scholarly journals Optimization and selection of Galileo triple-frequency carrier linear combination

2021 ◽  
Vol 54 (1-2) ◽  
pp. 116-128
Author(s):  
Jun Wang ◽  
Xurong Dong ◽  
Wei Fu ◽  
Di Yan ◽  
Zengkai Shi
Keyword(s):  
Linear Combination ◽  
Low Noise ◽  
Integer Ambiguity ◽  
Convergence Time ◽  
Linear Combinations ◽  
Long Wavelength ◽  
Triple Frequency ◽  
Cycle Slip Detection ◽  
Wide Lane ◽  
Speed Up

The triple-frequency linear combination with a low noise, a long wavelength, and a weak ionosphere is beneficial to effectively eliminate or weaken the common errors, advance the reliability of cycle slip detection and repair, and speed up the convergence time of fixed ambiguity. By establishing the Galileo triple-frequency carrier linear combination model, three types of linear combinations are derived: Geometry-free (GF) combinations, minimum noise (MN) combinations, and ionosphere-free (IF) combinations. The geometric relationships of these linear combinations are displayed in the form of image. The results indicate that the angle formed by the IF combinations and the MN combinations is between 75.02° and 86.01°, which also illustrates that it is more difficult to meet the carrier phase combinations with a low noise and a weak ionosphere. Moreover, to guarantee the integer cycle characteristics of ambiguity, the combination coefficient must be an integer. Galileo triple-frequency linear combination is solved utilizing the extremum method. To sum up, the sum of the coefficients of the extra wide lane (EWL) combinations and wide lane (WL) combinations is zero, and the sum of the coefficients of the narrow lane (NL) combinations is one. (0, 1, −1) is the optimal triple-frequency linear combination in Galileo. Three independent linear combinations are selected separately from the EWL, WL, and NL to jointly solve the integer ambiguity. Further, it creates a prerequisite for high-precision and real-time kinematic positioning.

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

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.

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

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.

scholarly journals Effective Cycle Slip Detection and Repair for PPP/INS Integrated Systems

Sensors ◽  
2019 ◽  
Vol 19 (3) ◽  
pp. 502 ◽  
Author(s):  
Sheng Yang ◽  
Leilei Li ◽  
Jingbin Liu ◽  
Qusen Chen ◽  
Xuewen Ding ◽  
...  
Keyword(s):  
Integrated Systems ◽  
Detection Accuracy ◽  
Cycle Slip ◽  
Long Wavelength ◽  
Cycle Slips ◽  
Vehicle Data ◽  
Global Positioning ◽  
Long Time ◽  
Cycle Slip Detection ◽  
Wide Lane

Cycle slip (CS) is a primary error source in Precise Point Positioning/Inertial Navigation System (PPP/INS) integrated systems. In this study, an INS-aided CS detection and repair method is presented. It utilizes high-precision INS information instead of a pseudorange to remove the satellite–receiver geometric range in the wide-lane (WL) and ionospheric-free (IF) phase combinations and creates an INS-aided WL (WL-INS) model and an INS-aided IF (IF-INS) model. Since INS information is superior to pseudorange, the INS-aided models have high detection accuracy. However, the effectiveness of INS-aided models cannot persist for a long time because of INS accumulation error. To overcome the disturbance of INS error, improved INS-aided models are proposed. This idea takes advantage of the long wavelength of WL combination and tries to fix WL CS. Once it succeeds, the INS error can be evaluated and removed. The proposed method was tested using land vehicle data, in which simulated cycle slips and signal interruption were introduced. The results show that this method can accurately detect and repair different cycle slips between the continuous Global Positioning System (GPS) epoch. When it comes to the cycle slip after a GPS interruption, the method can also accelerate PPP re-convergence, as it is not affected by the inertial accumulation error.

