Abstract High-precision Global Navigation Satellite Systems (GNSS) orbits are critical for real-time clock estimation and precise positioning service; however, the prediction error grows gradually with the increasing prediction session. In this study, we present a new efficient precise orbit determination (POD) strategy referred to as the epoch-parallel processing to reduce the orbit update latency, in which a 24-h processing job is split into several sub-sessions that are processed in parallel and then stacked to solve and recover parameters subsequently. With a delicate handling of parameters crossing different sub-sessions, such as ambiguities, the method is rigorously equivalent to the one-session batch solution, but is much more efficient, halving the time-consuming roughly. Together with paralleling other procedures such as orbit integration and using open multi-processing (openMP), the multi-GNSS POD of 120 satellites using 90 stations can be fulfilled within 30 min. The lower update latency enables users to access orbits closer to the estimation part, that is, 30–60-min prediction with a 30-min update latency, which significantly improves the orbit quality. Compared to the hourly updated orbit, the averaged 1D RMS values of predicted orbit in terms of overlap for GPS, GLONASS, Galileo, and BDS MEO are improved by 39%, 35%, 41%, and 37%, respectively, and that of BDS GEO and IGSO satellites is improved by 47%. We also demonstrate that the boundary discontinuities of half-hourly orbit are within 2 cm for the GPS, GLONASS, and Galileo satellites, and for BDS the values are 2.6, 15.5, and 9.8 cm for MEO, GEO, and IGSO satellites, respectively. This method can also be implemented for any batch-based GNSS processing to improve the efficiency.
Precise atmospheric delay and proper constraints are critical for achieving rapid convergence and accurate positioning. However, ionospheric delay models over wide-area face challenges due to significant spatial and temporal variations, impacting real-time correction precision. To address this, we propose a novel ionospheric slant delay fitting model that adaptively selects the optimal reference path within coverage areas, describing differences between the reference propagation path and others through trigonometric functions. With ten coefficients, the model surpasses legacy polynomial fitting accuracy. Using a 166-station, 150 km-spaced European networks for atmospheric delays and 113 external stations for validation, our model achieves a 59.6% standard deviation reduction compared to the legacy model. Compared to the legacy ionospheric delay model, new model positioning convergence time (≤10 cm) accelerates by 37.7% and 34.2% for horizontal and vertical components, respectively. Meanwhile, two 2° × 2° uncertainty grids, generated from tropospheric and ionospheric delay fitting residuals at 15-min intervals, accurately describe fitting performance in all coverage areas with a maximum of 475 points. Adaptive constraints from uncertainty grids can reduce convergence time by 42.1% and 28.8% for horizontal and vertical, surpassing three-time modeling sigma solutions. These findings underscore the effectiveness of our novel ionospheric delay fitting model and the associated uncertainty grids in providing precise information across extensive regions with minimal coefficients.
Abstract The BeiDou Navigation Satellite System (BDS) employs a hybrid constellation including GEO (Geosynchronous Earth Orbit), IGSO (Inclined Geosynchronous Orbit), and MEO (Medium Earth Orbit) satellites, where the GEO and IGSO satellites are critical to providing continuous and reliable Positioning, Navigation, and Timing (PNT) services in the Asia–Pacific region. To handle the inconsistency between the satellite orbits and clocks in the broadcast ephemeris, which are determined by the Orbit Determination and Time Synchronization (ODTS) and the Two-way Satellite Time Frequency Transfer (TWSTFT) technique, respectively, we present the strategies using ground-satellite-link observations to improve the accuracy of broadcast ephemeris. The clock differences between the ODTS and TWSTFT techniques are used for correcting the radial orbit component to derive the refined orbits, which are used to generate the refined broadcast ephemeris. The test results show the precision of the refined orbits is improved by 50–60% in the 3-h to 12-h predicted arcs for the GEO satellites, and by 40–50% for the IGSO satellites. Moreover, the validation using satellite laser ranging observations shows the mean precision of the refined broadcast ephemeris is improved by 27% compared to the original one. Applying the proposed strategies in the BDS Operational Control Segment (OCS), the time evolution of BDS Single Point Positioning (SPP) in the period from Jan. 2016 to April 2021 is evaluated. The SPP accuracy is improved from 1.94, 2.06 and 3.29 m to 1.39, 1.85, and 2.39 m in the north, east, and up components, respectively. Further update with the inclusion of BDS-3 satellites improve the corresponding SPP precision to 0.68, 0.70 and 1.91 m.
