The GNSS ambiguity ratio-test revisited: a better way of using it

Teunissen, Peter; Verhagen, Sandra

doi:10.1179/003962609x390058

Cited by 171 publications

(90 citation statements)

References 11 publications

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“…This is more difficult for the new-rising satellites, the ambiguities of which usually need longer convergence time after they first become visible. In the AR search strategy under ILS condition, if some estimated float ambiguities have large residuals, the validation process (e.g., Ratio test [27]) will reject the ambiguity fixing due to biases. Actually, for combined GPS and BDS, not all the ambiguities must be fixed in simultaneously since there are sufficient satellites available.…”

Section: Ambiguity Fixing Strategy For Nl Armentioning

confidence: 99%

Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning

Gao

Pan

et al. 2017

Remote Sensing

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An inter-system differencing model between two Global Navigation Satellite Systems (GNSS) enables only one reference satellite for all observations. If the associated differential inter-system biases (DISBs) are priori known, double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can also be fixed to integers. This can provide more redundancies for the observation model, and thus will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning. However, for Global Positioning System (GPS) and the regional BeiDou Navigation Satellite System (BDS-2), there are no overlapping frequencies. Tight combination of GPS and BDS needs to process not only the DISBs but also the single-difference ambiguity of the reference satellite, which is caused by the influence of different frequencies. In this paper, we propose a tightly combined dual-frequency GPS and BDS RTK positioning model for medium baselines with real-time estimation of DISBs. The stability of the pseudorange and phase DISBs is analyzed firstly using several baselines with the same or different receiver types. The dual-frequency ionosphere-free model with parameterization of GPS-BDS DISBs is proposed, where the single-difference ambiguity is estimated jointly with the phase DISB parameter from epoch to epoch. The performance of combined GPS and BDS RTK positioning for medium baselines is evaluated with simulated obstructed environments. Experimental results show that with the inter-system differencing model, the accuracy and reliability of RTK positioning can be effectively improved, especially for the obstructed environments with a small number of satellites available.

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Section: Ambiguity Fixing Strategy For Nl Armentioning

confidence: 99%

Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning

Gao

Pan

et al. 2017

Remote Sensing

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“…Similarly, counting the numbers that fall inside the IA acceptance region but not the correct one, we can have the fail-rate P IA f and the rest are the undecided P IA u . The detailed simulation procedures can be referred to Teunissen and Verhagen (2009), Li and Wang (2012). Note that by simulation, we have the knowledge that a mean value for a zero vector is the correct integer ambiguity and as the IA estimation totally relies on simulation, the success-rate for ILS and IA are all correct rates.…”

Section: N U M E R I Ca L a N A Ly S I Smentioning

confidence: 99%

“…When lacking confidence for the best ILS ambiguity candidate, the IA estimation is more user-controllable than the ILS estimation, such as the IA estimation can control the probabilities of three different outcomes. To make it clear, the inter-probability relationships among the ILS and IA estimators are shown as (Teunissen and Verhagen, 2009):…”

Section: T H E U P P E R B O U N D a N D Low E R B O U N D Fo R I A Ementioning

confidence: 99%

Theoretical Upper Bound and Lower Bound for Integer Aperture Estimation Fail-Rate and Practical Implications

Wang

2012

J. Navigation

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Integer ambiguity validation is pivotal in precise positioning with Global Navigation Satellite Systems (GNSS). Recent research has shown traditionally used ambiguity validation methods can be classified as members of the Integer Aperture (IA) estimators, and by the virtue of the IA estimation, a user controllable IA fail-rate is preferred. However, an appropriately chosen fail-rate is essential for ambiguity validation. In this paper, the upper bound and the lower bound for the IA fail-rate, which are extremely useful even at the designing stage of a GNSS positioning system, have been analysed, and numerical results imply that a meaningful IA fail-rate should be within this range.

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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 GNSS ambiguity ratio-test revisited: a better way of using it

Cited by 171 publications

References 11 publications

Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning

Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning

Theoretical Upper Bound and Lower Bound for Integer Aperture Estimation Fail-Rate and Practical Implications

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

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