High Dimensional Integer Ambiguity Resolution: A First Comparison between LAMBDA and Bernese

The LAMBDA method for integer least-squares ambiguity resolution has been widely used in a great variety of Global Navigation Satellite System (GNSS) applications. The popularity of this method stems from its numerical efficiency and its guaranteed optimality in the sense of maximising the success probability of integer ambiguity estimation. In the past two decades, the LAMBDA method has been typically used in cases where the number of ambiguities is less than several tens. With the advent of denser network processing and the availability of multi-frequency, multi-GNSS systems, it is important to understand LAMBDA's performance in high dimensional spaces. In this contribution, we will address this issue using real GPS data based on the Bernese software. We have embedded the LAMBDA method into the Bernese software and compared their ambiguity resolution performances. Twelve day dual-frequency GPS data with a sampling interval of 30 s was used in the experiment, which was collected from a network of 19 stations in the Perth area of Western Australia with an average baseline length of 380 km. Different experimental scenarios were examined and tested with different observation spans, which represent the different ambiguity dimensions. The results showed that LAMBDA is still efficient even when the number of ambiguities is more than 100, and that the baseline repeatability obtained with the ambiguities resolved from the LAMBDA method agreed well with that of Bernese. Therefore, for future dense network processing, the easy-to-use LAMBDA method should be considered as an alternative to baseline-per-baseline methods as those used in e.g. the Bernese software.

[1]  Christian Tiberius,et al.  Integer Ambiguity Estimation with the Lambda Method , 1996 .

[2]  X. Chang,et al.  MLAMBDA: a modified LAMBDA method for integer least-squares estimation , 2005 .

[3]  Bernhard Hofmann-Wellenhof,et al.  Global Positioning System , 1992 .

[4]  G. Blewitt Carrier Phase Ambiguity Resolution for the Global Positioning System Applied to Geodetic Baselines up to 2000 km , 1989 .

[5]  P. Teunissen,et al.  The least-squares ambiguity decorrelation adjustment: its performance on short GPS baselines and short observation spans , 1997 .

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

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

[8]  Charles C. Counselman,et al.  Miniature Interferometer Terminals for Earth Surveying: Ambiguity And Multipath with Global Positioning System , 1981, IEEE Transactions on Geoscience and Remote Sensing.

[9]  Peter Teunissen,et al.  The invertible GPS ambiguity transformations , 1995 .

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

[11]  L. Mervart,et al.  Bernese GPS Software Version 5.0 , 2007 .

[12]  A. Leick GPS satellite surveying , 1990 .

[13]  P. Teunissen,et al.  The Volume of the GPS Ambiguity Search Space and its Relevance for Integer Ambiguity Resolution , 1996 .

[14]  G. Gendt,et al.  Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations , 2008 .

[15]  M. Elizabeth Cannon,et al.  Mixed integer programming for the resolution of GPS carrier phase ambiguities , 2010, ArXiv.

[16]  B. Hofmann-Wellenhof,et al.  Global Positioning System , 1992 .

[17]  P. D. Jonge,et al.  The LAMBDA method for integer ambiguity estimation: implementation aspects , 1996 .

[18]  Peter Teunissen,et al.  GPS for geodesy , 1996 .

[19]  G. Strang,et al.  Linear Algebra, Geodesy, and GPS , 1997 .

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

[21]  Peter Teunissen,et al.  The istributional dependence of the range of triple frequency GPS ambiguity resolution , 2000 .

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

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