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Impact of Decorrelation on Success Rate Bounds of Ambiguity Estimation

Published online by Cambridge University Press:  28 March 2016

Lei Wang*
Affiliation:
(Queensland University of Technology, Brisbane, Australia) (School of Geodesy and Geomatics, Wuhan University, China)
Yanming Feng
Affiliation:
(Queensland University of Technology, Brisbane, Australia)
Jiming Guo
Affiliation:
(School of Geodesy and Geomatics, Wuhan University, China)
Charles Wang
Affiliation:
(Queensland University of Technology, Brisbane, Australia)
*

Abstract

Reliability is an important performance measure of navigation systems and this is particularly true in Global Navigation Satellite Systems (GNSS). GNSS positioning techniques can achieve centimetre-level accuracy which is promising in navigation applications, but can suffer from the risk of failure in ambiguity resolution. Success rate is used to measure the reliability of ambiguity resolution and is also critical in integrity monitoring, but it is not always easy to calculate. Alternatively, success rate bounds serve as more practical ways to assess the ambiguity resolution reliability. Meanwhile, a transformation procedure called decorrelation has been widely used to accelerate ambiguity estimations. In this study, the methodologies of bounding integer estimation success rates and the effect of decorrelation on these success rate bounds are examined based on simulation. Numerical results indicate decorrelation can make most success rate bounds tighter, but some bounds are invariant or have their performance degraded after decorrelation. This study gives a better understanding of success rate bounds and helps to incorporate decorrelation procedures in success rate bounding calculations.

Type
Research Article
Copyright
Copyright © The Royal Institute of Navigation 2016 

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References

REFERENCES

Cassels, J.W.S. (2012). An introduction to the geometry of numbers, Springer Science & Business Media.Google Scholar
De Jonge, P. and Tiberius, C.C.J.M. (1996). The LAMBDA method for integer ambiguity estimation: implementation aspects. Publications of the Delft Computing Centre, LGR-Series.Google Scholar
Feng, Y. and Wang, J. (2011). Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates. Journal of Geodesy, 85, 93103.CrossRefGoogle Scholar
Feng, S., Ochieng, W., Samson, J., Tossaint, M., Hernández-Pajares, M., Juan, J. M., Sanz, J., Aragón-Àngel, À., Ramos-Bosch, P. and Jofre, M. (2012). Integrity monitoring for carrier phase ambiguities. Journal of Navigation, 65, 4158.CrossRefGoogle Scholar
Grafarend, E.W. (2000). Mixed integer-real valued adjustment (IRA) problems: GPS initial cycle ambiguity resolution by means of the LLL algorithm. GPS solutions, 4, 3144.CrossRefGoogle Scholar
Hassibi, A. and Boyd, S. (1998). Integer parameter estimation in linear models with applications to GPS. IEEE Transactions on Signal Processing, 46, 29382952.CrossRefGoogle Scholar
Jazaeri, S., Amiri-Simkooei, A.R. and Sharifi, M.A. (2012). Fast integer least-squares estimation for GNSS high-dimensional ambiguity resolution using lattice theory. Journal of Geodesy, 86, 123136.CrossRefGoogle Scholar
Jazaeri, S., Amiri-Simkooei, A.R. and Sharifi, M.A. (2014). On lattice reduction algorithms for solving weighted integer least squares problems: comparative study. GPS Solutions 18, 105114.CrossRefGoogle Scholar
Li, B. and Teunissen, P.J.G. (2011). High Dimensional Integer Ambiguity Resolution: A First Comparison between LAMBDA and Bernese. Journal of Navigation 64, S192S210.CrossRefGoogle Scholar
Li, L., Li, Z., Yuan, H., Wang, L. and Hou, Y. (2015). Integrity monitoring-based ratio test for GNSS integer ambiguity validation. GPS Solutions.Google Scholar
Odijk, D. and Teunissen, P.J.G. (2008). ADOP in closed form for a hierarchy of multi-frequency single-baseline GNSS models. Journal of Geodesy, 82, 473492.CrossRefGoogle Scholar
Strang, G. and Borre, K. (1997). Linear algebra, geodesy, and GPS. Wellesley CambridgeGoogle Scholar
Teunissen, P.J.G. (1993). Least-Square Estimation of the Integer GPS Ambiguities. Section IV, Theory and Methodology, IAG General Meeting. BeijingGoogle Scholar
Teunissen, P.J.G. (1995). The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. Journal of Geodesy, 70, 6582.CrossRefGoogle Scholar
Teunissen, P.J.G. (1997). A canonical theory for short GPS baselines. Part IV: Precision versus reliability. Journal of Geodesy, 71, 513525.CrossRefGoogle Scholar
Teunissen, P.J.G. (1998a). On the integer normal distribution of the GPS ambiguities. Artificial Satellites, 33, 4964.Google Scholar
Teunissen, P.J.G. (1998b). Success probability of integer GPS ambiguity rounding and bootstrapping. Journal of Geodesy, 72, 606612.CrossRefGoogle Scholar
Teunissen, P.J.G. (1999). An optimality property of the integer least-squares estimator. Journal of Geodesy, 73, 587593.CrossRefGoogle Scholar
Teunissen, P.J.G. (2000a). ADOP based upperbounds for the bootstrapped and the least-squares ambiguity success rates. Artificial Satellites, 35, 171179.Google Scholar
Teunissen, P.J.G. (2000b). The success rate and precision of GPS ambiguities. Journal of Geodesy, 74, 321326.CrossRefGoogle Scholar
Teunissen, P.J.G. (2001). GNSS ambiguity bootstrapping: Theory and application. Proceedings of International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, 246–254.Google Scholar
Teunissen, P.J.G. (2003). An invariant upperbound for the GNSS bootstrappend ambiguity success rate. Journal of Global Positioning Systems, 2, 1317.CrossRefGoogle Scholar
Teunissen, P.J.G. and Odijk, D. (1997). Ambiguity dilution of precision: definition, properties and application. Proceedings of ION GPS-1997, 891–899.Google Scholar
Thomsen, H.E. (2000). Evaluation of upper and lower bounds on the success probability. Proceedings of ION GPS 2000, 183–188.Google Scholar
Verhagen, S. (2003). On the approximation of the integer least-squares success rate: which lower or upper bound to use. Journal of Global Positioning Systems, 2, 117124.CrossRefGoogle Scholar
Verhagen, S. (2005). The GNSS integer ambiguities: estimation and validation. Ph.D Thesis, Delft University of Technology.CrossRefGoogle Scholar
Verhagen, S., Li, B. and Teunissen, P.J.G. (2013). Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications. Computers & Geosciences, 54, 361376.CrossRefGoogle Scholar
Wang, L. (2015). Reliability control in GNSS carrier-phase integer ambiguity resolution. Queensland University of Technology.Google Scholar
Xu, P. (2001). Random simulation and GPS decorrelation. Journal of Geodesy, 75, 408423.CrossRefGoogle Scholar
Xu, P., Cannon, M.E. and Lachapelle, G. (1995). Mixed integer programming for the resolution of GPS carrier phase ambiguities. IUGG95 Assembly, 1–12.Google Scholar
Xu, P., Shi, C. and Liu, J. (2012). Integer estimation methods for GPS ambiguity resolution: an applications oriented review and improvement. Survey Review, 44, 5971.CrossRefGoogle Scholar