Precise Point Positioning Convergence Research Articles

Improving PPP positioning and troposphere estimates using an azimuth-dependent weighting scheme

Asymmetric troposphere modeling is crucial in Precise Point Positioning (PPP). The functional model of the asymmetric troposphere has been thoroughly studied, while the stochastic model lacks discussion. Currently, there is no suitable stochastic model for asymmetric tropospheric conditions, potentially degrading the positioning accuracy and the reliability of Zenith Total/Wet Delay (ZTD/ZWD) estimates. This paper introduces an Azimuth-Dependent Weighting (ADW) scheme that utilizes information from asymmetric mapping functions to adaptively weight Global Navigation Satellite System (GNSS) observations affected by azimuth-dependent errors. The concept of ADW has been validated using Numerical Weather Prediction data and International GNSS Service data. The results indicate that ADW effectively improves the coordinate repeatability of the PPP solution by approximately 10%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10\\%$$\\end{document} in the horizontal and 20%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$20\\%$$\\end{document} in the vertical direction. Additionally, ADW appears to be capable to improve the ZWD estimates during the PPP convergence period and yields smoother ZWD estimates. Consequently, it is recommended to adopt this new weighting scheme in PPP applications when an asymmetric mapping functions is employed.

LEO enhanced GNSS (LeGNSS) precise point positioning with emphasis on model comparison

With the rapid construction of the low-earth-orbit (LEO) constellation, LEO Enhanced Global Navigation Satellite System (LeGNSS) has become a hotspot in the research of GNSS applications and services, especially for fast convergence of precise point positioning (PPP). In this study, we analyze the impact of LEO satellites on the spatial geometry based on simulated LEO and real GNSS data, and evaluate the LeGNSS PPP performance with ionosphere-free (IF), undifferenced and uncombined (UDUC), and ionosphere-weighted (IW) models. Eight Multi-GNSS Experiment (MGEX) stations are selected for static and kinematic experiments. Results show that Position Dilution of Precision (PDOP) values of LeGNSS are about 0.5–1.2, which are improved by 38 % and 22 % compared with GPS-only and combined GPS, Galileo, and BDS (G\\E\\C) solutions. With LEO satellites, the positioning accuracy in east (E), north (N), and up (U) directions are improved by about 50 %, 30 %, and 50 % for the static mode, and about 35 %, 30 %, and 67 % for the kinematic mode. Moreover, the positioning accuracies of the IF, UDUC, and IW models are comparable. For convergence time, the static and kinematic results with LEO satellites are about 1.1 and 1.3 min, respectively, while those without LEO satellites are longer than 10.0 min. In addition, the model with inter-system bias (ISB) constraints can reduce the convergence time by within 1.0 min.

A static precise single-point positioning method based on carrier phase zero-baseline self-differencing

Satellite navigation positioning has become an indispensable component of everyday life, where precise pinpointing and rapid convergence are crucial in delivering timely and accurate location information. However, due to the damping of integer ambiguities and system residual errors, the rapid convergence of Precise Point Positioning (PPP) implementation is a significant challenge. To address this, this paper proposes a novel Carrier Phase Zero-Baseline Self-Differencing Precise Point Positioning (CZS-PPP) technique and its ionosphere-free fusion model. By employing the proposed CZS-PPP approach in separate scenarios involving BDS-3, GPS, and dual-system settings, we systematically validate the efficacy of the method. The experimental results indicate that the convergence time of the method is less than 4 min in a single-system scenario. Furthermore, in a dual-system scenario, the method can achieve rapid convergence in less than 3 min. The CZS-PPP technique presented demonstrates the elimination of integer ambiguities and the effective suppression of system residuals, in comparison to the conventional method. The proposed approach has demonstrated remarkable performance across different systems, offering a promising new pathway for achieving PPP fast convergence in BDS/GNSS.

