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Accurate ultra-short-term prediction of the Earth rotation parameters (ERP) holds paramount importance for real-time applications, particularly in reference frame conversion. Among them, diurnal rotation (UT1-UTC) which cannot be directly estimated through Global Navigation Satellite System (GNSS) techniques, significantly affects the rapid and ultra-rapid orbit determination of GNSS satellites. Presently, the traditional LS (least squares) + AR (autoregressive) and LS + MAR (multivariate autoregressive) hybrid methods stand as primary approaches for UT1-UTC ultra-short-term predictions (1–10 days). The LS + MAR hybrid method relies on the UT1-UTC and LOD (length of day) series. However, the correlation between LOD and first-order-difference UT1-UTC is stronger than that between LOD and UT1-UTC. In light of this, and with the aid of the first-order-difference UT1-UTC, we propose an enhanced LS + MAR hybrid method to UT1-UTC ultra-short-term prediction. By using the UT1-UTC and LOD data series of the IERS (International Earth Rotation and Reference Systems Service) EOP 14 C04 product, we conducted a thorough analysis and evaluation of the improved method's prediction performance compared to the traditional LS + AR and LS + MAR hybrid methods. According to the numerical results over more than 210 days, they demonstrate that, when considering the correlation information between the LOD and the first-order-difference UT1-UTC, the mean absolute errors (MAEs) of the improved LS + MAR hybrid method range from 21 to 934 μs in 1–10 days predictions. In comparison to the traditional LS + AR hybrid method, the MAEs show a reduction of 7–53 μs in 1–10 days predictions, with corresponding improvement percentages ranging from 1 to 28%. Similarly, when compared to the traditional LS + MAR hybrid method, the MAEs have a reduction of 5–42 μs in 1–10 days predictions, with corresponding improvement percentages ranging from 4–20%. Additionally, when aided by GNSS-derived LOD data series, the MAEs of improved LS + MAR hybrid method experience further reduction.

Abstract High-quality spatial atmospheric delay correction information is essential for achieving fast integer ambiguity resolution (AR) in precise positioning. However, traditional real-time precise positioning frameworks (i.e., NRTK and PPP-RTK) depend on spatial low-resolution atmospheric delay correction through the expensive and sparsely distributed CORS network. This results in limited public appeal. With the mass production of autonomous driving vehicles, more cost-effective and widespread data sources can be explored to create spatial high-resolution atmospheric maps. In this study, we propose a new GNSS positioning framework that relies on dual base stations, massive vehicle GNSS data, and crowdsourced atmospheric delay correction maps (CAM). The map is easily produced and updated by vehicles equipped with GNSS receivers in a crowd-sourced way. Specifically, the map consists of between-station single-differenced ionospheric and tropospheric delays. We introduce the whole framework of CAM initialization for individual vehicles, on-cloud CAM maintenance, and CAM-augmented user-end positioning. The map data are collected and preprocessed in vehicles. Then, the crowdsourced data are uploaded to a cloud server. The massive data from multiple vehicles are merged in the cloud to update the CAM in time. Finally, the CAM will augment the user positioning performance. This framework forms a beneficial cycle where the CAM’s spatial resolution and the user positioning performance mutually improve each other. We validate the performance of the proposed framework in real-world experiments and the applied potency at different spatial scales. We highlight that this framework is a reliable and practical positioning solution that meets the requirements of ubiquitous high-precision positioning.

Short-term (up to 30 days) predictions of Earth Rotation Parameters (ERPs) such as Polar Motion (PM: PMX and PMY) play an essential role in real-time applications related to high-precision reference frame conversion. Currently, least squares (LS) + auto-regressive (AR) hybrid method is one of the main techniques of PM prediction. Besides, the weighted LS + AR hybrid method performs well for PM short-term prediction. However, the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model. In this study, we have derived a modified stochastic model for the LS + AR hybrid method, namely the weighted LS + weighted AR hybrid method. By using the PM data products of IERS EOP 14 C04, the numerical results indicate that for PM short-term forecasting, the proposed weighted LS + weighted AR hybrid method shows an advantage over both the LS + AR hybrid method and the weighted LS + AR hybrid method. Compared to the mean absolute errors (MAEs) of PMX/PMY short-term prediction of the LS + AR hybrid method and the weighted LS + AR hybrid method, the weighted LS + weighted AR hybrid method shows average improvements of 6.61%/12.08% and 0.24%/11.65%, respectively. Besides, for the slopes of the linear regression lines fitted to the errors of each method, the growth of the prediction error of the proposed method is slower than that of the other two methods.

The ionosphere is one of the important error sources that affect the communication of radio signals. The international reference ionosphere (IRI) model is a commonly used model to describe ionospheric parameters. The driving parameter IG12 of the IRI-2016 model was optimally updated based on GNSS-TEC data from 2015 and 2019. The electron density profiles and NmF2 calculated by the IRI-2016 model (upda-IRI-2016) driven by the updated IG12 value (IG-up) were evaluated for their accuracy using ionosonde observations and COSMIC inversion data. The experiments show that both the electron density profiles and NmF2 calculated by upda-IRI-2016 driven by IG-up show significant optimization effects, compared to the IRI-2016 model driven by IG12. For electron density, the precision improvement (PI) for both MAE and RMSE at the Beijing station exceed 31.2% in January 2015 and 16.0% in January 2019. While the PI of MAE and RMSE at the Wuhan station, which is located at a lower latitude, both exceed 32.5% in January 2015, both exceed 42.1% in January 2019, which is significantly higher than that of the Beijing station. In 2015, the PI of MAE and RMSE compared with COSMIC are both higher than 20%. For NmF2, the PI is greater for low solar activity years and low latitude stations, with the Wuhan station showing a PI of more than 11.7% in January 2019 compared to January 2015. The PI compared to COSMIC was higher than 17.2% in 2015.

Ambiguity resolution (AR) can markedly enhance the precision of precise point positioning (PPP) and accelerate the convergence process. The decoupled clock model represents a pivotal approach for ambiguity resolution, yet current research on this topic is largely confined to GPS. Consequently, in this study, we extend the investigation of the decoupled clock model to multi-GNSS. Firstly, based on the conventional model, we derive the multi-GNSS decoupled clock estimation model and the precise point positioning with ambiguity resolution (PPP-AR) model. Secondly, we provide a detailed explanation of the estimation process for the multi-GNSS decoupled clock estimation. To validate the efficacy of the proposed model, we conduct multi-GNSS decoupled clock estimation and PPP-AR experiments using six days of observation data. The results demonstrate that the decoupled clocks of GPS, Galileo, and BDS-3 can all achieve high accuracy, thus fully meeting the requirement of ambiguity resolution. In terms of positioning performance, the joint three systems have higher positioning accuracy, reaching 3.10 cm and 6.13 cm in horizontal and vertical directions, respectively. Furthermore, the convergence time (CT) and time to first fix (TTFF) are shortened, to 23.13 min and 13.65 min, respectively. The experimental findings indicate that the proposed multi-GNSS decoupled clock model exhibits high precision and rapid positioning service capabilities.

Accurate tropospheric delays are of great importance for both Global Navigation Satellite System (GNSS)-based positioning and precipitable water vapor monitoring. The gridded tropospheric delay products, including zenith hydrostatic delays (ZHD) and zenith wet delays (ZWD), are the most ideal method for accessing accurate tropospheric delays. The vertical adjustment method is critical for implementing the gridded tropospheric products. In this work, we consider the different models used for grid products and assess their performance over Yunnan mountains with complex topography. We summarize the main results as follows: (1) The products can provide accurate ZHD with mean biases of −2.6 mm and mean Standard Deviation (STD) of 1.5 mm while the ZWD results from grid products show a performance with biases of −0.4 mm and STD of 1.3 cm over the Yunnan area. (2) The Tv-based model shows a better performance than the T0-based model and IGPZWD in rugged areas with large height differences. The grid products can provide hourly ZHD with biases of 3 mm and wet delay with mean biases of within 2 cm and mean STD of below 3 cm in the Yunnan mountains, which exhibit a large height difference of around 1.5 km. (3) The radiosondes results confirm that the Tv-based model has an obvious advantage in calculating ZHD height corrections for differences within 2 km while the T0-model suffers from a loss in accuracy in the case of large height differences. If the site is located more than 1 km below the reference height, the IGPZWD model can provide a better ZWD with a mean bias of 1.5 cm and a mean STD of 1.7 cm. With vertical reduction models, the grid products can provide accurate ZHD and ZWD in real time, even if in complex area.

