International Global Navigation Satellite System Research Articles

Inter-Satellite Link Enhanced Orbit Determination for BeiDou-3

The third generation of the BeiDou navigation satellite system (BDS-3) is a global navigation system, and is expected to be in full operation by 2020. High-precision orbits are a precondition for BDS-3 to provide a highly accurate service, which needs a global tracking and monitoring capability for the operational satellites. However, it is difficult for BDS to construct global ground monitoring stations. Fortunately, Ka-band Inter-Satellite Link (ISL) antennae fitted to the BDS-3 satellites can be used to extend the visible arc of the Medium Earth Orbit (MEO) satellites and to enhance the ground stations for orbit determination. This paper analyses the ISL-enhanced orbit determination for eight BDS-3 satellites, using the data from ten Chinese domestic stations and 13 international Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS) overseas stations. The results show that the Three-Dimensional (3D) position Root Mean Square (RMS) error of the Overlapping Orbit Differences (OODs) is approximately 1 m when only ten regional stations are used. When the ISL measurements are added, the 3D position RMS error is decreased to 0·5 m, and the accuracy of the 24-hour orbit prediction can also be improved from 2 m to 0·7 m, which is even better than that of the orbits determined using globally distributed stations. It can be expected that with the subsequent launch of BDS-3 satellites and the increasing number of ISLs, the advantage of the ISL enhanced orbit determination will become more significant.

A Sub-Regional Extraction Method of Common Mode Components from IGS and CMONOC Stations in China

There is always a need to extract more accurate regional common mode component (CMC) series from coordinate time series of Global Positioning System (GPS) stations, which would be of great benefit to describe the deformation features of the Earth’s surface with more reliability. For this purpose, this paper combines all 11 International Global Navigation Satellite System (GNSS) Service (IGS) stations in China with over 70 stations selected from the Crustal Movement Observation Network of China (CMONOC) to compute CMC series of IGS stations by using a principal component analysis (PCA) method under cases of one whole region and eight sub-regions. The comparison results show that the percentage of first-order principal component (PC1) in North, East and Up components increase by 10.8%, 16.1% and 25.1%, respectively, after dividing the whole China region into eight sub-regions. Meanwhile, Root Mean Square (RMS) reduction rates of residual series that have removed CMC also improve obviously after partitioning. In addition, we compute displacements of these IGS stations caused by environmental loadings (including atmospheric pressure loading, non-tidal oceanic loading and hydrological loading) to analyze their contributions to the non-linear variation in GPS coordinate time series. The comparison result shows that the method we raise, PCA filtering in sub-regions, performs better than the environmental loading corrections (ELCs) in improving the signal-to-noise ratio (SNR) of GPS coordinate time series. This paper raises new criteria for selecting appropriate CMONOC stations around IGS stations when computing sub-regional CMC, involving three criteria of interstation distance, geology and self-condition of stations themselves. According to experiments, these criteria are implemental and effective in selecting suitable stations, by which to extract sub-regional CMC with higher accuracy.

Assessment of BeiDou-3 and Multi-GNSS Precise Point Positioning Performance.

With the launch of BDS-3 and Galileo new satellites, the BeiDou navigation satellite system (BDS) has developed from the regional to global system, and the Galileo constellation will consist of 26 satellites in space. Thus, BDS, GPS, GLONASS, and Galileo all have the capability of global positioning services. It is meaningful to evaluate the ability of global precise point positioning (PPP) of the GPS, BDS, GLONASS, and Galileo. This paper mainly contributes to the assessment of BDS-2, BDS-2/BDS-3, GPS, GLONASS, and Galileo PPP with the observations that were provided by the international Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS). The Position Dilution of Precision (PDOP) value was utilized to research the global coverage of GPS, BDS-2, BDS-2/BDS-3, GLONASS, and Galileo. In particular, GPS-only, BDS-2-only, BDS-2/BDS-3, GLONASS-only, Galileo-only, and multi-GNSS combined PPP solutions were analyzed to verify the capacity of the PPP performances in terms of positioning accuracy, convergence time, and zenith troposphere delay (ZTD) accuracy. In view of PDOP, the current BDS and Galileo are capable of global coverage. The BDS-2/BDS-3 and Galileo PDOP values are fairly evenly distributed around the world similar to GPS and GLONASS. The root mean square (RMS) of positioning errors for static BDS-2/BDS-3 PPP and Galileo-only PPP are 10.7, 19.5, 20.4 mm, and 6.9, 18.6, 19.6 mm, respectively, in the geographic area of the selected station, which is the same level as GPS and GLONASS. It is worth mentioning that, by adding BDS-3 observations, the positioning accuracy of static BDS PPP is improved by 17.05%, 24.42%, and 35.65%, and the convergence time is reduced by 27.15%, 27.87%, and 35.76% in three coordinate components, respectively. Similar to the static positioning, GPS, BDS-2/BDS-3, GLONASS, and Galileo have the basically same kinematic positioning accuracy. Multi-GNSS PPP significantly improves the positioning performances in both static and kinematic positioning. In terms of ZTD accuracy, the difference between GPS, BDS-2/BDS-3, GLONASS, and Galileo is less than 1 mm, and the BDS-2/BDS-3 improves ZTD accuracy by 20.48% over the BDS-2. The assessment of GPS, BDS-2, BDS-2/BDS-3, GLONASS, Galileo, and multi-GNSS global PPP performance are shown to make comments for the development of multi-GNSS integration, global precise positioning, and the construction of iGMAS.