Performance Analysis of Multi-GNSS Real-Time PPP-AR Positioning Considering SSR Delay

For real-time (RT) precise point positioning (PPP), the state space representation (SSR) information is often delayed due to possible communication delays and specific broadcast intervals. In this case, the positioning results will diverge and re-converge due to the increase of SSR products extrapolation errors. In addition, RT orbit and clock offset accuracy, as well as their extrapolation errors, will vary in different systems and satellites. We propose a PPP with ambiguity resolution (PPP-AR) method that combines a time-differenced carrier phase (TDCP) model, in which the characteristics of the orbit and clock are considered. Under normal communication, the PPP-AR solution is obtained by fixing satellites with small SSR product errors. When the communication is abnormal, the TDCP model is utilized to extrapolate user coordinates by considering different extrapolation error characteristics of satellites. The experimental results show that GPS and Galileo SSR products have better accuracy than BDS, with signal-in-space user ranger errors (SISREs) of 2.7, 2.2, and 8.6 cm, respectively. Optimizing the PPP stochastic model based on SISREs can effectively reduce the convergence time. Under 5 min SSR delay, SISREs caused by clock and orbit extrapolation for GPS/Galileo/BDS are 3.5, 1.4, and 2.6 cm, respectively. After optimizing the TDCP stochastic model based on extrapolation errors, the horizontal and vertical positioning accuracies can be maintained at 0.7 cm and 5.0 cm. For multi-GNSS, the combination of the TDCP and PPP-AR can overcome the influence of short delay. After optimizing the stochastic model, the GPS/Galileo/BDS positioning accuracy can be maintained at about 2.4 cm under 3 min delay, showing an accuracy improvement rate of 59.3% compared with the traditional method using only PPP. Additionally, the rapid PPP convergence results can be obtained by inheriting previous filter state information when the communication recovers normally.

Improving GNSS PPP Performance in the South China Under Different Weather Conditions by Using the Weather Research and Forecasting (WRF) Model‐Derived Wet Delay Corrections

AbstractAtmospheric wet delay caused by Precipitable Water Vapor (PWV) significantly impacts the performance of many geodetic surveying systems such as Global Navigation Satellite System (GNSS). In this study, we use wet delay corrections forecast by the Weather Research and Forecasting (WRF) model to enhance GNSS Precise Point Positioning (PPP) during two observation periods with two different weather conditions, that is, period 1: March 01 to 14, 2020 (average PWV: 23.5 kg/m2) and period 2: June 02 to 15, 2020 (flooding weather with average PWV: 55.6 kg/m2), over the South China. PWV data from 277 to 263 GNSS stations are assimilated into WRF model to enhance the WRF water vapor forecasting capability for period 1 and period 2, respectively. Wet delay corrections from two different WRF configurations, that is, WRF no data assimilation and WRF with assimilation of GNSS PWV, are used to augment the PPP. Totally, eight WRF‐enhanced PPP schemes are tested. The results show that WRF‐enhanced PPP schemes generally have a better positioning performance in the up component than traditional PPP. After using WRF wet delay corrections, for static mode, the vertical positioning accuracy is improved by 14.6% and 33.7% for period 1 and period 2, respectively. The corresponding convergence time are reduced by 41.8% and 25.0% for period 1 and period 2, respectively. For kinematic mode, the positioning accuracy improvements in the up component reach 13.8% and 19.0% for period 1 and period 2, respectively. The kinematic PPP convergence time is reduced by up to 8.2% for period 1.

Reconstructed estimation method of the multi-frequency GNSS inter-frequency clock bias

In consideration of contributions from both carrier phase and pseudorange observations during computation, this study introduces a reconstructed method for estimating the multi-frequency global navigation satellite system (GNSS) inter-frequency clock biases (IFCB). Diverging from conventional approaches that separately calculate the time-varying and constant parts of IFCBs using carrier phase and pseudorange observations, the reconstructed method directly utilizes their combination to estimate satellite IFCBs. To validate the efficacy of the presented approach, 7 d observations from 87 International GNSS Service (IGS) stations are analyzed, with a specific focus on triple-frequency GPS, multi-frequency BDS-3, and Galileo IFCBs, aiming to scrutinize their distinctive characteristics. Furthermore, the performances of satellite IFCB estimation are investigated in both precise point positioning (PPP) and single-point positioning (SPP) using 35 IGS stations over 3 d. The results demonstrate that IFCBs of GPS BLOCK IIIA satellites exhibit centimeter-level variations, distinguishing them from BLOCK IIF counterparts. The Galileo IFCBs vary from millimeter to centimeter level, while those of BDS-3 reach a centimeter level. These variations significantly impact GPS PPP convergence performances but have minimal effects on Galileo and BDS-3 PPP. SPP performances are slightly enhanced when the time-varying IFCB part are taken into account. Additionally, we note disparities in the constant parts of satellite IFCBs computed with differential code bias (DCB) products, reconstructed, and pseudorange observation-based methods, particularly for BDS-3 C2I/C6I-C1P/C5P and C2I/C6I-C1P/C6I combinations. The differences of IFCB estimated with different strategies, SPP and PPP performances show that the reconstructed method is better than others, and the IFCB accuracy decreases when computed with satellite DCB products.