Precise point positioning (PPP) is a prevalent, high-precision spatial absolution positioning method, and its performance can be enhanced by ambiguity resolution (AR). To fulfill the growing need for high-precision positioning, we developed an open-source GNSS data processing package based on the decoupled clock model called Cube, which integrates decoupled clock offset estimation and precise point positioning with ambiguity resolution (PPP-AR). Cube is a secondary development based on RTKLIB. Besides the decoupled clock model, Cube can also estimate legacy clocks for the International GNSS Service (IGS), as well as clocks with satellite code bias extraction, and perform PPP-AR using the integer-recovered clock model. In this work, we designed satellite clock estimation and PPP-AR experiments with one week of GPS data to validate Cube’s performance. Results show that the software can produce high-precision satellite clock products and positioning results that are adequate for daily scientific study. With Cube, researchers do not need to rely on public PPP-AR products, and they can estimate decoupled clock products and implement PPP-AR anytime.

This paper investigates ionospheric response characteristics from multiple perspectives based on globally distributed GNSS data and products, ionosonde data, FORMOSAT-7/COSMIC-2 occultation data, and Swarm satellite observations caused by the total solar eclipse of 8 April 2024 across North and Central America. The results show that both GNSS-derived TEC products have detected the ionospheric TEC degradation triggered by the total solar eclipse, with the maximum degradation exceeding 10 TECU. The TEC data from nine GNSS stations in the path of the maximum eclipse reveal that the intensity of ionospheric TEC degradation is related to the spatial location, with the maximum degradation value of the ionospheric TEC being about 14~23 min behind the moment of the maximum eclipse. Additionally, a negative anomaly of foF2 with a maximum of more than 2.7 MHz is detected by ionosonde. In the eclipse region, NmF2 and hmF2 show trends of decrease and increase, with percentages of variation of 40~70% and 4~16%, respectively. The Ne profile of the Swarm-A satellite is significantly lower than the reference value during the eclipse period, with the maximum negative anomaly value reaching 11.2 × 105 el/cm3, and it failed to show the equatorial ionization anomaly.

Currently, network real-time kinematic (NRTK) technology is one of the primary approaches used to achieve real-time dynamic high-precision positioning, and virtual reference station (VRS) technology, with its high accuracy and compatibility, has become the most important type of network RTK solution. The key to its successful implementation lies in correctly fixing integer ambiguities and extracting spatially correlated errors. This paper first introduces real-time data processing flow on the VRS server side. Subsequently, an improved ionosphere-weighted VRS approach is proposed based on single-differenced observations of GPS, GAL, and BDS. With the prerequisite of ensuring estimable integer properties of ambiguities, it directly estimates the single-differenced ionospheric delay and tropospheric delay between reference stations, reducing the double-differenced (DD) observation noise introduced by conventional models and accelerating the system initialization speed. Based on this, we provide an equation for generating virtual observations directly based on single-differenced atmospheric corrections without specifying the pivot satellite. This further simplifies the calculation process and enhances the efficiency of the solution. Using Australian CORS data for testing and analysis, and employing the approach proposed in this paper, the average initialization time on the server side was 40 epochs, and the average number of available satellites reached 23 (with an elevation greater than 20°). Two positioning modes, ‘Continuous’ (CONT) and ‘Instantaneous’ (INST), were employed to evaluate VRS user positioning accuracy, and the distance covered between the user and the master station was between 20 and 50 km. In CONT mode, the average positioning errors in the E/N/U directions were 0.67/0.82/1.98 cm, respectively, with an average success fixed rate of 98.76% (errors in all three directions were within 10 cm). In INST mode, the average positioning errors in the E/N/U directions were 1.29/1.29/2.13 cm, respectively, with an average success fixed rate of 89.56%. The experiments in this study demonstrate that the proposed approach facilitates efficient ambiguity resolution (AR) and atmospheric parameter extraction on the server side, thus enabling users to achieve centimeter-level positioning accuracy instantly.

We launched this Special Issue with the aim of collecting papers that use satellite data and new methodologies to understand the preparatory phase of medium–large earthquakes in the world [...]

Approaching the peak year of the 25th solar activity cycle, the frequency of strong geomagnetic storms is gradually increasing, which seriously affects the navigation and positioning performance of GNSS. Based on the globally distributed GNSS station data and FORMOSAT-7/COSMIC-2 occultation data, this paper explores for the first time the effects of the G4-class geomagnetic storm that occurred on 23–24 April 2023 on the global ionosphere, especially the ionospheric equatorial anomalies and F-layer perturbations. It reveals the precise point positioning (PPP) accuracy degradation during a geomagnetic storm. The results show that the ionospheric rate of total electron content index (ROTI) and near high latitude GNSS phase scintillations index have varying levels of perturbation during geomagnetic storms, with the maximum ROTI and phase scintillations index exceeding 0.5 TECU/min and 0.8, respectively. The equatorial ionization anomaly (EIA) shows an enhanced state (positive ionospheric storms) during geomagnetic storms, and the cause of this phenomenon is most likely the equatorward neutral wind. The variation of the S4 index of the FORMOSAT-7/COSMIC-2 satellite reveals the uplift of the F-layer during geomagnetic storms. During geomagnetic storms, the PPP accuracy degrades most seriously at high latitudes, the maximum MAE exceeds 2.3 m, and the RMS in the three-dimensional (3D) direction exceeds 2.0 m. These investigations can provide case support for space weather and GNSS studies of the impact of geomagnetic storms during peak solar activity years.

Given the potential of low-earth orbit (LEO) satellites in terms of navigation enhancement, accurately estimating the differential code bias (DCB) of GNSS satellites and LEO satellites is an important research topic. In this study, to obtain accurate DCB estimates, the effects of vertical total electron content (VTEC) modeling parameters of the topside ionosphere on DCB estimation were investigated using LEO observations for the first time. Different modeling parameters were set in the DCB estimations, encompassing modeling spacing in the dynamic temporal mode and degree and order (D&O) in spherical harmonic modeling. The DCB precisions were then evaluated, and the impacts were analyzed. Thus, a number of crucial and beneficial conclusions are drawn: (1) The maximum differences in the GPS DCB estimates after adopting different modeling spacings and different D&Os exhibit that the different modeling spacings or D&Os both affect the GPS DCB estimates and their root-mean square (RMS), and the effects of the two are at the same level. (2) The maximum differences in receiver DCBs using different modeling spacings indicate that the modeling spacing has a significant impact on the receiver DCBs, compared with GPS DCBs. Whereas, the maximum differences in receiver DCBs with different modeling D&Os are inferior to the differences in the GPS DCBs. That is, the modeling spacing has a greater impact on the LEO DCBs than those of the modeling D&O. (3) The experimental results indicate that the GPS DCB estimates using a modeling spacing of 12H have higher precisions than the others, whereas LEO receiver DCBs using a spacing of 4H or 6H obtain optimal STD. In terms of modeling D&O, adopting 8D&O in the LEO-based VTEC modeling can attain superior estimates and precisions for both GPS and LEO DCBs. The research conclusions can provide references for LEO-augmented DCB estimation.

Sudden Stratospheric Warming (SSW) events have a strong impact on the tropospheric weather and climate. Past researchers have carried out extensive studies investigating the theories of interactions between the stratosphere and the troposphere. However, detailed studies on the influences of the global tropopause are rarely shown. This study uses Global Navigation Satellite System (GNSS) Radio Occultation (RO) data from the years 2007 to 2013 to investigate the influences of different types of SSW events on the tropopause over latitude bands from 30° S to 90° N. It was found that SSW events have strong influences on the tropopause over 60° N–90° N and over 20° N–30° N regions. In 60° N–90° N, SSW events cause a tropopause temperature increase and, therefore, a tropopause height decrease. The increment in the tropopause temperature are more than 10 K and the decrement in the tropopause height is about to 2 km during strong events. Such influences last for about 1.5 months for strong split events and about 10 days for weaker and/or displacement type events. The influences of SSW events on 20° N–30° N are weaker. Only the January 2009 SSW event shows a visible influence on the tropopause layer with a tropopause temperature decrease of about 4 K and a tropopause height increase of about 1 km. Other SSW events share no common characteristics on the tropical tropopause. This is mainly because SSW events are not strong enough to dominate the tropopause variations and other factors, especially the planetary waves in the troposphere, have stronger impacts on the tropopause layer.

