GLONASS real-time wide-lane ambiguity resolution with an enhanced geometry-based model for medium-range baselines

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.

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Algorithms for Sparse Network-based RTK GPS Positioning and Performance Assessment

Journal of Navigation ◽

10.1017/s0373463313000015 ◽

2013 ◽

Vol 66 (3) ◽

pp. 335-348 ◽

Cited By ~ 7

Author(s):

Weiming Tang ◽

Xiaolin Meng ◽

Chuang Shi ◽

Jingnan Liu

Keyword(s):

Real Time ◽

Long Range ◽

Ambiguity Resolution ◽

Reference Station ◽

Baseline Length ◽

Sparse Network ◽

Network Rtk ◽

Real Time Kinematic ◽

Wide Lane ◽

Time Required

The average inter-station distances in most established network Real Time Kinematic (RTK) systems are constrained to around 50 km. A sparse network RTK system with an average inter-station distance of up to 300 km would have many appealing advantages over a conventional one, including a significant reduction in the development and maintenance costs. The first part of this paper introduces the key approaches for sparse network RTK positioning technology. These include long-range reference baseline ambiguity resolution and real-time kinematic ambiguity resolution for the rover receivers. The proposed method for long-range kinematic ambiguity resolution can overcome the network weaknesses through three procedures: application of the interpolated corrections from the sparse network only to wide-lane combination; searching the ambiguities of wide-lane combination; and searching L1 ambiguities with wide-lane combination and ionosphere-free observables. To test these techniques, a network including ten reference stations was created from the Ordnance Survey's Network (OS NetTM) that covers the whole territory of the United Kingdom (UK). The average baseline length of this sparse network is about 300 km. To assess the positioning performance, nine rover stations situated inside and outside the network were also selected from the OS Net™. Finally, the accuracy of interpolated corrections, the positioning accuracy and the initialization time required for precise positioning were estimated and analysed. From the observed performance of each rover receiver, and the accuracy of interpolated network corrections, it can be concluded that it is feasible to use a sparse reference station network with an average inter-station distance up to 300 km for achieving similar performance to traditional network RTK positioning. The proposed approach can provide more cost-efficient use of network RTK (NRTK) positioning for engineering and environmental applications that are currently being delivered by traditional network RTK positioning technology.

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Algorithm for Real-Time Cycle Slip Detection and Repair for Low Elevation GPS Undifferenced Data in Different Environments

Remote Sensing ◽

10.3390/rs13112078 ◽

2021 ◽

Vol 13 (11) ◽

pp. 2078

Author(s):

Ning Liu ◽

Qin Zhang ◽

Shuangcheng Zhang ◽

Xiaoli Wu

Keyword(s):

Real Time ◽

High Voltage ◽

Second Order ◽

Cycle Slip ◽

Order Difference ◽

Cycle Slips ◽

Cycle Slip Detection ◽

Wide Lane ◽

Time Cycle ◽

Slip Detection

Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, cycle slip detection and repair in low elevation GPS observation data are more complicated than those in normal environments. For low elevation GPS undifferenced carrier phase data in different environments, a combined cycle slip detection algorithm is proposed. This method uses the first-order Gauss–Markov stochastic process to model the pseudorange multipath in the wide-lane phase minus narrow-lane pseudorange observation equation, and establishes the state equation of the wide-lane ambiguity with the pseudorange multipath as a parameter, and it uses the Kalman filter for real-time estimation and detects cycle slips based on statistical hypothesis testing with a predicted residual sequence. Meanwhile, considering there are certain correlations among low elevation, observation epoch interval, and ionospheric delay error, a second-order difference geometry-free combination cycle slip test is constructed that takes into account the elevation. By combining the two methods, real-time cycle slip detection for GPS low elevation satellite undifferenced data is achieved. A cycle slip repair method based on spatial search and objective function minimization criterion is further proposed to determine the correct solution of the cycle slips after they are detected. The whole algorithm is experimentally verified using the static and kinematic measured data of low elevation satellites under four different environments: normal condition, high-voltage transmission lines, dynamic condition in the sea, and ionospheric disturbances. The experimental results show that the algorithm can detect and repair cycle slips accurately for low elevation GPS undifferenced data, the difference between the float solution and the true value for the cycle slip does not exceed 0.5 cycle, and the differences obey the normal distribution overall. At the same time, the wide-lane ambiguity and second-order difference GF combination sequence calculated by the algorithm is smoother, which give further evidence that the algorithm for cycle slip detection and repair is feasible and effective, and has the advantage of being immune to the special observation environments.

