Combined BeiDou-2 and BeiDou-3 instantaneous RTK positioning: stochastic modeling and positioning performance assessment

Miao, Weikai; Li, Bofeng; Zhang, Zhiteng; Zhang, Xuewen

doi:10.1080/14498596.2019.1642250

Cited by 22 publications

(9 citation statements)

References 29 publications

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“…However, some bias variation occurs in the TF phase combination of G01, which is known as interfrequency clock bias (IFCB) [34]. In past studies [8,35], the presence of IFCB in GPS was identified, whereas no apparent bias variation appears in Galileo or BDS-3. To eliminate this kind of bias variation, the between-receiver difference is the method usually applied because the IFCB remains the same for a certain satellite in different stations.…”

Section: Triple-frequency Phase Combinationmentioning

confidence: 99%

Estimation of Inter-System Biases between BDS-3/GPS/Galileo and Its Application in RTK Positioning

Zhu

Zhang

2021

Remote Sensing

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For the development of a global navigation satellite system (GNSS), the third generation of BeiDou Navigation Satellite System (BDS-3) achieved full constellation for worldwide service on 23 June 2020. The new signals, B1C and B2a of BDS-3, further enhance the compatibility and interoperability between different GNSSs. In this study, we first assessed the quality of all the signals in BDS-3/GPS/Galileo. Then, to achieve the interoperability among BDS-3/GPS/Galileo, the inter-system bias (ISB), which appears if an inter-system difference exists between two GNSSs, was estimated at overlapping frequencies. Finally, we used the estimated ISBs in real-time kinematic (RTK) positioning. The results show the higher quality of the overlapping frequency B2a/L5/E5a than B1C/L1/E1 in terms of pseudo range multipath. The ISBs are stable both in the short term for one day and in the long term for over a year, which fit a zero-mean normal distribution well when the identical type of receiver is applied. Thus, it is reasonable to ignore the ISBs in the inter-system differences. With the estimated ISBs, the inter-system double-difference RTK can be achieved, which is called a tightly combined model (TCM) RTK. Compared with the traditional intra-system double-difference RTK, which is called a loosely combined model (LCM) RTK, the TCM RTK can achieve a higher success rate (SR) in terms of ambiguity resolution and higher positioning accuracy. In addition, the higher the cutoff elevation angle set, the greater the promotion can be obtained in SR. Even with a cutoff elevation angle of 50°, the SR of TCM is over 80%. Thus, it is important to apply TCM RTK when the observation conditions are limited, such as in dense jungles or the urban canyons.

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Section: Triple-frequency Phase Combinationmentioning

confidence: 99%

Estimation of Inter-System Biases between BDS-3/GPS/Galileo and Its Application in RTK Positioning

Zhu

Zhang

2021

Remote Sensing

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“…Apart from the numerous works related to the refinement of stochastic models for GPS and GLONASS observations, research on stochastic models of state-of-the-art Galileo and BeiDou systems has also been conducted in the recent years. These studies include analyses of single systems (e.g., variance of dual-frequency BeiDou B1/B2 code and phase observations [ 60 ], variance-covariance components as well as cross- and time-correlation parameters for dual-frequency [ 61 ] and triple-frequency BeiDou signals [ 4 ], a combination of BeiDou-2 and BeiDou-3 stochastic modeling [ 62 ], noise characteristic for five Galileo signals [ 63 ]), combined dual systems: GPS/Galileo [ 22 ], GPS/BeiDou [ 64 ], GPS/IRNSS [ 65 ] and triple systems GPS/Galileo/BeiDou [ 66 , 67 , 68 ] solutions as well as Multi-GNSS system solutions (e.g., [ 69 , 70 ]).…”

Section: Introductionmentioning

confidence: 99%

Empirical Stochastic Model of Multi-GNSS Measurements

Próchniewicz

Wezka

Kozuchowska

2021

Sensors

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The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

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“…In the past, several approaches were developed, most of them are based on searching the optimal integer ambiguities statistically closest to the corresponding float solution [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. The mostly used approach is the Least-Squares AMBiguity Decorrelation Adjustment (LAMBDA) method [ 1 ], for example, which is also applied in the recent contributions [ 18 , 19 , 20 ].…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of BDS Triple-Frequency Ambiguity Fixing Approaches for RTK Positioning

Zhu

Lü

Tang

et al. 2021

Sensors

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Concerning the triple-frequency ambiguity resolution, in principle there are three different realizations. The first one is to fix all the ambiguities of the original frequencies together. However, it is also believed that fixing the combined integer ambiguities with longer wavelength, such as extra-wide-lane (EWL), wide-lane (WL), should be advantageous. Also, it is demonstrated that fixing sequentially EWL, WL and one type of original ambiguities provides better results, as the previously fixed ambiguities increase parameters’ precision for later fixings. In this paper, we undertake a comparative study of the three fixing approaches by means of experimental validation. In order to realize the three fixing approaches from the same information in terms of adjustment, we developed a processing strategy to provide fully consistent normal equations. We first generate the normal equation with the original undifferentiated carrier phase ambiguities, then map it into that with the combined and double-differenced ambiguities required by the individual approach for fixing. Four baselines of 258 m, 22 km, 47 km and 53 km are selected and processed in both static and kinematic mode using the three ambiguity-fixing approaches. Indicators including time of first fixed solution (TFFS), the correct fixing rate, positioning accuracy and RATIO are used to evaluate and investigate results. We also made a preliminary theoretical explanation of the results by looking into the decorrelation procedure of the ambiguity searching algorithm and the intermediate results. As conclusions, integrated searching of original ambiguities or combined ambiguities has almost the same fixing performance, whereas the sequential fixing of EWL, WL and B1 ambiguities overperforms the integrated searching. By the way, the third-frequency data can shorten the TFFS significantly but can hardly improve the positioning.

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Combined BeiDou-2 and BeiDou-3 instantaneous RTK positioning: stochastic modeling and positioning performance assessment

Cited by 22 publications

References 29 publications

Estimation of Inter-System Biases between BDS-3/GPS/Galileo and Its Application in RTK Positioning

Estimation of Inter-System Biases between BDS-3/GPS/Galileo and Its Application in RTK Positioning

Empirical Stochastic Model of Multi-GNSS Measurements

A Comparative Study of BDS Triple-Frequency Ambiguity Fixing Approaches for RTK Positioning

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