Performance of GPS Precise Time and Frequency Transfer with Integer Ambiguity Resolution

2021 ◽  
Author(s):  
Pengfei Zhang ◽  
Rui Tu ◽  
Xiaochun Lu ◽  
Yuping Gao ◽  
Lihong Fan
Keyword(s):  
Real Time ◽  
Ambiguity Resolution ◽  
Integer Ambiguity Resolution ◽  
Integer Ambiguity ◽  
Convergence Time ◽  
Processing Modes ◽  
Wide Lane ◽  
Frequency Transfer ◽  
Fixed Solution ◽  
Precise Time

Abstract The global positioning system (GPS) carrier-phase (CP) technique is a widely used spatial tool for remote precise time and frequency transfer. However, the performance of traditional GPS time and frequency transfer has been limeted because the ambiguity paramter is still the float solution. This study focuses on the performance of GPS precise time and frequency transfer with integer ambiguity resolution and discusses the corresponding mathematical model. Fractional-cycle bias (FCB) products were estimated by using an ionosphere-free combination. The results show that the satellite wide-lane (WL) FCB products are stable, with a standard deviation (STD) of 0.006 cycles. The narrow-lane (NL) FCB products were estimated over 15 min with the STD of 0.020 cycles. More than 98% of the WL and NL residuals are smaller than 0.25 cycles, which helps to fix the ambiguity into integers during the time and frequency transfer. Subsequently, the performances of the time transfers with integer ambiguity resolution at two time links between international laboratories were assessed in real-time and post-processing modes and compared. The results show that fixing the ambiguity into an integer in the real-time mode significantly decreases the convergence time compared with the traditional float approach. The improvement is ~49.5%. The frequency stability of the fixed solution is notably better than that of the float solution. Improvements of 48.15% and 27.9% were determined for the IENG–USN8 and WAB2–USN8 time links, respectively.

scholarly journals Initial Assessment of Galileo Triple-Frequency Ambiguity Resolution between Reference Stations in the Hong Kong Area

2021 ◽  
Vol 13 (4) ◽  
pp. 778
Author(s):  
Yangyang Li ◽  
Mingxing Shen ◽  
Lei Yang ◽  
Chenlong Deng ◽  
Weiming Tang ◽  
...  
Keyword(s):  
Hong Kong ◽  
Ambiguity Resolution ◽  
Satellite System ◽  
Convergence Time ◽  
Initial Assessment ◽  
Triple Frequency ◽  
Ionosphere Disturbance ◽  
Wide Lane ◽  
Reliability And Robustness ◽  
Global Navigation Satellite

The European Global Navigation Satellite System Galileo is gradually deploying its constellation. In order to provide reliable navigation and position services, the effectiveness and reliability of ambiguity resolution between reference stations is necessary in network real-time kinematic (NRTK). The multifrequency signal of Galileo could much enhance the ambiguity resolution (AR) reliability and robustness. In this study, to exploit full advantage of this, the geometry-free (GF) TCAR and ionospheric-free (IF) triple-carrier ambiguity resolution (TCAR) methods were utilized in solving the ambiguity in the Hong Kong area, which is an ionosphere disturbance active area, and compared with each other. The IF TCAR method was then used to combine multi-systems to improve Galileo E1 AR performance, which is named as the combined IF (CIF) TCAR method. Three experiments were carried out in the Hong Kong area and the results showed that the Galileo-only system could fix ambiguities on all satellite pairs correctly and reliably by the IF TCAR method, while the GF TCAR method showed a weaker performance. The wide-lane (WL) convergence time of the IF TCAR method is improved by about 37.6%. The IF TCAR method with respect to the GF TCAR method could improve the WL accuracy by 21.6% and the E1 accuracy by 72.7%, respectively. Compared with GPS-only TCAR or Galileo-only TCAR, the ambiguity accuracy and the convergence time of the CIF TCAR method, which combines GPS and Galileo, could be improved by about 25.7% and 47.1%, respectively.

scholarly journals Precise Point Positioning using Triple-Frequency GPS Measurements

2014 ◽  
Vol 68 (3) ◽  
pp. 480-492 ◽  
Author(s):  
Mohamed Elsobeiey
Keyword(s):  
Precise Point Positioning ◽  
Satellite System ◽  
Global Network ◽  
Convergence Time ◽  
Linear Combinations ◽  
The Third ◽  
Triple Frequency ◽  
Estimated Parameters ◽  
Point Positioning ◽  
L5 Signal