The convergence mechanism of Low Earth Orbit enhanced GNSS (LeGNSS) Precise Point Positioning (PPP)

ABSTRACT The recruitment of the Low Earth Orbit (LEO) constellation is recognized as an effective way to augment Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) in the near future. Its potential to accelerate PPP convergence has been proved with simulated data. However, the mechanism of how the geometric change of LEO accelerates the convergence of GNSS PPP has not been studied from a theoretical perspective, which hampers the understanding and exploitation of the enhancement of LEO. In this article, the convergence mechanism of LEO enhanced GNSS PPP is investigated in terms of theoretical analysis and simulated verification. To show the characteristics of the ambiguities during convergence, eigenvalue decomposition is used to divide the ambiguities into orthogonal components, named geometric-related component, clock-error-related component, and independent component. The results show that the precision of geometric-related components of ambiguities, which correlates with position parameters, is low at a single epoch, while the precision can be greatly improved with the fast geometric change of LEO. On the other hand, the precision of clock-error-related components of ambiguities, which correlates with clock errors, cannot be improved by fast geometric change of LEO constellation due to its irrelevance to geometry, which causes the precision of each ambiguity to be low. Further investigations show that single-differenced ambiguities could overcome this drawback and are beneficial to ambiguity resolution.

Advancing Precise Orbit Determination and Precise Point Positioning of BDS-3 Satellites from B1IB3I to B1CB2a: Comparison and Analysis

The third generation of the Chinese BeiDou Navigation Satellite System (BDS-3) broadcasts new signals, i.e., B1C, B2a, and B2b, along with the legacy signals of BDS-2 B1I and B3I. The novel signals are demonstrated to show adequate upgraded performance, due to the restrictions on the ground tracking network for the BDS-3 satellites in new frequency bands, and in order to maintain the consistency of the hybrid BDS-2 and BDS-3 orbit/clock products using the common B1IB3I data, the use of B1CB2a observations is not sufficient for both precise orbit determination (POD) and precise point positioning (PPP) applications. In this study, one-year data of 2022 from the International GNSS Service (IGS) and the International GNSS Monitoring and Assessment System (iGMAS) are used in the precise orbit and clock determination for BDS-3 satellites based on the two sets of observations (i.e., B1IB3I and B1CB2a), and the orbit and clock accuracy along with the PPP ambiguity resolution (AR) performance are investigated. In general, the validations demonstrate that clear improvement can be achieved for the B1CB2a-based solution for both POD and PPP. In comparison to the B1IB3I, using BDS-3 B1CB2a observations can help to improve orbit consistency by around 25% as indicated by orbit boundary discontinuities (OBDs), and this use can further reduce the bias and enhance the orbit accuracy as revealed by satellite laser ranging (SLR) residuals. Similar improvement was also identified in the satellite clock performance. The B1CB2a-based solution obtains decreased Allan deviation (ADEV) values in comparison with the B1IB3I-based solution by 6~12%. Regarding the PPP-AR performance, the advantage of B1CB2a observations is evidently reflected through the estimates of wide-lane/narrow-lane fractional cycle bias (FCB), convergence time, and positioning accuracy, in which a significant reduction over 10 min is found in the PPP convergence time.

