Extended GNSS Ambiguity Resolution Models with Regularization Criterion and Constraints

This paper firstly presents an extended ambiguity resolution model that deals with an ill-posed problem and constraints among the estimated parameters. In the extended model, the regularization criterion is used instead of the traditional least squares in order to estimate the float ambiguities better. The existing models can be derived from the general model. Secondly, the paper examines the existing ambiguity searching methods from four aspects: exclusion of nuisance integer candidates based on the available integer constraints; integer rounding; integer bootstrapping and integer least squares estimations. Finally, this paper systematically addresses the similarities and differences between the generalized TCAR and decorrelation methods from both theoretical and practical aspects.

[1]  Bofeng Li,et al.  Three carrier ambiguity resolution: distance-independent performance demonstrated using semi-generated triple frequency GPS signals , 2010 .

[2]  Bofeng Li,et al.  Prior baseline information based fast GPS ambiguity resolution , 2008 .

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

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

[5]  Bofeng Li,et al.  Global navigation satellite system ambiguity resolution with constraints from normal equations , 2010 .

[6]  Gyu-In Jee,et al.  Efficient ambiguity resolution using constraint equation , 1996, Proceedings of Position, Location and Navigation Symposium - PLANS '96.

[7]  Bofeng Li.  Generation of Third Code and Phase Signals Based on Dual-Frequency GPS Measurements , 2008 .

[8]  Y. Bock,et al.  Global Positioning System Network analysis with phase ambiguity resolution applied to crustal deformation studies in California , 1989 .

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

[10]  E. Grafarend.  Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm , 2000, GPS Solutions.

[11]  Chris Rizos,et al.  Three Carrier Approaches for Future Global, Regional and Local GNSS Positioning Services: Concepts and Performance Perspectives , 2005 .

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

[13]  H. Hsu,et al.  A new approach to GPS ambiguity decorrelation , 1999 .

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

[15]  Peiliang Xu.  Random simulation and GPS decorrelation , 2001 .

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

[17]  Peiliang Xu.  Truncated SVD methods for discrete linear ill-posed problems , 1998 .

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

[19]  Bofeng Li,et al.  Regularized solution to fast GPS ambiguity resolution , 2007 .

[20]  Yanming Feng.  GNSS three carrier ambiguity resolution using ionosphere-reduced virtual signals , 2008 .

[21]  Ron Hatch,et al.  Instantaneous Ambiguity Resolution , 1991 .