GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA
Successful integer carrier-phase ambiguity resolution is crucial for high precision GNSS applications. It includes both integer estimation and evaluation. For integer estimation, the LAMBDA method has been applied in a wide variety of GNSS applications. H
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GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA Bofeng Li, Sandra Verhagen and Peter J.G. Teunissen
Abstract Successful integer carrier-phase ambiguity resolution is crucial for high precision GNSS applications. It includes both integer estimation and evaluation. For integer estimation, the LAMBDA method has been applied in a wide variety of GNSS applications. However, before conducting ambiguity resolution, one needs to infer how reliable the fixed solution is expected to be, as incorrect fixed ambiguity solutions often lead to unacceptable positioning errors. In this paper, two Matlab software tools are introduced for the evaluation and integer estimation: Ps-LAMBDA and an updated version of LAMBDA. Evaluation of the integer solution is based on the ambiguity success rate. Since the success rate is generally difficult to compute, some easy-to-use approximations and bounds are provided by the Ps-LAMBDA software. This success rate tool is valuable not only for inferring whether to fix the ambiguities but also for design and research purposes. For the integer estimation, the new version LAMBDA software provides more options of integer estimation and integer search, including the search-and-shrink strategy. In addition, the ratio test is incorporated to validate the significance of the fixed solution. Using these two software tools together allows for the combined execution of integer estimation and evaluation, thus benefiting multi-frequency, multiGNSS applications.
Keywords LAMBDA Ps-LAMBDA rate Ambiguity resolution
Search-and-shrink Ambiguity success
B. Li (&) P. J.G.Teunissen GNSS Research Center, Department of Spatial Sciences, Curtin University, Perth, Australia e-mail: [email protected]; [email protected] S. Verhagen Mathematical Geodesy and Positioning, Delft University of Technology, Delft, The Nertherlands
J. Sun et al. (eds.), China Satellite Navigation Conference (CSNC) 2013 Proceedings, Lecture Notes in Electrical Engineering 244, DOI: 10.1007/978-3-642-37404-3_26, Springer-Verlag Berlin Heidelberg 2013
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26.1 Introduction All high-precision Global Navigation Satellite Systems (GNSS) applications commonly rely on the very precise GNSS carrier-phase observations with successfully fixed ambiguities [1–5]. Hence ambiguity resolution (AR) is the key for precision GNSS applications; it comprises ambiguity estimation and evaluation. A variety of AR methods have been developed since the late 1980s [1–6], of which the Least squares AMBiguity Decorrelation Adjustment (LAMBDA) method has become one of the more popular methods. The method includes a numerically efficient implementation of the Integer Least-Squares (ILS) principle and as such maximizes the probability of successful integer estimation [7]. The key of the LAMBDA method is to find the integer solution based on a decorrelated float ambiguity solution instead of the original one. By means of the decorrelating ambiguity transformation the efficiency of the integer search is significan
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