Analysis of Wide-Lane Ambiguities Derived from Geometry-Free and Geometry-Based Precise Point Positioning Models and Their Implication for Orbit and Clock Quality

In this study, an uncombined precise point positioning (PPP) model was established and was used for estimating fractional cycle bias (FCB) products and for achieving ambiguity resolution (AR), using GPS, BDS-2, and Galileo raw observations. The uncombined PPP model is flexible and efficient for positioning services and generating FCB. The FCBs for GPS, BDS-2, and Galileo were estimated using the uncombined PPP model with observations from the Multi-GNSS Experiment (MGEX) stations. The root mean squares (RMSs) of the float ambiguity a posteriori residuals associated with all of the three GNSS constellations, i.e., GPS, BDS-2, and Galileo, are less than 0.1 cycles for both narrow-lane (NL) and wide-lane (WL) combinations. The standard deviation (STD) of the WL combination FCB series is 0.015, 0.013, and 0.006 cycles for GPS, BDS-2, and Galileo, respectively, and the counterpart for the NL combination FCB series is 0.030 and 0.0184 cycles for GPS and Galileo, respectively. For the BDS-2 NL combination FCB series, the STD of the inclined geosynchronous orbit (IGSO) satellites is 0.0156 cycles, while the value for the medium Earth orbit (MEO) satellites is 0.073 cycles. The AR solutions produced by the uncombined multi-GNSS PPP model were evaluated from the positioning biases and the success fixing rate of ambiguity. The experimental results demonstrate that the growth of the amount of available satellites significantly improves the PPP performance. The three-dimensional (3D) positioning accuracies associated with the PPP ambiguity-fixed solutions for the respective only-GPS, GPS/BDS-2, GPS/Galileo, and GPS/BDS-2/Galileo models are 1.34, 1.19, 1.21, and 1.14 cm, respectively, and more than a 30% improvement is achieved when compared to the results related to the ambiguity-float solutions. Additionally, the convergence time based on the GPS/BDS-2/Galileo observations is only 7.5 min for the ambiguity-fixed solutions, and the results exhibit a 53% improvement in comparison to the ambiguity-float solutions. The values of convergence time based on the only-GPS observations are estimated as 22 and 10.5 min for the ambiguity-float and ambiguity-fixed solutions, respectively. Lastly, the success fixing rate of ambiguity is also dramatically raised for the multi-GNSS PPP AR. For example, the percentage is approximately 99% for the GPS/BDS-2/Galileo solution over a 10 min processing period. In addition, the inter-system bias (ISB) between GPS, BDS-2, and Galileo, which is carefully considered in the uncombined multi-GNSS PPP method, is modeled as a white noise process. The differences of the ISB series between BDS-2 and Galileo indicate that the clock datum bias of the satellite clock offset estimation accounts for the variation of the ISB series.

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An assessment of wide-lane ambiguity resolution methods for multi-frequency multi-GNSS precise point positioning

Survey Review ◽

10.1080/00396265.2019.1634339 ◽

2019 ◽

Vol 52 (374) ◽

pp. 442-453 ◽

Cited By ~ 2

Author(s):

V. Duong ◽

K. Harima ◽

S. Choy ◽

D. Laurichesse ◽

C. Rizos

Keyword(s):

Ambiguity Resolution ◽

Precise Point Positioning ◽

Wide Lane ◽

Point Positioning

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Estimating the Fractional Cycle Biases for GPS Triple-Frequency Precise Point Positioning with Ambiguity Resolution Based on IGS Ultra-Rapid Predicted Orbits

Remote Sensing ◽

10.3390/rs13163164 ◽

2021 ◽

Vol 13 (16) ◽

pp. 3164

Author(s):

Lizhong Qu ◽

Pu Zhang ◽

Changfeng Jing ◽

Mingyi Du ◽

Jian Wang ◽

...

Keyword(s):