In this paper, GNSS stations’ observational data, global ionospheric maps (GIM) and the electron density of FORMOSAT-7/COSMIC-2 occultation are used to study ionospheric anomalies before the submarine volcanic eruption of Hunga Tonga–Hunga Ha’apai on 15 January 2022. (i) We detect the negative total electron content (TEC) anomalies by three GNSS stations on 5 January before the volcanic eruption after excluding the influence of solar and geomagnetic disturbances and lower atmospheric forcing. The GIMs also detect the negative anomaly in the global ionospheric TEC only near the epicenter of the eruption on 5 January, with a maximum outlier exceeding 6 TECU. (ii) From 1 to 3 January (local time), the equatorial ionization anomaly (EIA) peak shifts significantly towards the Antarctic from afternoon to night. The equatorial ionization anomaly double peak decreases from 4 January, and the EIA double peak disappears and merges into a single peak on 7 January. Meanwhile, the diurnal maxima of TEC at TONG station decrease by nearly 10 TECU and only one diurnal maximum occurred on 4 January (i.e., 5 January of UT), but the significant ionospheric diurnal double-maxima (DDM) are observed on other dates. (iii) We find a maximum value exceeding NmF2 at an altitude of 100~130 km above the volcanic eruption on 5 January (i.e., a sporadic E layer), with an electron density of 7.5 × 105 el/cm3.

Abstract As a new Ionosphere Associate Analysis Center (IAAC) of the International GNSS Service (IGS), Chinese Academy of Sciences (CAS) started the routine computation of the real-time, rapid, and final Global Ionospheric Maps (GIMs) in 2015. The method for the generation of CAS rapid and final GIMs and recent updates are presented in the paper. The quality of CAS post-processed GIMs is assessed during 2015–2018 after the maximum of solar cycle 24. To perform an independent and fair assessment, Jason-2/3 Vertical Total Electron Contents (VTEC) are first used as the references over the ocean. GPS differential Slant TECs (dSTEC) generated from 55 Multi-GNSS Experimental (MGEX) stations of the IGS are also employed, which provides a complementing way to evaluate the ability of electron content models to reproduce the spatial and temporal gradients in the ionosphere. During the test period, Jet Propulsion Laboratory (JPL) GIMs present significantly positive deviations compared to the Jason VTEC and GPS dSTEC. Technical University of Catalonia (UPC) rapid GIM UQRG exhibits the best performance in both Jason VTEC and GPS dSTEC analysis. The CAS GIMs show comparable performance with the results of the first four IAACs of the IGS. As expected, the poor performance of all GIMs is in equatorial regions and the high latitudes of the southern hemisphere. The consideration of generating multi-layer or three-dimensional ionospheric maps is emphasized to mitigate the inadequacy of ionospheric single-layer assumption in the presence of pronounced latitudinal gradients. The use of ionospheric observations from the new GNSS constellations and other space- or ground-based observation techniques is also suggested in the generation of future GIMs, given the sparse GPS/GLONASS stations in the southern hemisphere.

Global navigation satellite systems (GNSS) provide a great data source about the ionosphere state. These data can be used for testing ionosphere models. We studied the performance of nine ionospheric models (Klobuchar, NeQuickG, BDGIM, GLONASS, IRI-2016, IRI-2012, IRI-Plas, NeQuick2, and GEMTEC) both in the total electron content (TEC) domain—i.e., how precise the models calculate TEC—and in the positioning error domain—i.e., how the models improve single frequency positioning. The whole data set covers 20 years (2000–2020) from 13 GNSS stations, but the main analysis involves data during 2014–2020 when calculations are available from all the models. We used single-frequency positioning without ionospheric correction and with correction via global ionospheric maps (IGSG) data as expected limits for errors. Improvements against noncorrected solution were as follows: GIM IGSG—22.0%, BDGIM—15.3%, NeQuick2—13.8%, GEMTEC, NeQuickG and IRI-2016—13.3%, Klobuchar—13.2%, IRI-2012—11.6%, IRI-Plas—8.0%, GLONASS—7.3%. TEC bias and mean absolute TEC errors for the models are as follows: GEMTEC—−0.3 and 2.4 TECU, BDGIM—−0.7 and 2.9 TECU, NeQuick2—−1.2 and 3.5 TECU, IRI-2012—−1.5 and 3.2 TECU, NeQuickG—−1.5 and 3.5 TECU, IRI-2016—−1.8 and 3.2 TECU, Klobuchar—1.2 and 4.9 TECU, GLONASS—−1.9 and 4.8 TECU, and IRI-Plas—3.1 and 4.2 TECU. While TEC and positioning domains differ, new-generation operational models (BDGIM and NeQuickG) could overperform or at least be at the same level as classical empirical models.

For the timely retrieval of global positioning system based precipitable water vapor (GPS-PWV) over complex topography when there is no in situ pressure-derived zenith hydrostatic delays (ZHDs), this article evaluates three types of ready-made ZHD products, including two newly released products from the Vienna University of Technology (TU Wien, TUW-VMF3) and GeoForschungsZentrum Potsdam (GFZ-VMF1) and a legacy product TUW-VMF1. We implement them for the first time for GPS-PWV retrieval in regions with highly variable topography, such as the Tibetan plateau (TP). First, we present a refined method [model-assisted ZHD height adjustment, model-assisted ZHD height adjustment (MAZHA)] for implementing the above VMF1/VMF3-like ZHD products. The results reveal that the MAZHA method improves the implementation accuracy over the TP by 70% compared to the conventional method. Then, the above multisource VMF1/VMF3-like ZHD products are evaluated using the in situ pressure-derived ZHDs across the TP. The results show that the GFZ-VMF1 outperforms the TUW-VMF1 mainly because a more advanced underlying numerical weather model (ERA5) are adopted. TUW-VMF3 achieves the best performance mainly because it is provided with improved horizontal resolution. Finally, we find that implementing the state-of-the-art TUW-VMF3 ZHD product for GPS-PWV retrieval yields no statistically significant errors, even under extreme weather conditions, and the retrieved GPS-PWVs can well characterize the PWV diurnal variations in all seasons except winter. Additionally, considering the fact that the operational and forecasted TUW-VMF3 ZHDs present almost equivalent performance, this article is also beneficial to real-time GPS-PWV retrieval using forecasted TUW-VMF3 ZHDs, thus allowing for the ease of real-time GPS-PWV retrieval.

For positioning system based on wireless sensor networks, NLOS errors are one of the main factors to degrade localization performance of an algorithm, about which lots of research results and analysis have been published in previous literatures to enhance localization performance. However, those literatures have neglected computational time, another important index to performance. To decrease computational time and improve localization accuracy simultaneously, we firstly consider NLOS errors as outliers and transform the TOA-based localization problem into a sparse optimization one in LOS-dominating environment. Then, we introduce sparse technology into line-of-sight/none-line-of-sight (LOS/NLOS) scenarios formulating a L1-norm minimization problem, and solve it by alternating direction method of multipliers (ADMM) with a strategy of iterative adaptive. Monte Carlo simulation results show that our method has advantages of high computation speed and positioning accuracy under mixed sparse LOS/NLOS scenarios.

Tropospheric delay information is particularly important for network RTK (Network Real-time Kinematic) positioning. Conventionally, tropospheric delay information at a virtual reference station (VRS) is obtained using the linear interpolation method (LIM). However, the conventional LIM cannot work well when there is a substantial height difference between the rover station and the reference station. Consequently, we propose a modified linear interpolation method (MLIM) by carefully handling the height difference between the rover station and the reference station. The new MLIM method first corrects the systematic error of the double-difference (DD) tropospheric delay in the elevation direction caused by the height difference, and then utilizes the linear interpolation algorithm to obtain the tropospheric delay of the VRS station. To determine the parameters of the low-order surface model (LSM), we also propose a modified LSM (MLSM) interpolation method in the triangular network and evaluate it in the positioning domains. The two new interpolation methods are evaluated using two regional GNSS networks with obvious height disparities. Results show that the DD tropospheric delay interpolation accuracy obtained by the new MLIM and MLSM is improved by 56.5% and 78.7% on average in the two experiments compared to the conventional method. The new MLIM and MLSM are more accurate than the traditional LIM (TLIM) in cases with low elevation satellites. Additionally, the positioning accuracies are improved by using the MLIM and MLSM methods. The MLIM and MLSM outperform TLIM in the up-component by an average of 72.8% and 80.7%, respectively.