Precise Point Positioning (PPP) performance is improving under the ongoing Global Positioning System (GPS) modernisation program. The availability of the third frequency, L5, enables triple-frequency combinations. However, to utilise the modernised L5 signal along with the existing GPS signals, P1-C5 differential code bias must be determined. In this paper, the global network of Multi-Global Navigation Satellite System Experiment (MGEX) stations was used to estimate P1-C5 satellites differential code biases $(DCB_{P1 - C5}^S )$. Mathematical background for triple-frequency linear combinations was provided along with the resultant noise and ionosphere amplification factors. Nine triple-frequency linear combinations were chosen, based on different criteria, for processing the modernised L5 signal along with the legacy GPS signals. Finally, test results using real GPS data from ten MGEX stations were provided showing the benefits of the availability of the third frequency on PPP solution convergence time and the precision of the estimated parameters. It was shown that triple-frequency combinations could improve the PPP convergence time and the precision of the estimated parameters by about 10%. These results are considered promising for using the modernised GPS signals for precise positioning applications especially when the fully modernised GPS constellation is available.

scholarly journals Beyond three frequencies: An extendable model for single-epoch decimeter-level point positioning by exploiting Galileo and BeiDou-3 signals

2020 ◽  
Author(s):  
Jianghui Geng ◽  
Jiang Guo
Keyword(s):  
High Precision ◽  
Autonomous Driving ◽  
Convergence Time ◽  
Frequency Data ◽  
Positioning Accuracy ◽  
Safety Standards ◽  
Triple Frequency ◽  
Wide Lane ◽  
Point Positioning ◽  
Single Epoch

GNSS is indispensable to self-driving vehicles by delivering decimeter-level or better absolute positioning solutions. Such a high precision normally requires a convergence time spanning seconds to minutes, which is however unrealistic in extremely difficult driving conditions where GNSS signals are obstructed frequently. Such convergences, no matter how short, will greatly risk and discredit autonomous driving in satisfying stringent life-safety standards. In this study, we therefore developed an extendable GNSS precise point positioning (PPP) model to exploit the advanced Galileo/BeiDou-3 more-than-three-frequency signals with the goal of achieving instant or single-epoch 10-30 cm positioning accuracy and over 99% availability for the horizontal components over wide areas. In particular, uncombined Galileo/BeiDou-3 signals on all available frequencies were injected simultaneously into PPP to perform single-epoch wide-lane ambiguity resolution (PPP-WAR) after phase bias calibrations on raw observations. Experimenting on the Galileo five-frequency data from 36 stations in Australia, we found that instant PPP-WAR was accomplished at more than 99.5% of all epochs; we achieved an instant positioning accuracy of 0.10 and 0.11 m (1) for the east and north components, respectively, using Galileo E1/E5a/E5/E5b/E6 signals from less than 10 satellites, while 0.16 and 0.23 m using BeiDou-3 B1C/B1I/B2a/B2b/B3I signals from only 5-6 satellites per epoch observed by 10 stations within China. Moreover, we carried out vehicle-borne experiments collecting multi-frequency Galileo/BeiDou-3 signals in case of overpass and tunnel adversities. With 7 Galileo/BeiDou-3 satellites per epoch on average, instant PPP-WAR reached a mean positioning accuracy of 0.23 and 0.24 m for the horizontal components, which can be further improved to 0.14 and 0.12 m when multi-epoch filtering is preferably enabled. More encouragingly, though this positioning accuracy can also be ensured with triple-frequency data, the data redundancy favored by even more frequencies can reduce the high-precision recovery time from up to 4 s to 2 s in case of total signal blockages. With the rapidly ongoing deployment of Galileo, BeiDou-3 and other GNSS constellations, we can envision an instant global positioning service characterized by around 20-cm horizontal accuracy and over 99% availability for self-driving vehicles.

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

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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