Ambiguity Resolution ◽

Precise Point Positioning ◽

Triple Frequency ◽

Wide Lane ◽

Single Difference ◽

Point Positioning ◽

L5 Signal ◽

New Generation ◽

Orbit Errors ◽

The Impact

We investigate the estimation of the fractional cycle biases (FCBs) for GPS triple-frequency uncombined precise point positioning (PPP) with ambiguity resolution (AR) based on the IGS ultra-rapid predicted (IGU) orbits. The impact of the IGU orbit errors on the performance of GPS triple-frequency PPP AR is also assessed. The extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL) FCBs are generated with the single difference (SD) between satellites model using the global reference stations based on the IGU orbits. For comparison purposes, the EWL, WL and NL FCBs based on the IGS final precise (IGF) orbits are estimated. Each of the EWL, WL and NL FCBs based on IGF and IGU orbits are converted to the uncombined FCBs to implement the static and kinematic triple-frequency PPP AR. Due to the short wavelengths of NL ambiguities, the IGU orbit errors significantly impact the precision and stability of NL FCBs. An average STD of 0.033 cycles is achieved for the NL FCBs based on IGF orbits, while the value of the NL FCBs based on IGU orbits is 0.133 cycles. In contrast, the EWL and WL FCBs generated based on IGU orbits have comparable precision and stability to those generated based on IGF orbits. The use of IGU orbits results in an increased time-to-first-fix (TTFF) and lower fixing rates compared to the use of IGF orbits. Average TTFFs of 23.3 min (static) and 31.1 min (kinematic) and fixing rates of 98.1% (static) and 97.4% (kinematic) are achieved for the triple-frequency PPP AR based on IGF orbits. The average TTFFs increase to 27.0 min (static) and 37.9 min (kinematic) with fixing rates of 97.0% (static) and 96.3% (kinematic) based on the IGU orbits. The convergence times and positioning accuracy of PPP and PPP AR based on IGU orbits are slightly worse than those based on IGF orbits. Additionally, limited by the number of satellites transmitting three frequency signals, the introduction of the third frequency, L5, has a marginal impact on the performance of PPP and PPP AR. The GPS triple-frequency PPP AR performance is expected to improve with the deployment of new-generation satellites capable of transmitting the L5 signal.

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Performance of Single-Epoch EWL/WL/NL Ambiguity-Fixed Precise Point Positioning with Regional Atmosphere Modelling

Remote Sensing ◽

10.3390/rs13183758 ◽

2021 ◽

Vol 13 (18) ◽

pp. 3758

Author(s):

Wang Gao ◽

Qing Zhao ◽

Xiaolin Meng ◽

Shuguo Pan

Keyword(s):

Precise Point Positioning ◽

Atmospheric Model ◽

Dual Frequency ◽

Positioning Accuracy ◽

Time Performance ◽

Wide Lane ◽

Reference Networks ◽

Atmosphere Correction ◽

Point Positioning ◽

Single Epoch

Precise point positioning (PPP) with ambiguity resolution (AR) can improve positioning accuracy and reliability. The narrow-lane (NL) AR solution can reach centimeter-level accuracy but there is a certain initialization time. In contrast, extra-wide-lane (EWL) or wide-lane (WL) ambiguity can be fixed instantaneously. However, due to the limited correction accuracy of the empirical atmospheric model, the positioning accuracy is only a few decimeters. In order to further improve the real-time performance of PPP while ensuring accuracy, we developed a multi-system multi-frequency uncombined PPP single-epoch EWL/WL/NL AR method with regional atmosphere modelling. In the proposed method, the precise atmosphere, including zenith wet-troposphere delay (ZWD) and the slant ionosphere, is extracted through multi-frequency stepwise AR, which then is both interpolated and broadcast to users. By adding regional atmosphere constraints, users can achieve single-epoch PPP AR with centimeter-level accuracy. To verify the algorithm, four sets of reference networks with different inter-station distances are used for experiments. With atmosphere constraints, the accuracy of the single-epoch WL solution can be improved from the decimeter level to a few centimeters, with an improvement of more than 90%, and the epoch fix rate can also be improved to varying degrees, especially for the dual-frequency case. Due to the enlarged noise of the EWL combination, its accuracy is at the decimeter level, while the accuracy of the WL/NL solution can reach several centimeters. However, reliable NL ambiguity-fixing tightly relies on atmosphere constraints with sufficiently high accuracy. When the modelling of the atmosphere correction is not accurate enough, the NL AR performance is degraded, although this situation can be improved to a certain extent through the multi-GNSS combination. In contrast, in this case, the WL ambiguity can be successfully fixed and can support the precise positioning with an accuracy of several centimeters.

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Discovering Orbit and Clock Quality Based on Analysis of Wide-Lane Ambiguities Derived from PPP Models

10.20944/preprints201805.0157.v1 ◽

2018 ◽

Author(s):

Gang Chen ◽

Sijing Liu ◽

Qile Zhao

Keyword(s):

