Journal of Geodesy

, Volume 84, Issue 11, pp 683–698 | Cite as

Fast GNSS ambiguity resolution as an ill-posed problem

  • Bofeng LiEmail author
  • Yunzhong Shen
  • Yanming Feng
Original Article


A linear observational equation system for real-time GNSS carrier phase ambiguity resolution (AR) is often severely ill-posed in the case of poor satellite geometry. An ill-posed system may result in unreliable or unsuccessful AR if no care is taken to mitigate this situation. In this paper, the GNSS AR model as an ill-posed problem is solved by regularizing its baseline and ambiguity parameters, respectively, with the threefold contributions: (i) The regularization parameter is reliably determined in context of minimizing mean square error of regularized solution where the covariance matrix of initial values of unknowns is used as an approximate smoothness term instead of the quadratic matrix of the true values of unknowns; (ii) The different models for computing initial values of unknowns are systematically discussed in order to address the potential schemes in real world applications; (iii) The superior performance of the regularized AR are demonstrated through the numerically random simulations as well as the real GPS experiments. The results show that the proposed regularization strategies can effectively mitigate the model’s ill-condition and improve the success AR probability of the observational system with a severely ill-posed problem.


GNSS Ambiguity resolution Regularization Ill-posed problem Success probability 


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Surveying and Geo-Informatics EngineeringTongji UniversityShanghaiPeople’s Republic of China
  2. 2.Key Laboratory of Advanced Surveying Engineering of State Bureau of Surveying and MappingShanghaiPeople’s Republic of China
  3. 3.Faculty of Science and TechnologyQueensland University of TechnologyBrisbaneAustralia

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