On the role of lidar measurements in speeding up precise point positioning convergence

Global navigation satellite system (GNSS) and light detection and ranging (lidar) are well known to be complementary for vehicle positioning in urban canyons, where GNSS observations are prone to signal blockage and multi-path. As one of the most common carrier-phase-based precise positioning techniques, precise point positioning (PPP) enables single-receiver positioning as it utilizes state-space representation corrections for satellite orbits and clocks and does not require a nearby reference station. Yet PPP suffers from a long positioning convergence time. In this contribution, we propose to reduce the PPP convergence using an observation-level integration of GNSS and lidar. Lidar measurements, in the form of 3D keypoints, are generated by registering online scans to a pre-built high-definition map through deep learning and are then combined with dual-frequency PPP (DF-PPP) observations in an extended Kalman filter implementing the constant-velocity model that captures the vehicle dynamics. We realize real-time PPP (RT-PPP) in this integration using the IGS real-time service products for vehicle positioning. Comprehensive analyses are provided to evaluate different combinations of measurements and PPP corrections in both static and simulated kinematic modes using data captured by multiple receivers. Experimental results show that the integration achieves cm-level accuracy and instantaneous convergence by using redundant measurements. Accordingly, for classical PPP accuracy of 10 cm and convergence within minutes, respectively, lidar input is only required once every 10 s.

TECX-TCN: Prediction of ionospheric total electron content at different latitudes in China based on XGBoost algorithm and temporal convolution network

The correction of ionospheric delay error through the estimation of ionospheric total electron content (TEC) parameters is very important for the accuracy and rapid convergence of precise point positioning (PPP), especially for single frequency PPP position and double frequency undifferenced and uncombined PPP models. This paper studies the prediction method of ionospheric TEC by analyzing various influencing factors. Firstly, considering the influence of latitude, the TEC values of different observation stations in China at middle and low latitudes are used for research. Secondly, due to the influence of solar storms, the years with and without solar storms are selected for comparative study. At the same time, the moving average value of TEC and the lag value of each solar and geomagnetic index are also added. Because the influence of each feature on ionospheric TEC is not clear, the importance score of each feature is obtained according to the EXtreme Gradient Boosting (XGBoost) algorithm to establish a reasonable feature combination. Then, the temporal convolution network (TCN) is used to train according to data of the collected solar cycle and predict data for the next year. Through experiments, the prediction model with feature selection can obtain higher prediction accuracy, the error reaches ∼2TECU at middle latitude region and ∼3 TECU at low latitude region. Finally, compared with other algorithms, our ionospheric TEC prediction algorithm based on XGBoost and TCN (TECX-TCN) significantly has better performance. When the solar activity is low, its RMSE can reach ∼2.5TECU, the correlation coefficient can reach ∼0.9, and even in the low latitude area with high solar activity, its RMSE can reach ∼5TECU, the correlation coefficient can reach ∼0.85.

The Ionospheric Effects of the 2022 Hunga Tonga Volcano Eruption and the Associated Impacts on GPS Precise Point Positioning Across the Australian Region

AbstractThe Hunga Tonga Volcano eruption launched a myriad of atmospheric waves that have been observed to travel around the world several times. These waves generated traveling ionospheric disturbances (TIDs) in the ionosphere, which are known to adversely impact radio applications such as Global Navigation Satellite Systems (GNSS). One such GNSS application is Precise Point Positioning (PPP), which can achieve cm‐level accuracy using a single receiver, following a typical convergence time of 30 min to 1 hr. A network of ionosondes located throughout the Australian region were used in combination with GNSS receivers to explore the impacts of the Hunga Tonga Volcano eruption on the ionosphere and what subsequent impacts they had on PPP. It is shown that PPP accuracy was not significantly impacted by the arrival of the TIDs and Spread‐F, provided that PPP convergence had already been achieved. However, when the PPP algorithm was initiated from a cold start either shortly before or after the TID arrivals, the convergence times were significantly longer. GNSS stations in northeastern Australia experienced increases in convergence time of more than 5 hr. Further analysis reveals increased convergence times to be caused by a super equatorial plasma bubble (EPB), the largest observed over Australia to date. The EPB structure was found to be ∼42 TECU deep and ∼300 km across, traveling eastwards at 30 m/s. The Hunga Tonga Volcano eruption serves as an excellent example of how ionospheric variability can impact real‐world applications and the challenges associated with modeling the ionosphere to support GNSS.