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High-Accuracy Real-Time Kinematic Positioning with Multiple Rover Receivers Sharing Common Clock

Remote Sensing ◽

10.3390/rs13040823 ◽

2021 ◽

Vol 13 (4) ◽

pp. 823

Author(s):

Lin Zhao ◽

Jiachang Jiang ◽

Liang Li ◽

Chun Jia ◽

Jianhua Cheng

Keyword(s):

Real Time ◽

Ambiguity Resolution ◽

Temporal Stability ◽

Estimation Method ◽

Satellite System ◽

Integer Ambiguity ◽

Dual Frequency ◽

Kinematic Positioning ◽

Real Time Kinematic ◽

Satellite Visibility

Since the traditional real-time kinematic positioning method is limited by the reduced satellite visibility from the deprived navigational environments, we, therefore, propose an improved RTK method with multiple rover receivers sharing a common clock. The proposed method can enhance observational redundancy by blending the observations from each rover receiver together so that the model strength will be improved. Integer ambiguity resolution of the proposed method is challenged in the presence of several inter-receiver biases (IRB). The IRB including inter-receiver code bias (IRCB) and inter-receiver phase bias (IRPB) is calibrated by the pre-estimation method because of their temporal stability. Multiple BeiDou Navigation Satellite System (BDS) dual-frequency datasets are collected to test the proposed method. The experimental results have shown that the IRCB and IRPB under the common clock mode are sufficiently stable for the ambiguity resolution. Compared with the traditional method, the ambiguity resolution success rate and positioning accuracy of the proposed method can be improved by 19.5% and 46.4% in the restricted satellite visibility environments.

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Global ozone forecasting based on ERS-2 GOME observations

Atmospheric Chemistry and Physics Discussions ◽

10.5194/acpd-2-921-2002 ◽

2002 ◽

Vol 2 (4) ◽

pp. 921-942 ◽

Cited By ~ 3

Author(s):

H. J. Eskes ◽

P. F. J. van Velthoven, ◽

H. M. Kelder

Keyword(s):

Real Time ◽

Present Model ◽

Forecast Error ◽

Model Driven ◽

Medium Range ◽

Forecasting System ◽

Ozone Transport ◽

Model Setup ◽

The Tropics ◽

Total Column

Abstract. The availability of near-real time ozone observations from satellite instruments has recently initiated the development of ozone data assimilation systems. In this paper we present the results of an ozone assimilation and forecasting system, in use since Autumn 2000. The forecasts are produced by an ozone transport and chemistry model, driven by the operational medium range forecasts of ECMWF. The forecasts are initialised with realistic ozone distributions, obtained by the assimilation of near-real time total column observations of the GOME spectrometer on ERS-2. The forecast error diagnostics demonstrate that the system produces meaningful total ozone forecasts for up to 6 days in the extratropics. In the tropics meaningful forecasts of the small anomalies are restricted to shorter periods of about two days with the present model setup. It is demonstrated that important events, such as the breakup of the South Pole ozone hole and mini-hole events above Europe can be successfully predicted 4--5 days in advance.

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Analysis of Characteristics of BDS Observable Combinations for Wide-Lane Integer Ambiguity Resolution

Lecture Notes in Electrical Engineering - China Satellite Navigation Conference (CSNC) 2014 Proceedings: Volume I ◽

10.1007/978-3-642-54737-9_36 ◽

2014 ◽

pp. 411-425 ◽

Cited By ~ 2

Author(s):

Guangxing Wang ◽

Kees de Jong ◽

Xiaotao Li ◽

Qile Zhao ◽

Jing Guo

Keyword(s):

Ambiguity Resolution ◽

Integer Ambiguity Resolution ◽

Integer Ambiguity ◽

Wide Lane

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Real-Time Kinematic Precise Orbit Determination for LEO Satellites Using Zero-Differenced Ambiguity Resolution

Remote Sensing ◽

10.3390/rs11232815 ◽

2019 ◽

Vol 11 (23) ◽

pp. 2815 ◽

Cited By ~ 1

Author(s):

Xingxing Li ◽

Jiaqi Wu ◽

Keke Zhang ◽

Xin Li ◽

Yun Xiong ◽

...

