Abstract
In this contribution, we study the dependence of the bootstrapped success rate on the precision of the GNSS carrier phase ambiguities. Integer bootstrapping is, because of its ease of computation, a popular method for resolving the integer ambiguities. The method is however known to be suboptimal, because it only takes part of the information from the ambiguity variance matrix into account. This raises the question in what way the bootstrapped success rate is sensitive to changes in precision of the ambiguities. We consider two different cases. (1) The effect of improving the ambiguity precision, and (2) the effect of using an approximate ambiguity variance matrix. As a by-product, we also prove that integer bootstrapping is optimal within the restricted class of sequential integer estimators.
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References
Boon F, Ambrosius B (1997) Results of real-time applications of the LAMBDA method in GPS based aircraft landings. In: Proceedings KIS97, pp. 339–345
Boon F, de Jonge PJ, Tiberius CCJM (1997) Precise aircraft positioning by fast ambiguity resolution using improved troposphere modelling. In: Proceedings ION GPS-97, vol 2, pp 1877–1884
Chang XW, Yang X, Zhou T (2005) MLAMBDA: a modified LAMBDA method for integer ambiguity determination. In: Proceedings ION GNSS2005, Long Beach, CA, USA
Cox DB, Brading JDW (1999) Integration of LAMBDA ambiguity resolution with Kalman filter for relative navigation of spacecraft. In: Proceedings ION NTM 99, pp 739–745
Dai L, Nagarajan N, Hu G, Ling K (2005) Real-time attitude determination for micro satellites by LAMBDA method combined with Kalman filtering. In: AIAA proceedings 22nd ICSSC, Monterey, CA, USA
de Jonge PJ, Tiberius CCJM (1996a) The LAMBDA method for integer ambiguity estimation: implementation aspects. Publications of the Delft Computing Centre, LGR-Series No. 12
de Jonge PJ, Tiberius CCJM (1996b) Integer estimation with the LAMBDA method. In: Beutler G et al. (eds) Proceedings IAG Symposium No. 115, GPS trends in terrestrial, airborne and spaceborne applications. Springer, Berlin Heidelberg New York, pp 280–284
de Jonge PJ, Tiberius CCJM, Teunissen PJG (1996) aspects of the LAMBDA method for GPS ambiguity resolution. In: Proceedings ION GPS-96, pp 935–944
Han S (1995) Ambiguity resolution techniques using integer least- squares estimation for rapid static or kinematic positioning. Symposium Satellite Navigation Technology: 1995 and beyond, Brisbane, 10 pp
Hofmann-Wellenhof B, Lichtenegger H, Collins J (1997) Global positioning system: theory and practice, 4th edn. Springer, Heidelberg New York
Jonkman NF (1998) Integer ambiguity estimation without the receiver-satellite geometry. Publications of the Delft Geodetic computing centre, LGR-Series, No. 18
Leick A (1995) GPS satellite surveying, 2nd edn. Wiley, New York
Misra P, Enge P (2001) Global positioning system: signals, measurements, and performance. Ganga-Jamuna Press
Moenikes R, Wendel J, Trommer GF (2005) A modified LAMBDA method for ambiguity resolution in the presence of position domain constraints. In: Proceedings ION GNSS2005, Long Beach, CA, USA
Parkinson B, Spilker JJ (eds) (1996) GPS: theory and applications. vols 1 and 2, AIAA, Washington DC
Peng HM, Chang FR, Wang LS (1999) Attitude determination using GPS carrier phase and compass data. In: Proceedings ION NTM 99, pp 727–732
Strang G, Borre K (1997) Linear algebra, geodesy, and GPS. Wellesley-Cambridge Press
Svendsen JGG (2005) Some properties of decorrelation techniques in the ambiguity space. GPS Solutions. DOI 10.1007/ s10291-005-0004-6
Teunissen PJG (1993) Least-squares estimation of the integer GPS ambiguities. Invited lecture, Section IV theory and methodology, IAG general meeting, Beijing, China, August 1993. Also in: LGR Series, No. 6, Delft Geodetic computing centre
Teunissen PJG (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geodesy 70:65–82
Teunissen PJG (1997) On the GPS widelane and its decorrelating property. J Geodesy 71:577–587
Teunissen PJG (1998) On the integer normal distribution of the GPS ambiguities. Artif Satellites 33(2):49–64
Teunissen PJG (1999a) The probability distribution of the GPS baseline for a class of integer ambiguity estimators. J Geodesy 73:275–284
Teunissen PJG (1999b) An optimality property of the integer least-squares estimator. J Geodesy 73:587–593
Teunissen PJG (2000) Adjustment theory. Delft University Press, Delft, The Netherlands
Teunissen PJG (2001) The probability distribution of the ambiguity bootstrapped GNSS baseline. J Geodesy 75:267–275
Teunissen PJG, Kleusberg A (eds) (1998) GPS for geodesy. 2nd enlarged edn. Springer, Berlin Heidelberg New York
Tiberius CCJM, de Jonge PJ (1995) Fast positioning using the LAMBDA method. In: Proceedings DSNS-95, paper 30, 8 pp
Tiberius CCJM, Teunissen PJG, de Jonge PJ (1997) Kinematic GPS: performance and quality control. In: Proceedings KIS97, pp 289–299
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Teunissen, P.J.G. Influence of ambiguity precision on the success rate of GNSS integer ambiguity bootstrapping. J Geod 81, 351–358 (2007). https://doi.org/10.1007/s00190-006-0111-3
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DOI: https://doi.org/10.1007/s00190-006-0111-3