Real Time ◽

Quality Index ◽

Precise Point Positioning ◽

Line Of Sight ◽

New Approach ◽

Actual Time ◽

Estimation Procedures ◽

Wide Lane ◽

Point Positioning ◽

Analytical Expressions

Orbit and clock products are used in real-time GNSS precise point positioning without knowing their quality. This study develops a new approach to detect orbit and clock errors through comparing geometry-free and geometry-based wide-lane ambiguities in PPP model. The reparameterization and estimation procedures of the geometry-free and geometry-based ambiguities are described in detail. The effects of orbit and clock errors on ambiguities are given in analytical expressions. The numerical similarity and differences of geometry-free and geometry-based wide-lane ambiguities are analyzed using different orbit and clock products. Furthermore, two types of typical errors in orbit and clock are simulated and their effects on wide-lane ambiguities are numerically produced and analyzed. The contribution discloses that the geometry-free and geometry-based wide-lane ambiguities are equivalent in terms of their formal errors. Although they are very close in terms of their estimates when the used orbit and clock for geometry-based ambiguities are precise enough, they are not the same, in particular, in the case that the used orbit and clock, as a combination, contain significant errors. It is discovered that the discrepancies of geometry-free and geometry-based wide-lane ambiguities are coincided with the actual time-variant errors in the used orbit and clock at the line-of-sight direction. This provides a quality index for real-time users to detect the errors in real-time orbit and clock products, which potentially improves the accuracy of positioning.

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GPS and Galileo Triple-Carrier Ionosphere-Free Combinations for Improved Convergence in Precise Point Positioning

Journal of Navigation ◽

10.1017/s0373463320000454 ◽

2020 ◽

pp. 1-19

Author(s):

Francesco Basile ◽

Terry Moore ◽

Chris Hill ◽

Gary McGraw

Keyword(s):

Precision Agriculture ◽

Urban Areas ◽

Precise Point Positioning ◽

Simulated Data ◽

Satellite System ◽

Low Noise ◽

Convergence Time ◽

Triple Frequency ◽

Wide Lane ◽

Point Positioning

In recent years, global navigation satellite system (GNSS) precise point positioning (PPP) has become a standard positioning technique for many applications with typically favourable open sky conditions, e.g. precision agriculture. Unfortunately, the long convergence (and reconvergence) time of PPP often significantly limits its use in difficult and restricted signal environments typically associated with urban areas. The modernisation of GNSS will positively affect and improve the convergence time of the PPP solutions, thanks to the higher number of satellites in view that broadcast multifrequency measurements. The number and geometry of the available satellites is a key factor that impacts on the convergence time in PPP, while triple-frequency observables have been shown to greatly benefit the fixing of the carrier phase integer ambiguities. On the other hand, many studies have shown that triple-frequency combinations do not usefully contribute to a reduction of the convergence time of float PPP solutions. This paper proposes novel GPS and Galileo triple-carrier ionosphere-free combinations that aim to enhance the observability of the narrow-lane ambiguities. Tests based on simulated data have shown that these combinations can reduce the convergence time of the float PPP solution by a factor of up to 2·38 with respect to the two-frequency combinations. This approach becomes effective only after the extra wide-lane and wide-lane ambiguities have been fixed. For this reason, a new fixing method based on low-noise pseudo-range combinations corrected by the smoothed ionosphere correction is presented. By exploiting this algorithm, no more than a few minutes are required to fix the WL ambiguities for Galileo, even in cases of severe multipath environments.

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Analysis of Wide-Lane Ambiguities Derived from Geometry-Free and Geometry-Based PPP Model and Their Implication on Orbit and Clock Quality

10.20944/preprints201805.0157.v2 ◽

2018 ◽

Author(s):

Gang Chen ◽

Sijing Liu ◽

Qile Zhao

Keyword(s):

Real Time ◽

Quality Index ◽

Precise Point Positioning ◽

Line Of Sight ◽

New Approach ◽

Actual Time ◽

Estimation Procedures ◽

Wide Lane ◽

Point Positioning ◽

Analytical Expressions

Orbit and clock products are used in real-time GNSS precise point positioning without knowing their quality. This study develops a new approach to detect orbit and clock errors through comparing geometry-free and geometry-based wide-lane ambiguities in PPP model. The reparameterization and estimation procedures of the geometry-free and geometry-based ambiguities are described in detail. The effects of orbit and clock errors on ambiguities are given in analytical expressions. The numerical similarity and differences of geometry-free and geometry-based wide-lane ambiguities are analyzed using different orbit and clock products. Furthermore, two types of typical errors in orbit and clock are simulated and their effects on wide-lane ambiguities are numerically produced and analyzed. The contribution discloses that the geometry-free and geometry-based wide-lane ambiguities are equivalent in terms of their formal errors. Although they are very close in terms of their estimates when the used orbit and clock for geometry-based ambiguities are precise enough, they are not the same, in particular, in the case that the used orbit and clock, as a combination, contain significant errors. It is discovered that the discrepancies of geometry-free and geometry-based wide-lane ambiguities are coincided with the actual time-variant errors in the used orbit and clock at the line-of-sight direction. This provides a quality index for real-time users to detect the errors in real-time orbit and clock products, which potentially improves the accuracy of positioning.