GNSS rapid precise point positioning enhanced by low Earth orbit satellites

The Low Earth Orbit (LEO) satellites can be used to effectively speed up Precise Point Positioning (PPP) convergence. In this study, 180 LEO satellites with a global distribution are simulated to evaluate their contribution to the PPP convergence. LEO satellites can give more redundant observations and improve satellite geometric distributions, particularly for a single Global Navigation Satellite System (GNSS). The convergence speed of the PPP float solution using the Global Positioning System (GPS, G) or BeiDou Navigation Satellite System (BDS, C) single system as well as the G/C/Galileo navigation satellite system (Galileo, E)/GLObal NAvigation Satellite System (GLONASS, R) combined system with LEO satellites added is improved by 90.0%, 91.0%, and 90.7%, respectively, with respect to the system without LEO satellites added. We introduced LEO observations to assist GNSS in PPP-AR (Ambiguity Resolution) and PPP-RTK (Real Time Kinematic). The success fix rate of a single system is significantly improved, and the Time-To-First-Fix (TTFF) of G and G/C/E is reduced by 86.4% and 82.8%, respectively, for the PPP-AR solution. We analyzed the positioning performance of LEO satellite assisted G/C/E PPP-RTK in the reference networks of different scales, namely different atmospheric delay interpolation accuracies. The success fix rate of the G/C/E combined system is improved from 86.8 to 94.9%, and the TTFF is reduced by 36.8%, with the addition of LEO satellites in the 57 km reference network. In the 110 km reference network, the success fix rate of the G/C/E combined system is improved from 64.0 to 88.6%, and the TTFF is reduced by 32.1%. GNSS PPP-RTK with adding the LEO satellites in the reference networks of different scales shows obvious improvement because the atmospheric correlation decreases with increasing distance from the reference networks.

A Tropospheric Zenith Delay Forecasting Model Based on a Long Short-Term Memory Neural Network and Its Impact on Precise Point Positioning

Global navigation satellite system (GNSS) signals are affected by refraction when traveling through the troposphere, which result in tropospheric delay. Generally, the tropospheric delay is estimated as an unknown parameter in GNSS data processing. With the increasing demand for GNSS real-time applications, high-precision tropospheric delay augmentation information is vital to speed up the convergence of PPP. In this research, we estimate the zenith tropospheric delay (ZTD) from 2018 to 2019 by static precise point positioning (PPP) using the fixed position mode; GNSS observations were obtained from the National Geomatics Center of China (NGCC). Firstly, ZTD outliers were detected, and data gaps were interpolated using the K-nearest neighbor algorithm (KNN). Secondly, The ZTD differences between the KNN and periodic model were employed as input datasets to train the long short-term memory (LSTM) neural network. Finally, LSTM forecasted ZTD differences and the ZTD periodic signals were combined to recover the final forecasted ZTD results. In addition, the forecasted ZTD results were applied in static PPP as a prior constraint to reduce PPP convergence time. Numerical results show that the average root-mean-square error (RMSE) of predicting ZTD is about 1 cm. The convergence time of the PPP which was corrected by the LSTM-ZTD predictions is reduced by 13.9, 22.6, and 30.7% in the summer, autumn, and winter, respectively, over GPT2-ZTD corrected PPP and unconstrained conventional PPP for different seasons.

Satellite Clock Batch Estimation Accuracy Analysis and Its Impacts on PPP

The ultra-rapid satellite clock product based on the satellite clock batch estimation is commonly used for high-precision and reliable precise point positioning (PPP) services. In order to clarify the effect of different ranging errors on the satellite clock batch estimation accuracy, the source of the satellite clock bias induced by the batch observation model is classified into the initial clock bias (ICB) and time-dependent bias (TDB). In addition to the effect of the ICB and TDB, the analytic relationship between the observation redundancy and the satellite clock batch estimation accuracy are derived and verified. The suitable number of stations is suggested to be 40 for the satellite clock batch estimation to achieve the counterbalance between the efficiency and saturable accuracy. For the PPP based on the batch-estimated satellite clock, the impacts of the ICB and TDB on PPP are clarified. The satellite clock batch estimation and PPP experiments are carried out to investigate the impacts of the ICB and TDB on the satellite clock batch estimation accuracy and the PPP performance. The ICB causes a significant bias for the batch-estimated satellite clock. The TDB is impacted by the assimilation ability of the batch-estimated satellite clock to the satellite orbit error. The convergence time and the positioning accuracy after the convergence of PPP are primarily affected by the ICB and TDB, respectively.