With planet Earth being a deformable body, any geodetic marker attached to its crust exhibts slight motions in response to various geophysical forces. Prominent examples are the diurnal and semi-diurnal tides of the solid Earth, but also other periodic and non-periodic forces induced by mass transport divergence in atmosphere, oceans and the terrestrially stored water are deforming the Earth's surface and therefore displace any geodetic instrument attached to it. Based on a suite of different numerical model data-sets, the Earth System Modelling group at GFZ is routinely calculating both tidal and non-tidal surface deformations that can be readily applied as a priori information for the processing of space geodetic data. The model data-sets are publicly available as global grids with 3-hourly temporal sampling covering almost five decades from 1975 until present time. We present results from dedicated geodetic analysis experiments in order to demonstrate potential impact of such prior information on the GNSS-based coordinate estimates. We utilize data from 220 globally distributed IGS stations from 2005 until 2019 and apply the IGS repro3 strategies for the GPS daily precise orbit determination strategy. We apply non-tidal atmospheric and oceanic loading corrections from the ESMGFZ products on the (i) observation, (ii) normal equation, and (iii) parameter levels, and study the impact of such background models on the coordinate time-series of GNSS permanent stations and other associated parameters. 
Abstract Tropospheric delay modeling is challenging in high-precision Very Long Baseline Interferometry (VLBI) analysis due to the rapid water vapor variation and imperfect observation geometry, where observations from Global Navigation Satellite Systems (GNSS) co-locations can enhance the VLBI analysis. We investigate the impact of tropospheric ties in the VLBI and GNSS integrated processing during the CONT05–CONT17 campaigns, and present a method that automatically handles the systematic tropospheric tie biases. Applying tropospheric ties at VLBI–GNSS co-locations enhances the observation geometry and improves the solution reliability. The VLBI network is stabilized, with station coordinate repeatability improved by 12% horizontally and by 28% vertically, and the network scale improved by 32%. The Earth Orientation Parameters (EOP) improve by up to 20%. Both zenith delay and gradient ties contribute to the improvement of EOP, whereas the gradient ties contribute mainly to the improvement of length of day and celestial pole offsets.
Abstract Wide-lane (WL) uncalibrated phase delay (UPD) is usually derived from Melbourne–Wübbena (MW) linear combination and is a prerequisite in Global Navigation Satellite Systems (GNSS) precise point positioning (PPP) ambiguity resolution (AR). MW is a linear combination of pseudorange and phase, and the accuracy is limited by the larger pseudorange noise which is about one hundred times of the carrier phase noise. However, there exist inconsistent pseudorange biases which may have detrimental effect on the WL UPD estimation, and further degrade user-side ambiguity fixing. Currently, only the large part of pseudorange biases, e.g., the differential code bias (DCB), are available and corrected in PPP-AR, while the receiver-type-dependent biases have not yet been considered. Ignoring such kind of bias, which could be up to 20 cm, will cause the ambiguity fixing failure, or even worse, the incorrect ambiguity fixing. In this study, we demonstrate the receiver-type-dependent WL UPD biases and investigate their temporal and spatial stability, and further propose the method to precisely estimate these biases and apply the corrections to improve the user-side PPP-AR. Using a large data set of 1560 GNSS stations during a 30-day period, we demonstrate that the WL UPD deviations among different types of receivers can reach ± 0.3 cycles. It is also shown that such kind of deviations can be calibrated with a precision of about 0.03 cycles for all Global Positioning System (GPS) satellites. On the user side, ignoring the receiver-dependent UPD deviation can cause significant positioning error up to 10 cm. By correcting the deviations, the positioning performance can be improved by up to 50%, and the fixing rate can also be improved by 10%. This study demonstrates that for the precise and reliable PPP-AR, the receiver-dependent UPD deviations cannot be ignored and have to be handled.
