Fixed Failure Rate Ambiguity Validation Methods for GPS and Compass

Ambiguity resolution plays a crucial role in real time kinematic GNSS positioning which gives centimetre precision positioning results if all the ambiguities in each epoch are correctly fixed to integers. However, the incorrectly fixed ambiguities can result in large positioning offset up to several meters without notice. Hence, ambiguity validation is essential to control the ambiguity resolution quality. Currently, the most popular ambiguity validation is ratio test. The criterion of ratio test is often empirically determined. Empirically determined criterion can be dangerous, because a fixed criterion cannot fit all scenarios and does not directly control the ambiguity resolution risk. In practice, depending on the underlying model strength, the ratio test criterion can be too conservative for some model and becomes too risky for others. A more rational test method is to determine the criterion according to the underlying model and user requirement. Miss-detected incorrect integers will lead to a hazardous result, which should be strictly controlled. In ambiguity resolution miss-detected rate is often known as failure rate. In this paper, a fixed failure rate ratio test method is presented and applied in analysis of GPS and Compass positioning scenarios. A fixed failure rate approach is derived from the integer aperture estimation theory, which is theoretically rigorous. The criteria table for ratio test is computed based on extensive data simulations in the approach. The real-time users can determine the ratio test criterion by looking up the criteria table. This method has been applied in medium distance GPS ambiguity resolution but multi-constellation and high dimensional scenarios haven’t been discussed so far. In this paper, a general ambiguity validation model is derived based on hypothesis test theory, and fixed failure rate approach is introduced, especially the relationship between ratio test threshold and failure rate is examined. In the last, factors that influence fixed failure rate approach ratio test threshold is discussed according to extensive data simulation. The result shows that fixed failure rate approach is a more reasonable ambiguity validation method with proper stochastic model.

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

[2]  J Wang,et al.  Some remarks on GNSS integer ambiguity validation methods , 2012 .

[3]  Variable duration fixed failure rate ambiguity resolution , 2012, GPS Solutions.

[4]  Peter Teunissen,et al.  Penalized GNSS Ambiguity Resolution , 2004 .

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

[6]  Sandra Verhagen,et al.  New Global Navigation Satellite System Ambiguity Resolution Method Compared to Existing Approaches , 2006 .

[7]  Ming Wei,et al.  Fast Ambiguity Resolution Using an Integer Nonlinear Programming Method , 1995 .

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

[9]  Peiliang Xu,et al.  Voronoi cells, probabilistic bounds, and hypothesis testing in mixed integer linear models , 2006, IEEE Transactions on Information Theory.

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

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

[12]  Peter Teunissen,et al.  On the integer normal distribution of the GPS ambiguities. , 1998 .

[13]  HighWire Press.  Philosophical Transactions of the Royal Society of London , 1781, The London Medical Journal.

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

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

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

[17]  Peter Steigenberger,et al.  Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system , 2013, GPS Solutions.

[18]  P. Teunissen,et al.  The ratio test for future GNSS ambiguity resolution , 2013, GPS Solutions.

[19]  P. Teunissen.  Integer aperture least-squares estimation , 2005 .

[20]  Peter Teunissen,et al.  GNSS ambiguity resolution with optimally controlled failure-rate , 2005 .

[21]  Peter Teunissen,et al.  The probability distribution of the GPS baseline for a class of integer ambiguity estimators , 1999 .

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

[23]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

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

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

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

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

[28]  Herbert Landau,et al.  On-the-Fly Ambiguity Resolution for Precise Differential Positioning , 1992 .

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

[30]  Peter Teunissen,et al.  Integer aperture bootstrapping: a new GNSS ambiguity estimator with controllable fail-rate , 2005 .

[31]  B. Tabachnick,et al.  Using Multivariate Statistics , 1983 .