Usability of the Benford’s law for the results of least square estimation

Benford’s law (BL), also known as the first-digit or significant-digit law, is an intriguing pattern in data sets, considers the frequency of occurrence of the first digits, which are not uniformly distributed as might be expected, conversely follow a specified theoretical distribution. According to BL, the occurrence of first non-zero digit in a numerical data, which is generated or found in nature, depends on a logarithmic distribution. Least square estimation (LSE) method is mostly preferred for the estimation of the unknown parameters from different types of geodetic data. The residuals and the normalized residuals of the LSE method, which follow normal distribution and expected values of them are zero are used in outlier detection problem. In this study, BL is investigated for residuals and the normalized residuals estimated from LSE method. Three types of geodetic data are used: (1) simulated regression models, (2) global positioning system (GPS) data, (3) leveling network. The first group data sets are simulated based on linear regression and univariate models and each simulated group is generated for a number of 100, 1000, and 10,000 samples. To generate second group, an international global navigation satellite system (GNSS) service (IGS) station data (ISTA) is processed by kinematic PPP approach using GIPSY OASIS II v6.4 software. Here, the observation duration of GPS data is 4 days. For the last data, a leveling network with 55 points involving 110 observations of height differences is simulated. BL has been applied to the residuals (v) and normalized residuals (w) estimated from LSE method. Goodness-of-fit test has been implemented to determine whether a population has a specified BL distribution or not. This test is based on how good a fit we have between the frequency of occurrence of residuals and normalized residuals in an observed sample and the expected frequencies obtained from the hypothesized distribution. The results depending on the statistical test show that each data set (residuals and normalized residuals) used in this study follows BL.

Accuracy of Deformation Rates from Campaign GPS Surveys Considering Extended Observation Session and Antenna Set-Up Errors

GPS campaign measurements are still in use in the monitoring of ground deformation. Campaign measurements are frequently referred to because installing permanent stations are costly, and they cannot be installed at the desired density. Using the data from the International Global Navigation Satellite Systems (GNSS) Service (IGS) permanent GPS stations, the duration, sampling interval, etc. of the campaign measurements can be simulated. Thus, the contribution of the campaign data to the monitoring of the ground deformation can be evaluated. In this study, we carried out an experiment with the aim of determining the deformation of tectonic plates at the selected IGS stations more accurately considering by extending the observation duration to a full 24 h length. We also made an attempt to take into consideration the antenna set up errors developing a scenario referring to the information available in the literature. We have decimated the continuous data of 40 globally scattered IGS stations into monthly intervals between 2012 and 2016 and estimated the deformation rates at the IGS stations from a continuous time series of four years. The continuous time series solutions for those stations were produced by the Jet Propulsion Laboratory (JPL), NASA. We compare velocities (i.e., the deformation rates) determined from GPS campaigns (in which the sampling was performed monthly and four-monthly) with those of the continuous data. The major conclusion of this study is that the vertical velocity estimation accuracy of the GPS campaign measurements had been improved by about 85% by extending the session duration to 24 h. The repetition interval of GPS campaign measurements as per one observation every four months produced only slightly coarser accuracy (i.e., on the average 8% poorer) than those of the measurements repeated once every month.