The Chinese BeiDou-3 navigation satellite system (BDS-3) is capable of transmitting both old B1I, B3I signals and new B1C, B2a, B2b signals. Current BDS-3 precise orbits are generally calculated using a B1I/B3I combination considering overlap with the BeiDou-2 navigation satellite system (BDS-2). In this contribution, the observation quality of BDS-3 medium earth orbit (MEO) satellites and inclined geosynchronous orbit (IGSO) satellites are analyzed based on three aspects, i.e., carrier to noise ratio (C/N0), pseudo-range noise and pseudo-range multipath (MP). The C/N0 of the MEO satellite is 2~3 dB higher than that of the IGSO satellite at the same elevation angle. Meanwhile, the order of the Root Mean Square (RMS) values of both pseudo-range noise and MP is B1I < B1C < B3I < B2a ≈ B2b. Three kinds of combinations, i.e., B1CB2a, B1CB2b and B1IB3I, are selected for the BDS-3 precise orbit determination (POD) experiment. Orbits are assessed by the orbit-only signal-in-space range error (SISRE) computed between pairs of the three kinds of combinations in this contribution, CODE and GFZ final orbits. Orbit-only SISRE assessment shows that B1CB2a/CODE, B1CB2b/CODE, B1CB2a/GFZ and B1CB2b/GFZ are at the same level with CODE/GFZ, and the orbit-only SISRE is at the level of 5 cm for MEOs and 9 cm for IGSOs, respectively. Meanwhile, B1IB3I/CODE and B1IB3I/GFZ are about 1–2 cm worse. Inter-solution comparison between B1CB2a, B1CB2b and B1IB3I also indicate that B1CB2a and B1CB2b have good consistency, while B1IB3I shows poor performance. Satellite laser ranging (SLR) residuals indicate that the mean RMS is 3–4 cm for the four BDS-3 MEOs for CODE final orbit, GFZ final orbit, B1CB2a and B1CB2b combinations, while the mean RMS value for B1IB3I combination is a few millimeters worse, at approximately 4–5 cm.

Offering real-time precise point positioning (PPP) services for global and large areas based on global navigation satellite systems (GNSS) has drawn more and more attention from institutions and companies. A precise and reliable satellite orbit is a core premise for multi-GNSS real-time services, especially for the GPS and GLONASS, which are undergoing modernization, whereas the Galileo, BDS and QZSS have just fulfilled the construction stage. In this contribution, a real-time precise orbit determination (POD) strategy for the five operational constellations based on the hourly updated ultrarapid orbit prediction method is presented. After combination of 72 h arc through three adjacent 24 h arc normal equations, the predicted orbits are finally generated (hourly updated). The POD results indicate that the mean one-dimensional (1-D) root mean square (RMS) values compared with the Deutsches GeoForschungsZentrum (GFZ) final multi-GNSS orbits are approximately 3.7 cm, 10.2 cm, 5.8 cm, 5.7 cm, 4.1 cm and 25.1 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The mean 1-D RMS values of the hourly updated ultrarapid orbit boundary overlapping comparison are approximately 1.6 cm, 6.9 cm, 3.2 cm, 2.7 cm, 1.8 cm and 22.2 cm for GPS, BDS IGSOs, BDS MEOs, GLONASS, Galileo and QZSS NONE GEOs, respectively. The satellite laser ranging (SLR) validation illuminates that the mean RMS values are approximately 4.53 cm and 4.73 cm for the four MEOs of BDS-3 and four BDS-2 satellites, respectively.

Abstract Precipitable water vapor (PWV) and ionospheric vertical total electron content (VTEC) are two essential components of space‐atmosphere parameters. The zenith troposphere delay can be converted into PWV, which plays a crucial role in meteorological studies. In the meantime, the importance of the VTEC lies in providing ionospheric corrections for single‐frequency (SF) positioning, navigation, and timing users. Currently, the global navigation satellite system (GNSS) has become one of the most commonly used tools for retrieving PWV and VTEC and normally relies on dual‐frequency, geodetic‐grade receivers and antennas. However, this reliance also implies high hardware costs. In this paper, we propose a single‐frequency ionosphere and troposphere retrieval approach that enables the simultaneous retrieval of PWV and VTEC from multi‐GNSS data collected by low‐cost SF receivers. The use of SF receivers can greatly reduce the cost of hardware. Furthermore, the simultaneous provision of PWV and VTEC also has a positive effect on studying the coupling mechanisms of the ionosphere and troposphere. The accuracy of the estimated zenith troposphere delay can be better than 10 mm compared with the troposphere products published by the International GNSS Service, and the PWV is no more than 3 mm compared with radiosonde‐derived results. Referring to the final International GNSS Service global ionosphere map products and the Jason altimeter data, the VTEC retrieved from the single‐frequency ionosphere and troposphere retrieval method can perform at roughly equal levels compared to the customary dual‐frequency method.

We used Global Navigation Satellite System (GNSS) radio occultation (RO) temperature, density, and bending angle profiles to monitor tropical atmospheric anomalies during the January–February 2009 sudden stratospheric warming (SSW) event on a daily basis. We constructed RO anomaly profiles (tropical mean (30°S–30°N)) and gridded mean anomalies, as well as tropopause height and temperature anomalies. Based on the anomalies, we investigated the response time and region of the tropical atmosphere to SSW. It was found that the GNSS RO data were robust in monitoring tropical atmospheric anomalies during SSW. The tropical stratosphere revealed cooling simultaneously with polar stratospheric warming, although the magnitudes of the maximum tropical mean anomalies were 6–7 times smaller than the polar mean. Altitude variations showed that tropical stratospheric anomalies were largest within 35–40 km, which were 5 km higher than those in the polar region. On the onset day of 23 January, temperature anomalies over 0–30°N were mostly more than −5 K, which were larger than those of −2 K detected over the 0–30°S band, and the largest anomalies were detected over northern Africa with values more than −10 K. RO density and bending angle anomalies responded to SSW in a similar way as temperature but were 20 km higher. Following cooling, the tropical upper stratosphere and lower mesosphere revealed visible warming, with anomalies more than 10 K in the sector of 15°S–15°N. Tropopause anomalies revealed the largest variations over 20°N–30°N, further confirming that the extratropical region of the northern hemisphere is a key region for the dynamical coupling between the polar and tropical regions. Tropopause height anomalies had clear increase trends from 16 January to 8 February, with anomalies of the 20°N–30°N band that were −2 km on Jan 16 and increased to −0.5 km on Feb 6 with a variation of 1.5 km, while variations in other bands were within 0.5 km. Tropopause temperature anomalies had clear decrease trends over the same period, with anomalies at 20°N–30°N of 4 K on 16 January and decreasing to about −1 K on 8 February, while anomalies in other bands showed variations within 3 K.

High-precision localization through multi-sensor fusion has become a popular research direction in unmanned driving. However, most previous studies have performed optimally only in open-sky conditions; therefore, high-precision localization in complex urban environments required an urgent solution. The complex urban environments employed in this study include dynamic environments, which result in limited visual localization performance, and highly occluded environments, which yield limited global navigation satellite system (GNSS) performance. In order to provide high-precision localization in these environments, we propose a vision-aided GNSS positioning method using semantic information by integrating stereo cameras and GNSS into a loosely coupled navigation system. To suppress the effect of dynamic objects on visual positioning accuracy, we propose a dynamic-simultaneous localization and mapping (Dynamic-SLAM) algorithm to extract semantic information from images using a deep learning framework. For the GPS-challenged environment, we propose a semantic-based dynamic adaptive Kalman filtering fusion (S-AKF) algorithm to develop vision aided GNSS and achieve stable and high-precision positioning. Experiments were carried out in GNSS-challenged environments using the open-source KITTI dataset to evaluate the performance of the proposed algorithm. The results indicate that the dynamic-SLAM algorithm improved the performance of the visual localization algorithm and effectively suppressed the error spread of the visual localization algorithm. Additionally, after vision was integrated, the loosely-coupled navigation system achieved continuous high-accuracy positioning in GNSS-challenged environments.

For the two newly launched satellites (PRN number 27 and 28) of the future global BeiDou navigation satellite system (BDS-3), there is no available broadcast ephemeris data and other initial orbit information, but the initial orbit is the fundamental of the comprehensive analysis of the satellites and their signals. Precise orbit determination (POD) also requires determination of a priori initial value with a certain precision in order to avoid problems such as filter divergence during POD. Compared with the Newton iteration method, which relies on the initial value, this study utilizes the Bancroft algorithm to directly solve the nonlinear equations with the advantage of numerical stability. The initial orbits of these two satellites are calculated based on new code signals, and their results are analyzed and discussed. The experimental results show that, with the exception of very few epochs, when the new code signal is utilized, the median and robust variance factor of the observed residuals computed using pseudo-range observations and the solved initial orbits are less than 4 and 2 m, respectively. It also shows that this solution can be used for rapid initial orbit recovery after maneuvers of the new BeiDou satellites. Keywords: New-generation BeiDou satellites, New code signals, Initial orbit determination, Bancroft

Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) is an attractive positioning technology due to its high precision and flexibility. However, the vulnerability of PPP brings a safety risk to its application in the field of life safety, which must be evaluated quantitatively to provide integrity for PPP users. Generally, PPP solutions are processed recursively based on the extended Kalman filter (EKF) estimator, utilizing both the previous and current measurements. Therefore, the integrity risk should be qualified considering the effects of all the potential observation faults in history. However, this will cause the calculation load to explode over time, which is impractical for long-time missions. This study used the innovations in a time window to detect the faults in the measurements, quantifying the integrity risk by traversing the fault modes in the window to maintain a stable computation cost. A non-zero bias was conservatively introduced to encapsulate the effect of the faults before the window. Coping with the multiple simultaneous faults, the worst-case integrity risk was calculated to overbound the real risk in the multiple fault modes. In order to verify the proposed method, simulation and experimental tests were carried out in this study. The results showed that the fixed and hold mode adopted for ambiguity resolution is critical to an integrity risk evaluation, which can improve the observation redundancy and remove the influence of the biased predicted ambiguities on the integrity risk. Increasing the length of the window can weaken the impact of the conservative assumption on the integrity risk due to the smoothing effect of the EKF estimator. In addition, improving the accuracy of observations can also reduce the integrity risk, which indicates that establishing a refined PPP random model can improve the integrity performance.