Keyword(s):

Real Time ◽

Ambiguity Resolution ◽

Orbit Determination ◽

Precise Orbit Determination ◽

The Real ◽

Precise Orbit ◽

Ambiguity Fixing ◽

Real Time Kinematic ◽

Leo Satellites ◽

Fixed Solution

The rapid growing number of earth observation missions and commercial low-earth-orbit (LEO) constellation plans have provided a strong motivation to get accurate LEO satellite position and velocity information in real time. This paper is devoted to improve the real-time kinematic LEO orbits through fixing the zero-differenced (ZD) ambiguities of onboard Global Navigation Satellite System (GNSS) phase observations. In the proposed method, the real-time uncalibrated phase delays (UPDs) are estimated epoch-by-epoch via a global-distributed network to support the ZD ambiguity resolution (AR) for LEO satellites. By separating the UPDs, the ambiguities of onboard ZD GPS phase measurements recover their integer nature. Then, wide-lane (WL) and narrow-lane (NL) AR are performed epoch-by-epoch and the real-time ambiguity–fixed orbits are thus obtained. To validate the proposed method, a real-time kinematic precise orbit determination (POD), for both Sentinel-3A and Swarm-A satellites, was carried out with ambiguity–fixed and ambiguity–float solutions, respectively. The ambiguity fixing results indicate that, for both Sentinel-3A and Swarm-A, over 90% ZD ambiguities could be properly fixed with the time to first fix (TTFF) around 25–30 min. For the assessment of LEO orbits, the differences with post-processed reduced dynamic orbits and satellite laser ranging (SLR) residuals are investigated. Compared with the ambiguity–float solution, the 3D orbit difference root mean square (RMS) values reduce from 7.15 to 5.23 cm for Sentinel-3A, and from 5.29 to 4.01 cm for Swarm-A with the help of ZD AR. The SLR residuals also show notable improvements for an ambiguity–fixed solution; the standard deviation values of Sentinel-3A and Swarm-A are 4.01 and 2.78 cm, with improvements of over 20% compared with the ambiguity–float solution. In addition, the phase residuals of ambiguity–fixed solution are 0.5–1.0 mm larger than those of the ambiguity–float solution; the possible reason is that the ambiguity fixing separate integer ambiguities from unmodeled errors used to be absorbed in float ambiguities.

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GPS/BDS-2/Galileo Precise Point Positioning Ambiguity Resolution Based on the Uncombined Model

Remote Sensing ◽

10.3390/rs12111853 ◽

2020 ◽

Vol 12 (11) ◽

pp. 1853

Author(s):

Jin Wang ◽

Guanwen Huang ◽

Qin Zhang ◽

Yang Gao ◽

Yuting Gao ◽

...

Keyword(s):

Ambiguity Resolution ◽

Precise Point Positioning ◽

Three Dimensional ◽

Convergence Time ◽

Wide Lane ◽

3D Positioning ◽

System Bias ◽

Point Positioning ◽

Raw Observations ◽

Gps Observations

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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Recent Developments in Precise Point Positioning

GEOMATICA ◽

10.5623/cig2012-023 ◽

2012 ◽

Vol 66 (2) ◽

pp. 103-111 ◽

Cited By ~ 13

Author(s):

S. Bisnath ◽

P. Collins

Keyword(s):

Real Time ◽

Ambiguity Resolution ◽

Carrier Phase ◽

Precise Point Positioning ◽

Solution Convergence ◽

Similar Information ◽

Recent Developments ◽

Significant Step ◽

Point Positioning ◽

New Processing

In standard Precise Point Positioning (PPP), the carrier phase ambiguities are estimated as real-valued constants, so that the carrier-phases can provide similar information as the pseudoranges. As a consequence, it can take tens of minutes to several hours for the ambiguities to converge to suitably precise values. Recently, new processing methods have been identified that permit the ambiguities to be estimated more appropriately as integer-valued constants, as they are in relative Real-Time Kinematic (RTK) positioning. Under these conditions, standard ambiguity resolution techniques can be applied to strengthen the PPP solution. The result can be a greatly reduced solution convergence and re-convergence period, representing a significant step toward improving the performance of PPP with respect to that of RTK processing. This paper describes the underlying principles of the method, why the enhancements work, and presents some results.

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