The ratio test for future GNSS ambiguity resolution

Verhagen, Sandra; Teunissen, Peter

doi:10.1007/s10291-012-0299-z

Cited by 191 publications

(101 citation statements)

References 13 publications

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“…The symbol U represents the threshold for the ratio test value. Smaller thresholds sometimes lead to the acceptance of incorrectly fixed integer ambiguities, causing ambiguity failure; on the other hand, larger thresholds can avoid the ambiguity being incorrectly fixed but sometimes unnecessarily reject correctly fixed inter ambiguities, causing ambiguity false alarms [26]. The size of the threshold is commonly given from 2 to 3 [20,26].…”

Section: Generalized Phase-code Methodsmentioning

confidence: 99%

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BeiDou System (BDS) Triple-Frequency Ambiguity Resolution without Code Measurements

Chu

Yang

2018

Remote Sensing

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Phase and code measurements achieve ambiguity resolution in medium-or long-baseline computation. However, the code multipath effect on Global Navigation Satellite Systems (GNSS) phase and code measurements is a main source of error for ambiguity resolution, in particular the code multipath. The BeiDou System (BDS) of China is fully operational in the Asia-Pacific region and provides triple-frequency (B1, B2 and B3) measurements. Although previous research about BDS triple-frequency baseline computation indicated that using triple-frequency measurements improves the performance of ambiguity resolution, the respective methods are still impacted by code multipath since the code measurements are incorporated in the methods. Therefore, it is of interest to further improve the ambiguity resolution of BDS triple-frequency baseline computation by excluding the code multipath. We propose a modified phase-only method that only uses triple-frequency phase measurements to achieve BDS ambiguity resolution and evaluate the performance of the method. Observations from experimental medium and long baselines were collected with Trimble NetR9 receivers. The related ambiguity-resolution performances are computed with the phase-only method and a generalized phase-code method. The results show that the phase-only ambiguity resolution is feasible and generally performs better than the phase-code ambiguity resolution, but the improvement is subject to phase noise and satellite geometry.

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Section: Generalized Phase-code Methodsmentioning

confidence: 99%

“…Figure 7 displays the success percentages over the 37 km and 256 km baselines with commonly used ratio test thresholds (U = 2, 2.5, 3) [20,26]. Figure 7a,c show that the success percentages at cutoff angle = 15 • (representing a normal environment) decrease noticeably when the threshold is increased from 2 to 3 for both methods.…”

Section: Success Percentagementioning

confidence: 99%

BeiDou System (BDS) Triple-Frequency Ambiguity Resolution without Code Measurements

Chu

Yang

2018

Remote Sensing

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“…To prevent from a wrong xing to integer, the xed ambiguity vector has to be validated. This can be done for example thanks to discriminant tests such as the ratio test (Verhagen and Teunissen 2013). Eventually, a Fixed Failure-rate Ratio Test (Wang and Feng 2013) or look-up tables (Teunissen and Verhagen 2009) can be used.…”

Section: Fixing the Ambiguities To Integermentioning

confidence: 99%

Fully populated VCM or the hidden parameter

Kermarrec

Schön

2017

Journal of Geodetic Science

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Least-squares estimates are trustworthy with minimal variance if the correct stochastic model is used. Due to computational burden, diagonal models that neglect correlations are preferred to describe the elevation dependency of the variance of GPS observations. In this contribution, an improved stochastic model based on a parametric function to take correlations between GPS phase observations into account is presented. Built on an adapted and exible Mátern function accounting for spatiotemporal variabilities, its parameters can be xed thanks to Maximum Likelihood Estimation or chosen apriori to model turbulent tropospheric refractivity uctuations. In this contribution, we will show in which cases and under which conditions corresponding fully populated variance covariance matrices (VCM) replace the estimation of a tropospheric parameter. For this equivalence "augmented functional versus augmented stochastic model" to hold, the VCM should be made su ciently large which corresponds to computing small batches of observations. A case study with observations from a medium baseline of 80 km divided into batches of 600 s shows improvement of up to 100 mm for the 3Drms when fully populated VCM are used compared with an elevation dependent diagonal model. It con rms the strong potential of such matrices to improve the least-squares solution, particularly when ambiguities are let oat.

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“…Examples include the ratiotest, the difference-test and the projection-test [14][15][16][17][18]. All these tests can be cast in the framework of Integer Aperture Estimation (IAE) [19][20][21].The ratio-test is probably one of the most popular. Both the Fixed Critical-value Ratio Test (FC-RT) and the Fixed Failure-rate Ratio Test (FF-RT) are part of the new version of LAMBDA.…”

Section: Integer Solutionmentioning

confidence: 99%

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

Verhagen

Teunissen

2013

Lecture Notes in Electrical Engineering

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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.

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The ratio test for future GNSS ambiguity resolution

Cited by 191 publications

References 13 publications

BeiDou System (BDS) Triple-Frequency Ambiguity Resolution without Code Measurements

BeiDou System (BDS) Triple-Frequency Ambiguity Resolution without Code Measurements

Fully populated VCM or the hidden parameter

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

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