The International Reference Ionosphere (IRI) is an empirical model widely used to describe ionospheric characteristics. In the previous research, high-precision total ionospheric electron content (TEC) data derived from global navigation satellite system (GNSS) data were used to adjust the ionospheric global index IG12 used as a driving parameter in the standard IRI model; thus, the errors between IRI-TEC and GNSS-TEC were minimized, and IRI-TEC was calibrated by modifying IRI with the updated IG12 index (IG-up). This paper investigates various interpolation strategies for IG-up values calculated from GNSS reference stations and the calibrated TEC accuracy achieved using the modified IRI-2016 model with the interpolated IG-up values as driving parameters. Experimental results from 2015 and 2019 show that interpolating IG-up with a 2.5° × 5° spatial grid and a 1-h time resolution drives IRI-2016 to generate ionospheric TEC values consistent with GNSS-TEC. For 2015 and 2019, the mean absolute error (MAE) of the modified IRI-TEC is improved by 78.57% and 77.42%, respectively, and the root mean square error (RMSE) is improved by 78.79% and 77.14%, respectively. The corresponding correlations of the linear regression between GNSS-TEC and the modified IRI-TEC are 0.986 and 0.966, more than 0.2 higher than with the standard IRI-TEC.

Observable-specific bias (OSB) parameterization allows observation biases belonging to various signal types to be flexibly addressed in the estimation of ionosphere and global navigation satellite system (GNSS) clock products. In this contribution, multi-GNSS OSBs are generated by two different methods. With regard to the first method, geometry-free (GF) linear combinations of the pseudorange and carrier-phase observations of a global multi-GNSS receiver network are formed for the extraction of OSB observables, and global ionospheric maps (GIMs) are employed to correct ionospheric path delays. Concerning the second method, satellite and receiver OSBs are converted directly from external differential code bias (DCB) products. Two assumptions are employed in the two methods to distinguish satellite- and receiver-specific OSB parameters. The first assumption is a zero-mean condition for each satellite OSB type and GNSS signal. The second assumption involves ionosphere-free (IF) linear combination signal constraints for satellites and receivers between two signals, which are compatible with the International GNSS Service (IGS) clock product. Agreement between the multi-GNSS satellite OSBs estimated by the two methods and those from the Chinese Academy of Sciences (CAS) is shown at levels of 0.15 ns and 0.1 ns, respectively. The results from observations spanning 6 months show that the multi-GNSS OSB estimates for signals in the same frequency bands may have very similar code bias characteristics, and the receiver OSB estimates present larger standard deviations (STDs) than the satellite OSB estimates. Additionally, the variations in the receiver OSB estimates are shown to be related to the types of receivers and antennas and the firmware version. The results also indicate that the root mean square (RMS) of the differences between the OSBs estimated based on the CAS- and German Aerospace Center (DLR)-provided DCB products are 0.32 ns for the global positioning system (GPS), 0.45 ns for the BeiDou navigation satellite system (BDS), 0.39 ns for GLONASS and 0.22 ns for Galileo.

In network real-time kinematic (NRTK) positioning, atmospheric delay information is critical for generating virtual observations at a virtual reference station (VRS). The traditional linear interpolation method (LIM) is widely used to obtain the atmospheric delay correction. However, even though the conventional LIM is robust in the horizontal direction of the atmospheric error, it ignores the influence of the vertical direction, especially for the tropospheric error. If the height difference between the reference stations and the rover is large and, subsequently, tropospheric error and height are strongly correlated, the performance of the traditional method is degraded for tropospheric delay interpolation at the VRS. Therefore, considering the height difference between the reference stations and the rover, a modified linear interpolation method (MLIM) is proposed to be applied to a conventional single Delaunay triangulated network (DTN). The systematic error of the double-differenced (DD) tropospheric delay in the vertical direction is corrected first. The LIM method is then applied to interpolate the DD tropospheric delay at the VRS. In order to verify the performance of the proposed method, we used two datasets from the American NOAA continuously operating reference stations (CORS) network with significant height differences for experiments and analysis. Results show that the DD tropospheric delay interpolation accuracy obtained by the modified method is improved by 84.1% and 69.6% on average in the two experiments compared to the conventional method. This improvement is significant, especially for low elevation satellites. In rover positioning analysis, the traditional LIM has a noticeable systematic deviation in the up component. Compared to the conventional method, the positioning accuracy of the MLIM method is improved in the horizontal and vertical directions, especially in the up component. The accuracy of the up component is reduced from tens of centimeters to a few centimeters and demonstrates better positioning stability.

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior.

Many Beidou navigation satellite system (BDS) receivers or boards provide dual-frequency measurements to conduct precise positioning and navigation for low-power consumption. Cycle-slip processing is a primary work to guarantee consistent, precise positioning with the phase data. However, the cycle-slip processing of BDS dual-frequency phases still follows with those of existing GPS methods. For single-satellite data, cycle-slip detection (CSD) with the geometry-free phase (GF) is disturbed by severe ionospheric delay variations, while CSD or cycle-slip repair (CSR) with the Melbourne–Wubbena combination (MW) must face the risk of the tremendous disturbance from large pseudorange errors. To overcome the above limitations, a new cycle-slip repair method for BDS dual-frequency phases (BDCSR) is proposed: (1) An optimal model to minimize the variance of the cycle-slip calculation was established to the dual-frequency BDS, after correcting the ionospheric variation with a reasonable and feasible way. (2) Under the BDS dual-frequency condition, a discrimination function was built to exclude the adverse disturbance from the pseudorange errors on the CSR, according to the rankings of the absolute epoch-difference GFs calculated by the searched cycle-slip candidates after correcting the ionospheric variation. Subsequently, many compared CSR tests were implemented in conditions of low and medium elevations during strong geomagnetic storms. Comparisons from the results of different methods show that: (1) The variations of ionospheric delays are intolerable in the cycle-slip calculation during the geomagnetic storm, and the tremendous influence from the ionospheric variation should be corrected before calculating the cycle-slip combination with the BDS dual-frequency data. (2) Under the condition of real dual-frequency BDS data during the geomagnetic storm, the actual success rate of the conventional dual-frequency CSR (CDCSR) by employing the optimized combinations, but absenting from the discrimination function, is lower than that of BDCSR by about 2%; The actual success rate of the CSD with MW (MWCSD), is lower than that of BDCSR by about 2%. (3) After adding gross errors of 0.7 m to all real epoch-difference pseudoranges epoch-by-epoch, results of CDCSR and MWCSD showed many errors. However, BDCSR achieved a higher actual success rate than those of CDCSR and MWCSD, about 43% and 16%, respectively, and better performance of refraining the disturbance of large pseudorange error on the cycle-slip determination was achieved in the BDCSR methodology.

In advance of precise positioning with phase data, cycle slip detection (CSD) is a basic work that should be implemented in phase data possessing. When the cycle slip occurred, cycle slip repair (CSR) can be taken to rebuild the continuity of phase data. Unfortunately, the large pseudorange errors can contaminate the combinations with the pseudoranges and phases such as the Hatch–Melbourne–Wubbena combination (HMW) and cause false CSD or wrong CSR results. On the other hand, the severe ionospheric time variation can deteriorate the epoch-difference geometry-free phase (GF), and tremendously interfere with the performances of CSD and CSR. To handle the aforementioned limitations, a global position system (GPS) triple-frequency CSR method (GTCSR) is proposed with two efficient treatments: (1) the significant ionospheric variations are corrected, and the influences from the residual ionospheric effects are minimized along with the observational noises; and (2) the impacts of large pseudorange errors are refrained by designing a discrimination function with a geometry-free and ionosphere-free phase to identify the correct cycle slip values. Consequently, CSR tests were conducted with three monitoring stations at different regions. First, during a strong geomagnetic storm, without correcting the ionospheric variation of CSR (WICSR) displayed obvious failures, and many epochs of cycle slip values from WICSR deviated from the known values. However, the results of the GTCSR were correct, and GTCSR presented a higher success rate than that of WICSR. Furthermore, for the real triple-frequency data, by adding gross errors of 2.5 m on all epoch-difference pseudoranges epoch by epoch, the conventional triple-frequency CSR with the optimized combinations (CTCSR) and the CSD with HMW (HMWCSD) showed many mistakes, where the results of CTCSR and HMWCSD on numerous epochs were inconsistent with the actual situations, but the success rate of GTCSR was significantly higher than those of CTCSR and HMWCSD. In summary, in the condition of the cutoff elevation being larger than 10 degrees, improved performances and higher success rates were achieved from GTCSR under environments of large pseudorange errors and severe ionospheric variations.

