GNSS integer ambiguity validation based on posterior probability

Wu, Zemin; Bian, Shaofeng

doi:10.1007/s00190-015-0826-0

Cited by 19 publications

(10 citation statements)

References 23 publications

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“…Although the critical value of the ratio is always determined by experimental experience, the empirical critical value of the ratio cannot fully reflect the strength of the positioning model owing to the complexity of the observations and randomness of the ambiguity parameters. Under the framework of the Bayesian hypothesis testing theory, the reliability of ambiguity fixing can be judged if the posterior probability of ambiguity is greater than the defined confidence level [43]. A detailed derivation can be found in the work of Wu et al (2015).…”

Section: Ucppp Partial Ambiguity Resolutionmentioning

confidence: 99%

The Performance of Three-Frequency GPS PPP-RTK with Partial Ambiguity Resolution

Yan

Zhang

2022

Atmosphere

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The correct ambiguity resolution of real-time kinematic precise point positioning (PPP-RTK) plays an essential role in achieving fast, reliable, and high-precision positioning. However, the ambiguity of incorrect fixing will cause poor PPP-RTK positioning performance. Hence, it is essential to optimize the selected strategy of the ambiguity subset to obtain a more reliable ambiguity resolution performance for PPP-RTK. For this reason, a partial ambiguity resolution (PAR) method combining quality control and Schmidt orthogonalization (Gram–Schmidt) is proposed in this study. To investigate the performance of global positioning system (GPS) dual- and three-frequency PPP-RTK comprehensively, the PAR method based on the Gram–Schmidt method was analyzed and compared with the highest elevation angle method, which considered the satellite with the highest elevation angle as the reference satellite. The performance of ambiguity fixing, atmospheric corrections, and positioning were evaluated using five stations in Belgium and its surrounding area. The results showed average epoch fixing rates of 81.01%, 95.92%, 82.05%, and 97.93% in the dual-frequency highest elevation angle (F2-MAX), dual-frequency Gram–Schmidt (F2-ALT), three-frequency highest elevation angle (F3-MAX), and three–frequency Gram–Schmidt (F3-ALT), respectively. In terms of the time to first fix (TTFF), 89.02%, 94.25%, 90.24%, and 95.69% of the single-differenced (SD) narrow lane (NL) ambiguity fell within 3 min in F2-MAX, F2-ALT, F3-MAX, and F3-ALT, respectively. As far as the ionospheric corrections are concerned, the proportion of SD ionospheric residuals within ±0.25 total electron content units (TECU) were 95.08%, 95.93%, 95.68%, and 96.98% for the F2-MAX, F2-ALT, F3-MAX, and F3-ALT, respectively. The centimeter-level accuracy of both the horizontal and vertical positioning errors can be achieved almost instantaneously in F3-ALT. This is attributed to the accurate and reliable SD NL ambiguity fixing based on the Gram–Schmidt approach.

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Section: Ucppp Partial Ambiguity Resolutionmentioning

confidence: 99%

The Performance of Three-Frequency GPS PPP-RTK with Partial Ambiguity Resolution

Yan

Zhang

2022

Atmosphere

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“…Smaller

means the implementation is closer to the theory and consequently heavier computation burden. Then, the integers within the radius

are considered as the valid integer set and used to compute the

[ 4 , 30 , 31 ]. The integer set can be defined as:

…”

Section: The Sub-optimality Of the Difference Testmentioning

confidence: 99%

Improving GNSS Ambiguity Acceptance Test Performance with the Generalized Difference Test Approach

