Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 12
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Li, Liang Li, Zishen Yuan, Hong Wang, Liang and Hou, Yanqing 2016. Integrity monitoring-based ratio test for GNSS integer ambiguity validation. GPS Solutions, Vol. 20, Issue. 3, p. 573.

    Feng, Shaojun and Jokinen, Altti 2015. Integer ambiguity validation in high accuracy GNSS positioning. GPS Solutions,

    He, Pan Liu, Gang Tan, Chun and Lu, Yan-e 2015. Nonlinear fault detection threshold optimization method for RAIM algorithm using a heuristic approach. GPS Solutions,

    Moradi, Ramin Schuster, Wolfgang Feng, Shaojun Jokinen, Altti and Ochieng, Washington 2015. The carrier-multipath observable: a new carrier-phase multipath mitigation technique. GPS Solutions, Vol. 19, Issue. 1, p. 73.

    Chen, Yiming Zhao, Sheng Zheng, Dongfang and Farrell, Jay A. 2014. 53rd IEEE Conference on Decision and Control. p. 6609.

    Li, Tao and Wang, Jinling 2014. Analysis of the upper bounds for the integer ambiguity validation statistics. GPS Solutions, Vol. 18, Issue. 1, p. 85.

    Liu, Haiying Chen, Zhiming Ye, Weisong and Wang, Huinan 2014. GNSS carrier phase ambiguity resolution based on integrity restriction in ambiguity domain. Advances in Space Research, Vol. 53, Issue. 8, p. 1207.

    Feng, Shaojun Jokinen, Altti Milner, Carl and Ochieng, Washington 2013. New methods for dual constellation single receiver positioning and integrity monitoring. Geo-spatial Information Science, Vol. 16, Issue. 3, p. 201.

    Jokinen, Altti Feng, Shaojun Schuster, Wolfgang Ochieng, Washington Hide, Chris Moore, Terry and Hill, Chris 2013. GLONASS Aided GPS Ambiguity Fixed Precise Point Positioning. Journal of Navigation, Vol. 66, Issue. 03, p. 399.

    Jokinen, Altti Feng, Shaojun Schuster, Wolfgang Ochieng, Washington Hide, Chris Moore, Terry and Hill, Chris 2013. Integrity monitoring of fixed ambiguity Precise Point Positioning (PPP) solutions. Geo-spatial Information Science, Vol. 16, Issue. 3, p. 141.

    Li, Tao and Wang, Jinling 2013. Theoretical Upper Bound and Lower Bound for Integer Aperture Estimation Fail-Rate and Practical Implications. Journal of Navigation, Vol. 66, Issue. 03, p. 321.

    Jokinen, Altti Feng, Shaojun Ochieng, Washington Hide, Chris Moore, Terry and Hill, Chris 2012. Proceedings of the 2012 IEEE/ION Position, Location and Navigation Symposium. p. 643.


Integrity Monitoring for Carrier Phase Ambiguities

  • Shaojun Feng (a1), Washington Ochieng (a1), Jaron Samson (a2), Michel Tossaint (a2), Manuel Hernandez-Pajares (a3), J. Miguel Juan (a3), Jaume Sanz (a3), Àngela Aragón-Àngel (a3), Pere Ramos-Bosch (a3) and Marti Jofre (a4)
  • DOI:
  • Published online: 25 November 2011

The determination of the correct integer number of carrier cycles (integer ambiguity) is the key to high accuracy positioning with carrier phase measurements from Global Navigation Satellite Systems (GNSS). There are a number of current methods for resolving ambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method, which is a combination of least-squares and a transformation to reduce the search space. The current techniques to determine the level of confidence (integrity) of the resolved ambiguities (i.e. ambiguity validation), usually involve the construction of test statistics, characterisation of their distribution and definition of thresholds. Example tests applied include ratio, F-distribution, t-distribution and Chi-square distribution. However, the assumptions that underpin these tests have weaknesses. These include the application of a fixed threshold for all scenarios, and therefore, not always able to provide an acceptable integrity level in the computed ambiguities. A relatively recent technique referred to as Integer Aperture (IA) based on the ratio test with a large number of simulated samples of float ambiguities requires significant computational resources. This precludes the application of IA in real time.

This paper proposes and demonstrates the power of an integrity monitoring technique that is applied at the ambiguity resolution and positioning stages. The technique has the important benefit of facilitating early detection of any potential threat to the position solution, originating in the ambiguity space, while at the same time giving overall protection in the position domain based on the required navigation performance. The proposed method uses the conventional test statistic for ratio testing together with a doubly non-central F distribution to compute the level of confidence (integrity) of the ambiguities. Specifically, this is determined as a function of geometry and the ambiguity residuals from least squares based ambiguity resolution algorithms including LAMBDA. A numerical method is implemented to compute the level of confidence in real time.

The results for Precise Point Positioning (PPP) with simulated and real data demonstrate the power and efficiency of the proposed method in monitoring both the integrity of the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolution algorithms, it is easily transferable to conventional Real Time Kinematic (RTK) positioning.

Corresponding author
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

W. G. Bulgren (1971). On Representations of the Doubly Non-Central F Distribution. Journal of American Statistical Association, 66(333), 184186.

S. Feng , W. Y. Ochieng , D. Walsh and R. Ioannides (2006). A Measurement Domain Receiver Autonomous Integrity Monitoring Algorithm. GPS Solutions, Springer, 10(2), 8596.

S. Feng , W. Y. Ochieng , T. Moore , C. Hill and C. Hide (2009). Carrier-Phase Based Integrity Monitoring for High Accuracy Positioning. GPS Solutions, DOI 10.1007/s10291-008-0093-0, 1322.

P. J. G. Teunissen (2005). Integer Aperture Bootstrapping: A New GNSS Ambiguity Estimator with Controllable Fail-Rate. Journal of Geodesy, 79(6&7), 389397.

P. J. G. Teunissen and S. Verhagen (2009b). The GNSS ambiguity ratio-test revisited: a better way of using it. Survey Review, 41(312), 138151.

S. Verhagen (2004). Integer ambiguity validation: an open problem? GPS Solutions, 8(1), 3643.

J. Wang , M. P. Stewart and M. Tsakiri (2000). A comparative study of the integer ambiguity validation procedures. Earth Planets Space, 52, 813817.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Navigation
  • ISSN: 0373-4633
  • EISSN: 1469-7785
  • URL: /core/journals/journal-of-navigation
Please enter your name
Please enter a valid email address
Who would you like to send this to? *