Neural network-based ionospheric modeling and predicting—To enhance high accuracy GNSS positioning and navigation

As a highly variable space plasma, the sophisticated monitoring and expression of the ionosphere are critically important for the performance of Global Navigation Satellite System (GNSS). To satisfy the requirement of more precise positioning and navigation, it is necessary to model and predict the ionosphere in a more accurate way. In this paper, the potential advantages of neural networks in ionosphere modeling and predicting are explored. Radial Basis Function Neural Network (RBF-NN) is used for modeling and the Long- and Short-Term Memory Neural Network (LSTM-NN) is used for predicting. Results validate that performance of the RBF-NN is superior to the traditional spherical harmonic and polynomial model. The average root mean square error of one-day modeling residuals by RBF-NN is 1.2951 Total Electron Content Unit (TECU, 1 TECU = 1016 electron/m2), which is reduced by 0.4172 and 0.2710 TECU respectively, compared with the traditional spherical harmonic and polynomial model. The predicting results show that the LSTM-NN has better short-time performance, compared with the finite Fourier series model and the autoregressive integrated moving average model. Finally, one-day predicted products are used as priori constraints for single-frequency static and dynamic precise point positioning (PPP). Positioning results show that constraint effect of the predicted products is equivalent to that of the International GNSS Services (IGS) final products. Compared with the results without ionospheric constraint, the PPP convergence time is obviously reduced, and the positioning performance in the horizontal direction is significantly improved.

Regional Ionospheric Corrections for High Accuracy GNSS Positioning

Centimetre-level accurate ionospheric corrections are required for a high accuracy and rapid convergence of Precise Point Positioning (PPP) GNSS positioning solutions. This research aims to evaluate the accuracy of a local/regional ionospheric delay model using a linear interpolation method across Australia. The accuracy of the ionospheric corrections is assessed as a function of both different latitudinal regions and the number and spatial density of GNSS Continuously Operating Reference Stations (CORSs). Our research shows that, for a local region of 5° latitude ×10° longitude in mid-latitude regions of Australia (~30° to 40°S) with approximately 15 CORS stations, ionospheric corrections with an accuracy of 5 cm can be obtained. In Victoria and New South Wales, where dense CORS networks exist (nominal spacing of ~100 km), the average ionospheric corrections accuracy can reach 2 cm. For sparse networks (nominal spacing of >200 km) at lower latitudes, the average accuracy of the ionospheric corrections is within the range of 8 to 15 cm; significant variations in the ionospheric errors of some specific satellite observations during certain periods were also found. In some regions such as Central Australia, where there are a limited number of CORSs, this model was impossible to use. On average, centimetre-level accurate ionospheric corrections can be achieved if there are sufficiently dense (i.e., nominal spacing of approximately 200 km) GNSS CORS networks in the region of interest. Based on the current availability of GNSS stations across Australia, we propose a set of 15 regions of different ionospheric delay accuracies with extents of 5° latitude ×10° longitude covering continental Australia.

Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution

The performance of precise point positioning (PPP) has been significantly improved thanks to the continuous improvements in satellite orbit, clock, and ambiguity resolution (AR) technologies, but the convergence speed remains a limiting factor in real-time PPP applications. To improve the PPP precision and convergence time, tropospheric delays from a regional network can be modeled to provide precise correction for users. We focus on the precise modeling of zenith wet delay (ZWD) over a wide area with large altitude variations for improving PPP-AR. By exploiting the water vapor exponential vertical decrease, we develop a modified optimal fitting coefficients (MOFC) model based on the traditional optimal fitting coefficients (OFC) model. The proposed MOFC model provides a precision better than 1.5 cm under sparse inter-station distances over the Europe region, with a significant improvement of 70% for high-altitude stations compared to the OFC model. The MOFC model with different densities of reference stations is further evaluated in GPS and Galileo kinematic PPP-AR solutions. Compared to the PPP-AR solutions without tropospheric delay augmentation, the positioning precision of those with 100-km inter-station spacing MOFC and OFC is improved by 25.7% and 17.8%, respectively, and the corresponding time to first fix (TTFF) is improved by 36.9% and 33.0% in the high-altitude areas. On the other hand, the OFC model only slightly improves the TTFF and positioning accuracy when using the 200 km inter-station spacing modeling and even degrades the positioning for high-altitude stations, whereas using the MOFC model, the PPP-AR solutions always improve. Moreover, the positioning precision improvement of MOFC compared with OFC is about 22.1%, 21.7%, and 25.7% for the Galileo-only, GPS-only, and GPS + Galileo PPP-AR solutions, respectively.

