Some remarks on GNSS integer ambiguity validation methods

Abstract Ambiguity resolution is an indispensable step in fast and high precision Global Navigation Satellite System (GNSS) based positioning. In general, ambiguity resolution consists of three steps. The first step is to estimate the ambiguities using a least-squares estimation process, from which the so called ‘float solution’ or real valued solution is obtained. Then in the second step, the float solution is used to search for the integer ambiguities. Once integer ambiguities are resolved, the last step is to apply the integer ambiguities into the models so that fairly accurate fixed solution can be generated. Owing to the importance of the integer ambiguities, one indispensable procedure that needs to be implemented in the second step is integer ambiguity validation. Over the past decades, considerable work has been concentrated on this procedure and various approaches have been proposed, such as R-ratio test, F-ratio test, W-ratio test, integer aperture estimator, etc. However, their performances are controversial. Therefore, in this contribution, an overview of the existing ambiguity validation methods is firstly presented, and then some numerical analysis is carried out to evaluate their performances.

[1]  Peter Teunissen.  The parameter distributions of the integer GPS model , 2002 .

[2]  P. Teunissen.  An optimality property of the integer least-squares estimator , 1999 .

[3]  P. Teunissen.  The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation , 1995 .

[4]  Jinling Wang,et al.  STOCHASTIC MODELING FOR REAL-TIME KINEMATIC GPS/GLONASS POSITIONING. , 1999 .

[5]  P. Teunissen.  Least-squares estimation of the integer GPS ambiguities , 1993 .

[6]  Stephen P. Boyd,et al.  Integer parameter estimation in linear models with applications to GPS , 1998, IEEE Trans. Signal Process..

[7]  C. C. J. M. Tiberius,et al.  FAST POSITIONING USING THE LAMBDA-METHOD , 1995 .

[8]  Peter Teunissen,et al.  Integer aperture GNSS ambiguity resolution , 2003 .

[9]  P. Clarke.  GPS Satellite Surveying , 2007 .

[10]  Xiaoli Ding,et al.  Ambiguity validation with combined ratio test and ellipsoidal integer aperture estimator , 2010 .

[11]  C. Rizos,et al.  VALIDATION AND REJECTION CRITERIA FOR INTEGER LEAST-SQUARES ESTIMATION , 1996 .

[12]  Sandra Verhagen,et al.  On the probability density function of the GNSS ambiguity residuals , 2006 .

[13]  Peter Teunissen.  A carrier phase ambiguity estimator with easy-to-evaluate fail-rate , 2003 .

[14]  W. Baarda,et al.  A testing procedure for use in geodetic networks. , 1968 .

[15]  Charles C. Counselman,et al.  Method of resolving radio phase ambiguity in satellite orbit determination , 1989 .

[16]  Jinling Wang,et al.  A comparative study of the integer ambiguity validation procedures , 2000 .

[17]  Jinling Wang,et al.  A discrimination test procedure for ambiguity resolution on-the-fly , 1998 .

[18]  H.-J. Euler,et al.  On a Measure for the Discernibility between Different Ambiguity Solutions in the Static-Kinematic GPS-Mode , 1991 .

[19]  P. Teunissen.  A new method for fast carrier phase ambiguity estimation , 1994, Proceedings of 1994 IEEE Position, Location and Navigation Symposium - PLANS'94.

[20]  Sandra Verhagen,et al.  On GNSS Ambiguity Acceptance Tests , 2007 .

[21]  Sandra Verhagen,et al.  The GNSS ambiguity ratio-test revisited: a better way of using it , 2009 .

[22]  P. Teunissen.  Success probability of integer GPS ambiguity rounding and bootstrapping , 1998 .

[23]  Tomoji Takasu,et al.  Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB , 2009 .

[24]  Shaowei Han,et al.  Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning , 1996 .

[25]  S. Verhagen.  Integer ambiguity validation: an open problem? , 2004 .

[26]  Gerhard Beutler,et al.  Rapid static positioning based on the fast ambiguity resolution approach , 1990 .

[27]  Alexandra Verhagen,et al.  The GNSS integer ambiguities: estimation and validation , 2005 .