region is first expanded to compensate for errors caused by the inaccurate float solution. Then the constraints are used to shrink the region to a proper size, which maintains the true integer ambiguity. Experimental results demonstrate that this scheme gives a fast search time and a higher success rate in determining the fixed integer ambiguity than the unconstrained method. The accuracy of attitude angles is also improved.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Agrell E, Eriksson T, Vardy A, Zeger K (2002) Closest point search in lattices. IEEE Trans Inf Theory 48(9):2201–2214. doi:10.1109/TIT.2002.800499

    Article  Google Scholar 

  • Bar-Itzhack IY, Montgomery PY, Garrick JC (1998) Algorithms for attitude determination using the global positioning system. J Guid Control Dyn 21(6):846–852. doi:10.2514/2.4347

    Article  Google Scholar 

  • Chang XW, Yang X, Zhou T (2005) MLAMBDA: a modified LAMBDA method for integer least-squares estimation. J Geod 79(10):552–565. doi:10.1007/s00190-005-0004-x

    Article  Google Scholar 

  • Cohen CE (1996) Attitude determination. In: Parkinson BW, Spilker JJ (eds) Global positioning system: theory and applications II. AIAA, Washington, pp 519–538

    Google Scholar 

  • Crassidis JL, Markley FL, Lightsey EG (1999) Global positioning system integer ambiguity resolution without attitude knowledge. J Guid Control Dyn 22(2):212–218. doi:10.2514/2.4395

    Article  Google Scholar 

  • De Jonge P, Tiberius CCJM (1996) The LAMBDA method for integer ambiguity estimation: implementation aspects. Technical report LGR series, no. 12. Delft Geodetic Computing Centre, Delft University of Technology, The Netherlands

    Google Scholar 

  • Feng C, Tian W, Jin Z (2004) OTF ambiguity resolution based on GPS double-differential carrier phase. J Chin Inert Technol 12(5):26–30

    Google Scholar 

  • Hatch R (1990) Instantaneous ambiguity resolution. In: Proceedings of KIS’90, Banff, Canada, pp 299–308

  • Hide C, Pinchin J, Park D (2007) Development of a low cost multiple GPS antenna attitude system. Proc ION GNSS 2007:88–95

    Google Scholar 

  • Joosten P, Tiberius C (2002) LAMBDA: FAQs. GPS Solut 6:109–114. doi:10.1007/s10291-002-0004-8

    Article  Google Scholar 

  • Kim D, Langley RB (2000) GPS ambiguity resolution and validation: methodologies, trends and issues. In: 7th GNSS workshop international symposium on GPS/GNSS, Seoul, Korea, pp 213–221

  • Li Y, Zhang K, Roberts C, Murata M (2004) On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements. GPS Solut 8(2):93–102. doi:10.1007/s10291-004-0089-3

    Article  Google Scholar 

  • Lu G (1995) Development of a GPS multi-antenna system for attitude determination. Ph.D. thesis, Department of Geomatics, University of Calgary, Calgary

  • Moon Y, Verhagen S (2006) Integer ambiguity estimation and validation in attitude determination environments. Proc ION-GPS 2006:335–344

    Google Scholar 

  • Park C, Kim I (1998) Integer ambiguity resolution for GPS based attitude determination system. In: Proceedings of the 37th SICE annual conference, pp 1115–1120

  • Park C, Kim I (2000) An error analysis of 2-dimensional attitude determination system using global positioning system. IEICE Trans Commun E 83-B(6):1370–1373

    Google Scholar 

  • Park C, Teunissen PJG (2003) A new carrier phase ambiguity estimation for GNSS attitude determination system. In: Proceedings of international symposium on GPS/GNSS, pp 249–255

  • Park C, Kim I, Lee JG, Lee GI (1997) Efficient technique to fix GPS carrier phase integer ambiguity on-the-fly. IEE P-Radar Son Nav 144(3):148–155. doi:10.1049/ip-rsn:19971237

    Article  Google Scholar 

  • Teunissen PJG (1994) A new method for fast carrier phase ambiguity estimation. In: Proceedings of IEEE PLANS’94, Las Vegas, NV, pp 562–573

  • Teunissen PJG (1997) A canonical theory for short GPS baselines, Part IV: precision versus reliability. J Geod 71:513–525. doi:10.1007/s001900050119

    Article  Google Scholar 

  • Teunissen PJG (2006) The LAMBDA method for the GNSS compass. Artif Satell 41(3):89–103. doi:10.2478/v10018-007-0009-1

    Article  Google Scholar 

  • Teunissen PJG, Verhagen S (2008) GNSS ambiguity resolution: when and how to fix or not to fix? In: Xu P, Liu J, Dermanis A (eds) VI Hotine–Marussi symposium on theoretical and computational geodesy. Springer, Berlin, pp 143–148

    Chapter  Google Scholar 

  • Verhagen S (2004) Integer ambiguity validation: an open problem? GPS Solut 8(1):36–43. doi:10.1007/s10291-004-0087-5

    Article  Google Scholar 

  • Verhagen S (2005) The GNSS integer ambiguities: estimation and validation. Ph.D. thesis publications on geodesy, vol 58, Netherlands Geodetic Commission, Delft

  • Wahba G (1965) A least squares estimate of spacecraft attitude. SIAM Rev 7(3):409. doi:10.1137/1007077

    Article  Google Scholar 

  • Wang J, Stewart MP, Tsakiri M (1998) A discrimination test procedure for ambiguity resolution on the fly. J Geod 72(12):644–653. doi:10.1007/s001900050204

    Article  Google Scholar 

  • Wang J, Stewart MP, Tsakiri M (2000) A comparative study of the integer ambiguity validation procedures. Earth Planets Space 52(11):813–817

    Google Scholar 

  • Wang B, Miao L, Wang S (2007) Improvements on quaternion-based iterative algorithms for attitude determination using GPS. T Beijing Inst Technol 27(6):521–526

    Google Scholar 

  • Yoon SP, Lundberg JB (2002) An integer ambiguity resolution algorithm for real-time GPS attitude determination. Appl Math Comput 129(1):21–41. doi:10.1016/S0096-3003(01)00029-7

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by Program for New Century Excellent Talents in University, Ministry of Education, China (Ncet-05-0177). The authors would like to thank the Editor-in-Chief Prof. Leick and the anonymous reviewers for their valuable comments on the early version of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bo Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, B., Miao, L., Wang, S. et al. A constrained LAMBDA method for GPS attitude determination. GPS Solut 13, 97–107 (2009). https://doi.org/10.1007/s10291-008-0103-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10291-008-0103-2

Keywords

Navigation