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Integrity Monitoring for Carrier Phase Ambiguities

Published online by Cambridge University Press:  25 November 2011

Shaojun Feng ,
Washington Ochieng ,
Jaron Samson ,
Michel Tossaint ,
Manuel Hernandez-Pajares ,
J. Miguel Juan ,
Jaume Sanz ,
Àngela Aragón-Àngel ,
Pere Ramos-Bosch  and
Marti Jofre
Shaojun Feng*
Affiliation:
Centre for Transport Studies, Department of Civil & Environmental Engineering Imperial College London
Washington Ochieng
Affiliation:
Centre for Transport Studies, Department of Civil & Environmental Engineering Imperial College London
Jaron Samson
Affiliation:
ESA (ESTEC/TEC-ETN), The Netherlands
Michel Tossaint
Affiliation:
ESA (ESTEC/TEC-ETN), The Netherlands
Manuel Hernandez-Pajares
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
J. Miguel Juan
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
Jaume Sanz
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
Àngela Aragón-Àngel
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
Pere Ramos-Bosch
Affiliation:
Research Group of Astronomy and Geomatics (gAGE), Universitat Politècnica de Catalunya (UPC), Barcelona (Spain)
Marti Jofre
Affiliation:
CTAE - Aerospace Research & Technology Centre, Barcelona, Spain
*
(E-mail: s.feng@imperial.ac.uk)
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Abstract

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.

Keywords

GNSSPPPRNPCRAIM
Type
Research Article
Information
The Journal of Navigation , Volume 65 , Issue 1 , January 2012 , pp. 41 - 58
Copyright
Copyright © The Royal Institute of Navigation 2011

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