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Precise Point Positioning Method Based on Wide-lane and Narrow-lane Phase Observations and Between Satellites Single Differencing

Proceedings of the 2016 International Technical Meeting of The Institute of Navigation ◽

10.33012/2016.13494 ◽

2016 ◽

Cited By ~ 2

Author(s):

Grzegorz Nykiel ◽

Mariusz Figurski

Keyword(s):

Precise Point Positioning ◽

Positioning Method ◽

Wide Lane ◽

Point Positioning

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Precise point positioning with decimetre accuracy using wide-lane ambiguities and triple-frequency GNSS data

Journal of Applied Geodesy ◽

10.1515/jag-2019-0068 ◽

2020 ◽

Vol 14 (3) ◽

pp. 263-284

Author(s):

Manoj Deo ◽

Ahmed El-Mowafy

Keyword(s):

Linear Combination ◽

Carrier Phase ◽

Precise Point Positioning ◽

Low Noise ◽

Positioning Accuracy ◽

The Third ◽

Triple Frequency ◽

Wide Lane ◽

Point Positioning ◽

Gnss Data

AbstractThis paper proposes precise point positioning (PPP) methods that offer an accuracy of a few decimetres (dm) with triple frequency GNSS data. Firstly, an enhanced triple frequency linear combination is presented for rapid fixing of the extra wide-lane (EWL) and wide-lane (WL) ambiguities for GPS, Beidou-2 and Galileo. This has improved performance compared to the Melbourne-Wübbena (MW) linear combination, and has 6.7 % lower measurement noise for the GPS L1/L2 signals, 12.7 % for L1/L5 and 0.7 % for L2/L5. Analysis with tested data showed a 5–6 % reduction in time required to fix the {N_{21}} and {N_{51}} ambiguities.Once the EWL/WL ambiguities are fixed with the proposed linear combinations, three methods are presented that aim to provide positioning accuracy of a few dm. In the first approach, the three EWL/WL ambiguities in their respective phase equations are used to derive a low-noise ionosphere-free (IF) linear combination. The second method uses a low noise IF combination with two carrier-phase EWL/WL equations and a single pseudorange measurement. The third method uses a low noise IF combination with a single carrier phase EWL equation and two pseudorange measurements. These proposed methods can provide dm level positioning accuracy if carrier phase measurements with mm precision is tracked by the receiver. When comparing these combinations with a combination proposed in [22], it is found that superior performance is achieved with the third method when carrier phase noise is >5–6 mm for GPS and Beidou-2 and >2–3 mm for Galileo. This model only requires the EWL ambiguity to be fixed which typically takes just one epoch of data. Thus, the user achieves instant decimetre level PPP accuracy.

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Triple-Frequency GPS Precise Point Positioning Ambiguity Resolution Using Dual-Frequency Based IGS Precise Clock Products

International Journal of Aerospace Engineering ◽

10.1155/2017/7854323 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11

Author(s):

Fei Liu ◽

Yang Gao

Keyword(s):

Ambiguity Resolution ◽

Carrier Phase ◽

Precise Point Positioning ◽

Free Carrier ◽

Convergence Time ◽

Dual Frequency ◽

Phase Measurements ◽

Triple Frequency ◽

Wide Lane ◽

Point Positioning

With the availability of the third civil signal in the Global Positioning System, triple-frequency Precise Point Positioning ambiguity resolution methods have drawn increasing attention due to significantly reduced convergence time. However, the corresponding triple-frequency based precise clock products are not widely available and adopted by applications. Currently, most precise products are generated based on ionosphere-free combination of dual-frequency L1/L2 signals, which however are not consistent with the triple-frequency ionosphere-free carrier-phase measurements, resulting in inaccurate positioning and unstable float ambiguities. In this study, a GPS triple-frequency PPP ambiguity resolution method is developed using the widely used dual-frequency based clock products. In this method, the interfrequency clock biases between the triple-frequency and dual-frequency ionosphere-free carrier-phase measurements are first estimated and then applied to triple-frequency ionosphere-free carrier-phase measurements to obtain stable float ambiguities. After this, the wide-lane L2/L5 and wide-lane L1/L2 integer property of ambiguities are recovered by estimating the satellite fractional cycle biases. A test using a sparse network is conducted to verify the effectiveness of the method. The results show that the ambiguity resolution can be achieved in minutes even tens of seconds and the positioning accuracy is in decimeter level.

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