Wang

Chen

Shen

et al. 2018

Sensors

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In Global navigation satellite system (GNSS) data processing, integer ambiguity acceptance test is considered as a challenging problem. A number of ambiguity acceptance tests have been proposed from different perspective and then unified into the integer aperture estimation (IA) framework. Among all the IA estimators, the optimal integer aperture (OIA) achieves the highest success rate with the fixed failure rate tolerance. However, the OIA is of less practical appealing due to its high computation complexity. On the other hand, the popular discrimination tests employ only two integer candidates, which are the essential reason for their sub-optimality. In this study, a generalized difference test (GDT) is proposed to exploit the benefit of including three or more integer candidates to improve their performance from theoretical perspective. The simulation results indicate that the third best integer candidates contribute to more than 70% success rate improvement for integer bootstrapping success rate higher than 0.8 case. Therefore, the GDT with three integer candidates (GDT3) achieves a good trade-off between the performance and computation burden. The threshold function is also applied for rapid determination of the fixed failure rate (FF)-threshold for GDT3. The performance improvement of GDT3 is validated with real GNSS data set. The numerical results indicate that GDT3 achieves higher empirical success rate while the empirical failure rate remains comparable. In a 20 km baseline test, the success rate GDT3 increase 7% with almost the same empirical failure rate.

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“…Jazaeri et al [42] developed integer search estimation based on the lattice theory whose search algorithms were presented and proved to be many times faster than the least-squares ambiguity decorrelation adjustment (LAMBDA) [43] and modified LAMBDA [44]. Wu and Bian [45] developed a posterior probability test to validate each ambiguity subset, which can guarantee the correct fixing confidence. However, in the above-mentioned methods, the fixing and computing efficiency of high-dimensional ambiguity for the MBRTK has not been investigated.…”

Section: Introductionmentioning

confidence: 99%

GPS/BDS RTK Positioning Based on Equivalence Principle Using Multiple Reference Stations

Wang

Nie

et al. 2020

Remote Sensing

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Reliable real-time kinematic (RTK) is crucially important for emerging global navigation satellite systems (GNSSs) applications, such as drones and unmanned vehicles. The performance of conventional single baseline RTK (SBRTK) with one reference station degrades greatly in dense, urban environments, due to signal blockage and multipath error. The increasing use of multiple reference stations for kinematic positioning can improve RTK positioning accuracy and availability in urban areas. This paper proposes a new algorithm for multi-baseline RTK (MBRTK) positioning based on the equivalence principle. The advantages of the solution are to keep observation independent and increase the redundancy to estimate the unknown parameters. The equivalent double-differenced (DD) observation equations for multiple reference stations are firstly developed through the equivalent transform. A modified Kalman filter with parameter constraints is proposed, as well as a partial ambiguity resolution (PAR) strategy is developed to determine an ambiguity subset. Finally, the static and kinematic experiments are carried out to validate the proposed algorithm. The results demonstrate that, compared with single global positioning system (GPS) and Beidou navigation system (BDS) RTK positioning, the GPS/BDS positioning for MBRTK can enhance the positioning accuracy with improvement by approximately (45%, 35%, and 27%) and (12%, 6%, and 19%) in the North (N), East (E), and Up (U) components, as well as the availability with improvement by about 33% and 10%, respectively. Moreover, the MBRTK model with two and three reference receivers can significantly increase the redundancy and provide smaller ambiguity dilution of precision (ADOP) values. Compared with the scheme-one and scheme-two for SBRTK, the MBRTK with multiple reference receivers have a positioning accuracy improvement by about (9%, 0%, and 6%) and (9%, 16%, and 16%) in N, E, and U components, as well as the availability improvement by approximately 10%. Therefore, compared with the conventional SBRTK, the MBRTK can enhance the strength of the kinematic positioning model as well as improve the positioning accuracy and availability.

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GNSS integer ambiguity validation based on posterior probability

Cited by 19 publications

References 23 publications

The Performance of Three-Frequency GPS PPP-RTK with Partial Ambiguity Resolution

The Performance of Three-Frequency GPS PPP-RTK with Partial Ambiguity Resolution

Improving GNSS Ambiguity Acceptance Test Performance with the Generalized Difference Test Approach

GPS/BDS RTK Positioning Based on Equivalence Principle Using Multiple Reference Stations

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