Under mixed sparse line-of-sight/non-line-of-sight (LOS/NLOS) conditions, how to quickly achieve high positioning accuracy is still a challenging task and a critical problem in the last dozen years. To settle this problem, we propose a constrained L1 norm minimization method which can reduce the effects of NLOS bias for improve positioning accuracy and speed up calculation via an iterative method. We can transform the TOA-based positioning problem into a sparse optimization one under mixed sparse LOS/NLOS conditions if we consider NLOS bias as outliers. Thus, a relatively good method to deal with sparse localization problem is L1 norm. Compared with some existing methods, the proposed method not only has the advantages of simple and intuitive principle, but also can neglect NLOS status and corresponding NLOS errors. Experimental results show that our algorithm performs well in terms of computational time and positioning accuracy.

Following the continuous and stable regional service of BDS2, the BDS3 officially announced its global service in July 2020. To fully take advantage of the new multi-frequency BDS3 signals in ionosphere sensing and positioning, it is essential to understand the characteristics of the differential code bias (DCB) of new BDS3 signals and BDS performance in global ionospheric maps (GIMs) estimation. This article presents an evaluation of the characteristics of 13 types of BDS DCBs and the accuracy of BDS-based GIM based on the data provided by the International GNSS Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS) for the first time. The GIMs and DCBs are estimated by the APM (Innovation Academy for Precision Measurement Science and Technology) method in a time efficient manner, which can be divided into two main steps. The first step is to produce GIMs based on BDS observations at the B1I, B2I and B3I signals, and the second step is to estimate DCBs among the other frequency bands by removing the ionospheric delay using the precomputed GIMs. Good agreement is found between the APM-based satellite DCB estimates and those from the Chinese Academy of Sciences (CAS) and the German Aerospace Center (DLR) at levels of 0.26 ns and 0.18 ns, respectively. The results, spanning one month, show that the stability of BDS DCB estimates among different frequency bands are related to the contributed observations, and the receiver DCB estimates represent larger STD values than the satellite DCB estimates. The differences in receiver DCB estimates between BDS2 and BDS3 are found to be related to the types of receivers and antennas and firmware version, and the bias of the JAVAD receivers reaches 1.03 ns. The results also indicate that the difference in the single-frequency standpoint positioning (SPP) accuracy using GPS-based and BDS-based GIMs for ionospheric delay corrections is less than 0.03 m in both the horizontal and vertical directions.

Errors in ultra-rapid UT1-UTC primarily affect the overall rotation of spatial datum expressed by GNSS (Global Navigation Satellite System) satellite ultra-rapid orbit. In terms of existing errors of traditional strategy, e.g., piecewise linear functions, for ultra-rapid UT1-UTC determination, and the requirement to improve the accuracy and consistency of ultra-rapid UT1-UTC, the potential to improve the performance of ultra-rapid UT1-UTC determination based on an LS (Least Square) + AR (Autoregressive) combination model is explored. In this contribution, based on the LS+AR combination model and by making joint post-processing/rapid UT1-UTC observation data, we propose a new strategy for ultra-rapid UT1-UTC determination. The performance of the new strategy is subsequently evaluated using data provided by IGS (International GNSS Services), iGMAS (international GNSS Monitoring and Assessment System), and IERS (International Earth Rotation and Reference Systems Service). Compared to the traditional strategy, the numerical results over more than 1 month show that the new strategy improved ultra-rapid UT1-UTC determination by 29–43%. The new strategy can provide a reference for GNSS data processing to improve the performance of ultra-rapid products.

The Global Navigation Satellite System (GNSS) Radio Occultation (RO) retrieved temperature and specific humidity profiles can be widely used for weather and climate studies in troposphere. However, some aspects, such as the influences of background data on these retrieved moist profiles have not been discussed yet. This research evaluates RO retrieved temperature and specific humidity profiles from Wegener Center for Climate and Global Change (WEGC), Radio Occultation Meteorology Satellite Application Facility (ROM SAF) and University Corporation for Atmospheric Research (UCAR) Boulder RO processing centers by comparing with measurements from 10 selected Integrated Global Radiosonde Archive (IGRA) radiosonde stations in different latitudinal bands over 2007 to 2010. The background profiles used for producing their moist profiles are also compared with radiosonde. We found that RO retrieved temperature profiles from all centers agree well with radiosonde. Mean differences at polar, mid-latitudinal and tropical stations are varying within ±0.2 K, ±0.5 K and from −1 to 0.2 K, respectively, with standard deviations varying from 1 to 2 K for most pressure levels. The differences between RO retrieved and their background temperature profiles for WEGC are varying within ±0.5 K at altitudes above 300 hPa, and the differences for ROM SAF are within ±0.2 K, and that for UCAR are within 0.5 K at altitudes below 300 hPa. Both RO retrieved and background specific humidity above 600 hPa are found to have large positive differences (up to 40%) against most radiosonde measurements. Discrepancies of moist profiles among the three centers are overall minor at altitudes above 300 hPa for temperature and at altitudes above 700 hPa for specific humidity. Specific humidity standard deviations are largest at tropical stations in June July August months. It is expected that the outcome of this research can help readers to understand the characteristics of moist products among centers.

Because of the frequency division multiple access (FDMA) technique, Russian global navigation satellite system (GLONASS) observations suffer from pseudo-range inter-channel biases (ICBs), which adversely affect satellite clock offset estimation. In this study, the GLONASS pseudo-range ICB is treated in four different ways: as ignorable parameters (ICB-NONE), polynomial functions of frequency (ICB-FPOL), frequency-specific parameters (ICB-RF), and satellite-specific parameters (ICB-RS). Data from 110 international global navigation satellite system (GNSS) service stations were chosen to obtain the ICBs and were used for satellite clock offset estimation. The ICBs from the different schemes varied from −20 ns to 80 ns. The ICB-RS model yielded the best results, improving the clock offset accuracy from 300 ps to about 100 ps; it could improve the GLONASS precise point positioning (PPP) accuracy and the converging time by approximately 50% and 30%, respectively. Along similar lines, we introduced the GPS-ICB parameters in the process of GPS satellite clock estimation and GPS/GLONASS PPP, as ICBs may exist for GPS because of different chip shape distortions among GPS satellites. This possibility was found to be the case. Further, the GPS-ICB magnitude ranged from −2 ns to 2 ns, and the estimated satellite clock offsets could improve the accuracy of the GPS and combined GPS/GLONASS PPP by 10%; it also accelerated the converging time by more than 15% thanks to the GPS-ICB calibration.

At present, Global Position System (GPS) navigation ephemeris mainly broadcasts satellite orbits with meter-level precision for standard point positioning and precise relative positioning. With the rapid development of real-time precise point positioning (PPP), the receiver or smartphone has begun to demand more and more convenient, continuous, and reliable access to real-time services of precise orbits. Therefore, this study proposes a solution of utilizing the 18-parameter ephemeris to directly broadcast ultra-rapid precise predicted orbits with centimeter-level precision for real-time PPP. For the first time in GPS, the difference in the PPP results between the precise orbits and the calculated orbits broadcasted from the generated ephemeris parameters is supplied as follows: (1) During the validity period of 2 h, root mean square (RMS) of the relative distance offsets between the results of PPP with the precise orbits and the results of PPP the 18-parameter ephemeris is only 0.0098 m. (2) Within 15 min after the validity period of 2 h, RMS of the relative distance offsets between the results of PPP with the precise orbits and the results of PPP with the predicted orbits by 18-parameter ephemeris is only 0.0057 m. Consequently, the 18-parameter ephemeris is feasible and advisable to broadcast precise predicted orbits for real-time PPP applications. Compared with the classic precise orbits broadcast mode with the orbit corrections defined by the radio technical commission for maritime services standards 10403.2 (RTCM), the mode of broadcasting the precise orbits with the 18-parameter ephemeris achieved the following improvements in convenience, continuity, and reliability: (1) The calculation of satellite position is the same as that of the navigation ephemeris excluding the additional correction operations required to the RTCM; (2) the amount of broadcast parameters was reduced by 20 times; (3) the length of the validity period was expanded 120 times, where the longer valid period helped to overcome the orbit corrections loss caused by RTCM stream failures; and (4) within 15 min after the validity period, the predicted orbits with an accuracy of 2 cm could still be provided by the 18-parameter ephemeris, which can ensure the real-time services of precise orbits in the case of a 15 min communication interruption of the RTCM orbit correction data stream.