Tropospheric delay is one of the most important error sources for space geodetic techniques, such as the Global Navigation Satellite Systems (GNSS). A priori tropospheric Zenith Hydrostatic and Wet Delays (ZHD and ZWD) should be obtained properly in advance to the GNSS data processing. Numerical Weather Model (NWM) is capable to provide accurate tropospheric zenith delays at any specific location with sophisticated calculation. As a more convenient alternative, the tropospheric zenith delays can be first modeled with NWM as a 2-D grid on the Earth surface and then corrected to the height of the specific location. In this case, accurate vertical correction algorithm is crucial. However, though empirical analytical models have been developed for the vertical correction of tropospheric zenith delays, their accuracies are limited due to the large spatiotemporal variability of the delays. In this work, we propose a Machine Learning (ML) model based on neural network for the vertical corrections of both ZHD and ZWD. The training data is obtained from the state-of-the-art NWM, the fifth-generation global reanalysis of European Centre for Medium-Range Weather Forecasts (ERA5). The proposed ML model is capable to reconstruct the tropospheric delays at any height from the Earth surface to up to 14 km. The precision of the ML model is superior to the analytical models with global average RMS values less than 2 and 3 mm for ZHD and ZWD, respectively. Therefore, it provides a convenient alternative to the sophisticated vertical integration of NWM for ordinary users with slight precision loss.
The orbit maneuver detection is crucial in Global Navigation Satellite System (GNSS) precise orbit determination, which is necessary for adjusting data processing strategies. The frequency of orbit maneuvers for the BeiDou Navigation System is significantly higher than that of other navigation systems, especially for geosynchronous orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. We propose a novel real-time and postprocessing method for detecting orbit maneuvers for BeiDou satellites based on the orbit differences between the epoch-updated orbit estimated using square root information (SRIF) and the predicted orbit according to the precise orbit estimated during non-maneuver period, as well as the orbital state difference during maneuver and non-maneuver periods. This method has significant advantages over using observation residuals and it is not affected by observation outliers, thus improving the accuracy and timeliness of orbit maneuver detection. We demonstrated that 32 orbit maneuver events of BeiDou satellites were successfully detected in 2022, of which 1 was for medium Earth orbit (MEO), 7 were for IGSO with an average detected maneuvering time of 7–8 min, and 24 were for GEO satellites with an average detected time of 4–5 min. Moreover, our method can be easily integrated into current real-time filter-based precise orbit determination (POD) processing without any extra task line, which simplifies the overall data processing. The data used in this method can be accessed easily, including GNSS observation data, broadcast ephemeris, and other open-source information files.
The wet tropospheric correction (WTC) retrieved from the onboard calibration microwave radiometer (CMR) of Haiyang-2A (HY-2A) is critical in monitoring the global sea level. However, the CMR WTC became significantly biased from June 2017 due to the failure of the 18.7-GHz band, which caused massive errors in the sea surface height (SSH) measurements. We investigate the accuracy of the CMR WTC derived from the two remaining bands to address this problem. A comprehensive evaluation using multisource data demonstrates that the dual-band + backscattering coefficient (BC) algorithm achieves comparable accuracy to the three-band algorithm, and it does not suffer from any large errors when the equipment works well. Hence, we calibrated the HY-2A CMR data with the dual-band + BC algorithm when the 18.7-GHz band failed, and the accuracy of the CMR WTC is improved from 2.34 to 1.39 cm compared with European Center for Medium-Range Weather Forecasts (ECMWF) ERA5 data. In addition, the SSH measurements are improved significantly by a maximum of 2 cm in mean value using the dual-band + BC WTC during the failure period of HY-2A CMR. Compared with Jason-3 SSH measurements, the HY-2A with dual-band + BC shows a slightly larger difference than HY-2A with three-band by 0.1 cm in rms. This method prolongs the operational lifetime of the HY-2A CMR and could be used in the reprocessing of HY-2A observations.
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