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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.

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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.

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The Journal of Navigation
  • ISSN: 0373-4633
  • EISSN: 1469-7785
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