The cycle slip detection (CSD) and cycle slip repair (CSR) are easily affected by ionospheric delay and observational noise. Aiming at mitigating the above disadvantage, a new BeiDou navigation satellite system (BDS) triple-frequency CSR method (BTCSR) is proposed for the undifferenced phase. BTCSR learns from the classic triple-frequency CSR (CTCSR), with combinations of phases and pseudoranges in correcting ionospheric delay and optimizing observational noise. Different from CTCSR, though, BTCSR has made the following improvements: (1) An optimal model of calculating cycle slip combination is established, which further takes into account the minimization of the effect of residual ionospheric error after the correction. The calculation of cycle slip combination is obtained with the root mean squared errors (0.0646, 0.1261, 0.1069) of cycles, resulting in CSR success rate of 99.9927%, and the wavelengths (4.8842,3.5738,8.1403) of m. (2) A discriminant function is added to guarantee the CSR correctness. This function utilizes epoch-difference value of the ionosphere-free and geometry-free phase to select the correct cycle slip value, which eliminates the interference of large pseudorange errors in determining the final cycle slip. Consequently, the performances of BTCSR and CTCSR have been compared. For the real BDS pseudorange observation with additional 1.5 m errors, which can cover situations of 99.96% pseudorange noise, results of CTCSR show failure, but results of BTCSR keep correct. Moreover, BTCSR has made the following improvements relative to the geometry-free cycle slip detection method (GFCSD) and Melboune–Wubbena cycle slip combination detection method (MWCSD): (1) During a moderate magnetic storm of level 6, CSR testing, with the BDS monitoring station in a low latitude region, showed that some failures occur in GFCSD because of severe ionospheric variation, but BTCSR could correctly identify and fix cycle slips. (2) For the BDS observation data with an additional 1.5 m error on the actual pseudoranges, MWCSD exhibited failures, but the repair results of BTCSR were correct and reliable. (3) For the special slips of (0,59,62) cycles, and equal slips of (1,1,1) cycles on (B1,B2,B3), that are hard to detect by GFCSD and MWCSD, respectively, BTCSR could repair these correctly. Finally, BTCSR obtains reliable repair results under large pseudorange errors and severe ionospheric variations, and the cut-off elevation larger than 10 degrees is the suggested background.

The Global Navigation Satellite System (GNSS) is becoming important for monitoring the variations in the earth's ionosphere based on the total electron content (TEC) and ionospheric electron density (IED). The Crustal Movement Observation Network of China (CMONOC), which includes GNSS stations across mainland China, enables the continuous monitoring of the ionosphere over China as accurately as possible. A series of approaches for GNSS-based ionospheric remote sensing and software has been proposed and developed by the Institute of Geodesy and Geophysics (IGG) in Wuhan. Related achievements include the retrieval of ionospheric observables from raw GNSS data, differential code biases estimations in satellites and receivers, models of local and regional ionospheric TEC, and algorithms of ionospheric tomography. Based on these achievements, a software for processing GNSS data to determine the variations in ionospheric TEC and IED over China has been designed and developed by IGG. This software has also been installed at the CMONOC data centers belonging to the China Earthquake Administration and China Meteorological Administration. This paper briefly introduces the related research achievements and indicates potential directions of future work.

Abnormal information of satellite orbits inevitably appears in the broadcast ephemeris. Failure to obtain unhealthy information on GPS satellite orbits in precise orbit determination (POD) degrades GPS service performance. At present, the reliable unhealthy information published by the Center for Orbit Determination in Europe (CODE) is usually used, but it has at least one-day latency, and the current level of unhealthy information cannot fully meet the requirements of rapid and real-time geodetic applications, especially for non-IGS (International global navigation satellite systems (GNSS) Service) analysis centers and BeiDou navigation satellite system (BDS) users. Furthermore, the unhealthy orbit information detected by the traditional method, which is based on the synchronized pseudo-range residuals and regional observation network, cannot meet the requirement of setting separate sub-arcs in POD. In view of these problems, we propose a three-step method for determining unhealthy time periods of GPS satellite orbit in broadcast ephemeris during POD to provide reliable unhealthy information in near-real time. This method is a single-epoch solution, and it can detect unhealthy time periods in each sampling of observation in theory. It was subsequently used to detect unhealthy time periods for satellites G09 and G01 based on the 111 globally distributed tracking stations in the IGS. The performance of the new method was evaluated using cross-validation. Based on the test results, it detected an orbital leap for G09 in the broadcast ephemeris from 09:59:42 to 14:00:42 on 25 August 2017. Compared to the traditional method, the unhealthy start time using the three-step method was in better agreement with the information provided by CODE’s satellite crux files. G01 did not appear to have an orbital leap on the specified date, but it was misjudged by the traditional method. Furthermore, compared to the traditional method, the three-step method can perform unhealthy time period detection for a satellite all day long. In addition, precise orbit determination for unhealthy satellites is realized successfully with the unhealthy orbit arc information identified in this study. Compared to the CODE orbit, the root mean square and standard deviation of the new method for G09 are less than 2 cm, and the three-step method shows an improvement in accuracy compared with the traditional method. From the above results, it can be seen that this study can provide a feasible approach to meet the real-time unhealthy time period detection requirements of a satellite orbit in a broadcast ephemeris during POD. Furthermore, compared to waiting for updates of CODE’s satellite crux files or for accumulating delayed observation data, it has the potential to provide additional information in the process of generating ultra-rapid/real-time orbits.

We focused on the researches of two models used for Jason-3 precise orbit determination (POD)—Jason-3 attitude modes and receiver phase center variation (PCV) model. A combined attitude mode for the Jason-3 satellite is designed based on experimental analysis used in some special cases, such as in the absence of quaternions or when inconvenient to use. We researched the linking of satellite attitude with antenna phase center. Specially, to verify the validity of the combined attitude, we analyzed the effects of different attitude modes on receiver phase center offset (PCO) estimation, PCO correction and POD. Meanwhile, the difference analysis of PCO correction based on attitude modes also contains the combined attitude modeling processes. The POD results showed that the orbital accuracies with the combined attitude are slightly more stable than those with attitude event file. By introducing receiver PCVs into POD, the mean residuals root-mean-square (RMS) is reduced by 1.9 mm and orbital 3D-RMS position difference is improved by 5.7 mm. The eight schemes were designed to integratedly verify the effectiveness of different attitude modes and receiver PCVs model. The results conclude that the accuracy using the combined attitude is higher than that of event file, which also prove the feasibility of the combined attitude in integrated POD and it can be as a revision of attitude event file. Using all mentioned attitude modes, the orbital accuracy by introducing PCVs can be improved by the millimeter level. The integrated effects of attitude modes and receiver PCVs on POD are almost consistent with the effects of a single variable. The optimal results of Jason-3 POD indicate that orbital mean radial RMS is close to 1 cm, and the 3D-RMS position difference is within 3 cm.

The predicted parts of ultra-rapid orbits are important for (near) real-time Global Navigation Satellite System (GNSS) precise applications; and there is little research on GPS/GLONASS/BDS/Galileo/QZSS five-system ultra-rapid precise orbit determination; based on the one-step method and double-difference observation model. However; the successful development of a software platform for solving five-system ultra-rapid orbits is the basis of determining and analyzing these orbits. Besides this; the different observation models and processing strategies facilitate to validate the reliability of the various ultra-rapid orbits. In this contribution; this paper derives the double-difference observation model of five-system ultra-rapid precise orbit determination; based on a one-step method; and embeds this method and model into Bernese v5.2; thereby forming a new prototype software platform. For validation purposes; 31 days of real tracking data; collected from 130 globally-distributed International GNSS Service (IGS) multi-GNSS Experiment (MGEX) stations; are used to determine a five-system ultra-rapid precise orbit. The performance of the software platform is evaluated by analysis of the orbit discontinuities at day boundaries and by comparing the consistency with the MGEX orbits from the Deutsches GeoForschungsZentrum (GFZ); between the results of this new prototype software platform and the ultra-rapid orbit provided by the International GNSS Monitoring and Assessment System (iGMAS) analysis center (AC) at the Institute of Geodesy and Geophysics (IGG). The test results show that the average standard deviations of orbit discontinuities in the three-dimension direction are 0.022; 0.031; 0.139; 0.064; 0.028; and 0.465 m for GPS; GLONASS; BDS Inclined Geosynchronous Orbit (IGSO); BDS Mid-Earth Orbit (MEO); Galileo; and QZSS satellites; respectively. In addition; the preliminary results of the new prototype software platform show that the consistency of this platform has been significantly improved compared to the software package of the IGGAC.

