MLAMBDA: a modified LAMBDA method for integer least-squares estimation

Chang, Xiao-Wen; Yang, Xiaohua; Zhou, Tianyang

doi:10.1007/s00190-005-0004-x

Cited by 324 publications

(186 citation statements)

References 18 publications

Supporting

Mentioning

183

Contrasting

Unclassified

Order By: Relevance

“…The positive constant χ 2 can be predetermined according to different strategies and then gradually shrunk during the search (Chang et al, 2005;De Jonge and Tiberius, 1996;Teunissen, 1993Teunissen, , 1995b.…”

Section: The Lambda Methodmentioning

confidence: 99%

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

Teunissen

2011

J. Navigation

View full text Add to dashboard Cite

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 maximizing the success probability of integer ambiguity estimation. In the past two decades, the LAMBDA method has been typically used for the cases where the number of ambiguities was generally 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. The 12-day dual-frequency GPS 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 the baseline repeatabilities obtained with the ambiguities resolved from LAMBDA method agreed well with that of Bernese. Therefore, for the future's 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. KEY WORDS1. LAMBDA method. 2. Bernese software. 3. High-dimensional integer space. 4. Ambiguity resolution.

show abstract

Section: The Lambda Methodmentioning

confidence: 99%

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

Teunissen

2011

J. Navigation

View full text Add to dashboard Cite

show abstract

“…This paper applies the ILS estimation implementation in the form of the MLAMBDA method (Chang et al, 2005), which is based on the modified LAMBDA method (Teunissen, 1993(Teunissen, , 1995De Jonge and Tiberius, 1996). This method is the most effective implementation of ambiguity estimation (Hofmann-Wellenhof et al, 2008), especially with respect to kinematic applications (Seeber, 2003).…”

Section: Application Parameters and Solution Algorithmmentioning

confidence: 99%

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

Próchniewicz

2014

Artificial Satellites

View full text Add to dashboard Cite

ABSTRACT. The reliability of precision GNSS positioning primarily depends on correct carrier-phase ambiguity resolution. An optimal estimation and correct validation of ambiguities necessitates a proper definition of mathematical positioning model. Of particular importance in the model definition is the taking into account of the atmospheric errors (ionospheric and tropospheric refraction) as well as orbital errors. The use of the network of reference stations in kinematic positioning, known as Network-based Real-Time Kinematic (Network RTK) solution, facilitates the modeling of such errors and their incorporation, in the form of correction terms, into the functional description of positioning model. Lowered accuracy of corrections, especially during atmospheric disturbances, results in the occurrence of unaccounted biases, the so-called residual errors. The taking into account of such errors in Network RTK positioning model is possible by incorporating the accuracy characteristics of the correction terms into the stochastic model of observations. In this paper we investigate the impact of the expansion of the stochastic model to include correction term variances on the reliability of the model solution. In particular the results of instantaneous solution that only utilizes a single epoch of GPS observations, is analyzed. Such a solution mode due to the low number of degrees of freedom is very sensitive to an inappropriate mathematical model definition. Thus the high level of the solution reliability is very difficult to achieve. Numerical tests performed for a test network located in mountain area during ionospheric disturbances allows to verify the described method for the poor measurement conditions. The results of the ambiguity resolution as well as the rover positioning accuracy shows that the proposed method of stochastic modeling can increase the reliability of instantaneous Network RTK performance.

show abstract

“…The search efficiency is governed by the size χ 2 and the shape of ellipsoid. The constant χ 2 can be predetermined us-ing different strategies and can also be shrunken during the search [8,26]. The shape and orientation of the ellipsoid are defined by the variance matrix ˆâa Q .…”

Section: Ils Search Spacementioning

confidence: 99%

GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA

Verhagen

Teunissen

2013

Lecture Notes in Electrical Engineering

View full text Add to dashboard Cite

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. The method's popularity stems from its numerical efficiency and statistical optimality. However, before conducting ambiguity resolution, one needs to infer how reliable the fixed solution can 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 this probability of correct integer estimation is generally difficult to compute, easy-to-use approximations and bounds of the ambiguity success rate 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 actual integer estimation, the updated version of the LAMBDA software, provides now more options of integer estimation and integer search, including the searchand-shrink strategy. In addition, the Fixed Failure-rate Ratio Test (FF-RT) and the Fixed Critical-value Ratio Test (FC-RT) are incorporated for users 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, multi-GNSS applications.

show abstract

MLAMBDA: a modified LAMBDA method for integer least-squares estimation

Cited by 324 publications

References 18 publications

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

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

Study on the influence of stochastic properties of correction terms on the reliability of instantaneous network RTK

GNSS Integer Ambiguity Estimation and Evaluation: LAMBDA and Ps-LAMBDA

Contact Info

Product

Resources

About