BDS near real-time maneuver detection based on triple-differenced phase observations

The BeiDou Navigation Satellite System (BDS) geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites need frequent orbital maneuvers to keep them in position due to various perturbations. However, common users cannot obtain the exact maneuver times, which may yield a decline in the real-time service performance of the BDS. To solve this problem, we presented a near real-time maneuver detection method for BDS based on triple-differenced phase observations, which can automatically detect the exact start and end times of satellite orbital maneuvers. In this method, the carrier-phase triple-differences residuals are firstly computed using the precise station coordinates, broadcast ephemeris and dual-frequency observations of ground tracking stations. Afterward, the residuals are be modeled using linear regression to identify maneuver times. The observations from the BDS Experimental Tracking Stations (BETS) and the reference time announced by the Beijing Satellite Navigation Center (BSNC) from Day of year (DOY) 100 to DOY 300, 2017 are used to evaluate the performance of the proposed method. The detected maneuver periods are consistent with the announced ones, except the detected start times lag 42 min and end times advance 23 min on average. Then, the detected times are further validated by dynamic precise orbit determination (POD) after the maneuver. The phase residuals and 3D RMS of the orbit differences of maneuvered satellites proved that the accuracy of detected maneuver times is better than 5-minute. At last, the kinematic precise point positioning (PPP) validation is implemented to evaluate the effect of more accurate GEO and IGSO satellites to BDS positioning. Results show that both the convergence and accuracy of BDS PPP are improved by adding one satellite that has ended maneuvering.

Performance Analysis of Zero-Difference GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 Point Positioning Using CNES Uncombined Bias Products

The modernization of Global Navigation Satellite System (GNSS) including the transmission of signals on multiple frequencies has greatly promoted the development of the popular PPP (Precise Point Positioning) technique. A key issue of multi-frequency PPP is the handling of the observable-specific signal biases in order to allow for carrier-phase ambiguity resolution (AR). As a result, PPP modeling at a user side in the multi-frequency case varies depending on the definition of the applied phase bias products. In this study, we investigate the positioning performance of GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 undifferenced ionosphere-float model in the conventional PPP mode and the single-epoch mode using the uncombined code and phase bias products generated at the French CNES (Centre National D’Etudes Spatiales). A series of widelane ambiguities are configured in our multi-frequency PPP functional model instead of forming the classical Melbourne–Wübbena (MW) combination. The best integer equivariant (BIE) estimator is used for the ambiguity resolution in a conventional cascading scheme according to the wavelength of the combined ambiguities for each constellation. Real data collected at IGS stations with a 30-s sampling interval is applied to evaluate the above models. For the conventional kinematic PPP configuration, a significant accuracy improvement of 63% on the east component of the fixed solution is obtained with respect to the ambiguity-float solution. The PPP convergence is accelerated by 17% after the AR. Regarding the single-epoch positioning, an accuracy of 32 and 31 cm for north and east components can be achieved, respectively, (68th percentile) with the instantaneous widelane-ambiguity resolution, which is improved by 13% and 16% compared to multi-frequency code-based or float solution.

On Enhanced PPP with Single Difference Between-Satellite Ionospheric Constraints

<h3>Abstract</h3> Applications of precise point positioning (PPP) are limited by PPP’s long convergence time. One effective way to shorten the convergence time is to apply ionospheric constraints because of the external ionospheric information. The conventional way to do this is to apply high precision but biased ionospheric corrections. The limitations of the method are that all ionospheric constraints must be derived from the same set of reference stations to have the same data. An approach based on single differences between satellite ionospheric constraints (SDBS-IONO) is developed to address the data issue due to having no common satellite visibility. The proposed method is more flexible and scalable in terms of adding ionospheric constraints. Based on a network of about 130 stations, we validated the proposed SDBS-ION method and compared it to the conventional method. Our results confirm that the ionospheric constraints enhance the PPP convergence time significantly depending on the accuracy of ionospheric constraints. Finally, we discuss crucial factors regarding how long and accurate the effectiveness of ionospheric constraints are in reducing PPP convergence time.