Signal-in-space (SIS) User Range Error (URE) is one of the major error sources for BeiDou Navigation Satellite System (BDS) applications and can reach tens of meters or even more. Therefore, real-time monitoring of SIS anomalies has a great realistic significance to guarantee the safety of users. According to an analysis of the BDS navigation messages, it showed that the User Range Accuracy (URA) index could not reflect the change of URE when it was abnormal. The conventional models using the relationship between URA and URE to monitor SIS anomalies are not suitable to the present BDS. Therefore, we use a prior information of SIS URE derived from ground observational data instead of URA to monitor BDS SIS anomalies. In order to realize the corresponding functions, we analysed the distribution of SIS UREs and obtained their prior models. Then, the monitoring threshold is determined using the prior models and a confidence interval instead of URA. The scheme was tested by applying to BDS SIS anomalies monitoring based on 13 ground tracking stations. The performance of this method was assessed by comparison with the satellite-health indicators from broadcast ephemeris. The results confirm that the method developed in this paper can rightly and timely detect abnormal SIS.

The failure to detect anomalies and maneuvering of the orbits of navigation satellite sensors will deteriorate the performance of positioning and orbit determination. Motivated by the influence of the frequent maneuvering of BDS GEO and IGSO satellites, this paper analyzes the limitations of existing methods, where BDS orbit maneuvering and anomalies can be detected, and develops a method to solve this problem based on the RMS model of orbit mutual differences proposed in this paper. The performance of this method was assessed by comparison with the health flag of broadcast ephemeris, precise orbit products of GFZ, the O-C values of a GNSS station and a conventional method. The results show that the performance of the method developed in this paper is better than that of the conventional method when the periodicity and trend items are obvious. Meanwhile, three additional verification results show that the method developed in this paper can find error information in the merged broadcast ephemeris provided by iGMAS. Furthermore, from the testing results, it can be seen that the detection of anomaly and maneuvering items do not affect each other based on the robust thresholds constructed in this paper. In addition, the precise orbit of the maneuvering satellites can be determined under the circumstances that the maneuver information detected in this paper is used, and the root mean square (RMS) of orbit overlap comparison for GEO-03/IGSO-03 in Radial, Along, Cross, 1D-RMS are 0.7614/0.4460 m, 1.8901/0.3687 m, 0.3392/0.2069 m, 2.0657/0.6145 m, respectively.

In this study, the characteristics of the total electron content (TEC) fluctuations and their regional differences over China were analyzed by utilizing the rate of the TEC index (ROTI) based on GPS data from 21 reference stations across China during a solar cycle. The results show that there were significant regional differences at different latitudes. Strong ionospheric TEC fluctuations were usually observed at lower latitudes in southern China, where the occurrence of TEC fluctuations demonstrated typical nighttime- and season-dependent (equinox months) features. This phenomenon was consistent with the ionospheric scintillation characteristics of this region. Additionally, compared to low-latitude China, the intensity of TEC fluctuations over mid-latitude China was significantly weaker, and the occurrence of TEC fluctuations was not a nighttime-dependent phenomenon. Moreover, the intensity of TEC fluctuations was much stronger during high solar activity than during low solar activity. Furthermore, the summer-dependent characteristics of TEC fluctuations gradually emerged over lower mid-latitude areas as equinox characteristics weakened. Similar to the equinox characteristics, the summer-dependent characteristics gradually weakened or even disappeared with the increasing latitude. Relevant discussions of this phenomenon are still relatively rare, and it requires further study and analysis.

Global navigation satellite sensors can transmit three frequency signals. When the classical three-carrier ambiguity resolution (TCAR) is applied to long baselines of hundreds of kilometres, the narrow-lane integer ambiguity resolution (IAR) is affected by the remaining double-differenced (DD) ionospheric delays. As such, large amounts of observational data are typically needed for successful recovery. To strengthen ionospheric delays, we analysed the combination of three frequency signals and a new ambiguity-free ionospheric combination where the least amount of noise is defined, which is enhanced with epoch-differenced ionospheric delays to provide better absolute ionospheric delay and temporal change. To optimize ionosphere estimations, we propose defining the optimal smoothing length, and also propose a strategy to diagnose wrongly determined ionospheric estimations. With such ionospheric information, we can obtain the ionosphere-weighted model by incorporating the ionospheric information to the geometry-based model and use the real triple-frequency observations to evaluate our method. Our results show that the precision of ionospheric estimations from our new ionospheric model is 25% higher than that from the current combination method and that it can provide real-time smoothed ionospheric delay with magnitudes defined to the nearest centimetre. Additionally, using ionospheric estimation as a constraint, the ionosphere-weighted model requires 20% less time to generate the first-fixed solution (TFFS) than the geometry-based model.

By August 2016, 5 new-generation BeiDou satellites (BeiDou-3) have successfully been launched. The observations of a very limited number of 9 International GNSS (Global Navigation Satellite System) Monitoring and Assessment Service (iGMAS) stations and 52 Multi-GNSS Experiment (MGEX) stations from 16 July to 14 August 2016 are processed to determine the orbits of BeiDou-3 and BeiDou-2 satellites, respectively. The internal consistency and satellite laser ranging (SLR) validations are conducted for the orbit validation. BeiDou-3 MEO (Medium Earth Orbit) (C33 and C34) have larger root mean square (RMS) values than those BeiDou-3 IGSO (C31 and C32), whereas BeiDou-2 MEO satellites have smaller RMS values than the BeiDou-2 IGSO satellites. Furthermore, BeiDou-3 IGSO and BeiDou-2 satellites have RMS values at identical levels, whereas BeiDou-3 MEO satellites have larger RMS values than the BeiDou-2 MEO satellites. The RMS residuals are approximately 10 cm in the radial component and approximately 25 cm in the along component for BeiDou-3 IGSO satellites. For BeiDou-3 MEO satellites, the RMS residuals are approximately 40 cm in the radial component and approximately 60 cm in the along component. The SLR validation reports that the orbit radial component can reach an accuracy on the level of 1 decimeter and 4 decimeters for BeiDou-3 IGSO and MEO, respectively.

The Beidou navigation satellite system is a very important sensor for positioning in the Asia-Pacific region. The Beidou inclined geosynchronous orbit (IGSO) and medium Earth orbit (MEO) satellites have been analysed in some studies previously conducted by other researchers; this paper seeks to gain more insight regarding the geostationary earth orbit (GEO) satellites. Employing correlation analysis, Fourier transformation and wavelet decomposition, we validate whether there is a systematic bias in their multipath combinations. These biases can be observed clearly in satellites C01, C02 and C04 and have a great correlation with time series instead of elevation, being significantly different from those of the Beidou IGSO and MEO satellites. We propose a correction model to mitigate this bias based on its daily periodicity characteristic. After the model has been applied, the performance of the positioning estimations of the eight stations distributed in the Asia-Pacific region is evaluated and compared. The results show that residuals of multipath series behaves random noise; for the single point positioning (SPP) and precise point positioning (PPP) approaches, the positioning accuracy in the upward direction can be improved by 8 cm and 6 mm, respectively, and by 2 cm and 4 mm, respectively, for the horizontal component.

Tropospheric delays are one of the main sources of errors in the Global Navigation Satellite System (GNSS). They are usually corrected by using tropospheric delay models, which makes the accuracy of the models rather critical for accurate positioning. To provide references for suitable models to be chosen for GNSS users in China, we conduct herein a comprehensive study of the performances of the IGGtrop, EGNOS and UNB3m models in China. Firstly, we assess the models using 5 years’ Global Positioning System (GPS) derived Zenith Tropospheric Delay (ZTD) series from 25 stations of the Crustal Movement Observation Network of China (CMONOC). Then we study the effects of the models on satellite positioning by using various Precise Point Positioning (PPP) cases with different tropospheric delay resolutions, the observation data processed in PPP is from 21 base stations of CMONOC for a whole year of 2012. The results show that: (1) the Root Mean Square (RMS) of the IGGtrop model is about 4.4 cm, which improves the accuracy of ZTD estimations by about 24% for EGNOS and 19% for UNB3m; (2) The positioning error in the vertical component of the PPP solution obtained by using the IGGtrop model is about 15.0 cm, which is about 30% and 21% smaller than those of the EGNOS and UNB3m models, respectively. In summary, the IGGtrop model achieves the best performance among the three models in the Chinese region.