Current Activity of the Long Point Fault in Houston, Texas Constrained by Continuous GPS Measurements (2013–2018)

The Long Point Fault is one of the most active urban faults in Houston, Texas, which belong to a complex system of normal growth faults along the Texas Gulf Coast. To assess the activity of the Long Point Fault, a GPS array with 12 permanent stations was installed along the two sides of the 16-km-long fault scarp in 2013. GPS datasets were processed with the Precise Point Positioning (PPP) and Double-Difference (DD) methods. The daily PPP solutions with respect to the International Global Navigation Satellite System (GNSS) Reference Frame 2014 (IGS14) were converted to the Stable Houston Reference Frame (Houston16). The six-year continuous GPS observations indicate that the Long Point Fault is currently inactive, with the rates of down-dip-slip and along-strike-slip being below 1 mm/year. The Long Point Fault area is experiencing moderate subsidence varying from 5 to 11 mm/year and a coherent horizontal movement towards the northwest at a rate of approximately 2 to 4 mm/year. The horizontal movement is induced by the subsidence bowl that has been developing since the 1980s in the Jersey Village area. Current surficial damages in the Long Point Fault area are more likely caused by ongoing uneven subsidence and its induced horizontal strains, as well as the significant seasonal ground deformation, rather than deep-seated or tectonic-controlled fault movements. The results from this study suggest a cause-and-effect relationship between groundwater withdrawals and local faulting, which is pertinent to plans for future urban development, use of groundwater resources, and minimization of urban geological hazards.

A new datum jump detection and mitigation method of Real-Time Service (RTS) clock products

Real-time orbit and clock products are crucial for real-time precise point positioning (PPP) applications. The International Global Navigation Satellite System (GNSS) Service (IGS) launched the Real-Time Service (RTS) in 2013 to provide real-time satellite orbit and clock products which have since found wide applications. Currently, the IGS RTS provides two different types of satellite orbit and clock products: the products generated from individual Analysis Centers such as CLK01, CLK22 and CLK90 and the combination products such as IGS01 and IGS03. These IGS RTS products are different in terms of precision and reliability. First, we verify that the phenomenon of clock datum jumps is obvious in IGS01, which has not been considered by the GNSS community when applying the IGS01 product to the real-time PPP. Afterward, the causes of the clock datum jump are investigated. The results indicate that a switchover of the reference product or a datum jump in the reference product will cause a clock datum jump. In order to solve the clock datum jumps issue, a new clock datum jump detection and mitigation algorithm is proposed. Real-time kinematic PPP experiments are then carried out to validate the proposed satellite clock detection and mitigation algorithm. The positioning results with 27 globally distributed IGS stations show that the root mean square improvements in the north, east and up components are 61.5%, 36.5% and 55.1% after detecting and mitigating the datum jumps.

A Three-Step Method for Determining Unhealthy Time Period of GPS Satellite Orbit in Broadcast Ephemeris and Its Preliminary Applications for Precise Orbit Determination

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.

A Real-Time Precipitable Water Vapor Monitoring System Using the National GNSS Network of China: Method and Preliminary Results

The development of the International Global Navigation Satellite System (GNSS) Service (IGS) Real-Time Pilot Project shows promise for real-time GNSS-based precipitable water vapor (GNSS-PWV) retrieval. For better applications of real-time GNSS meteorology over China, a method is proposed to establish a real-time GNSS-PWV monitoring system using the national GNSS network of China. The prototype system generating the zenith tropospheric delay (ZTD) is based on the real-time precise point positioning technique, in which the real-time data streams and state-space-representative satellite orbit and clock corrections are processed. The parallel computing technology is embedded in the system for decoding and processing the real-time data streams, which enables the multistation processing mode and improves the computing efficiency. At the initial phase, a total of 215 global positioning system (GPS) stations from the crustal movement observation network of China are used to generate the real-time GPS-ZTDs. The pressure data for separating the zenith wet delay (ZWD) from the ZTD are obtained from the collocated meteorological sensors. An advanced weighted mean temperature model, namely, Gridded-Mixed Tm , is adopted in the system to determine the conversion factor “Π” (converting GPS-ZWD to GPS-PWV) in real-time mode with the measured temperatures input. The generated real-time GPS-PWV products have a time resolution of 5 min. To validate the system performance, comparisons between the real-time GPS-PWV and the PWVs derived from nearby radiosonde data (RS-PWV) and reanalysis data from the National Centers for Environmental Prediction (NCEP)-Department of Energy Reanalysis II (NCEP-II-PWV) are conducted over a period of 83 days. The comparisons show a mean bias of −0.1 mm with a root mean square (RMS) of 1.7 mm between the real-time GPS-PWV and RS-PWV. The agreement between the real-time GPS-PWV and NCEP-II-PWV is approximately 2.0 mm in terms of RMS and has a mean bias of −0.8 mm. These results confirm that the established system can be used for real-time PWV monitoring across China.

Performance Evaluation of the CNAV Broadcast Ephemeris

The new Global Positioning System (GPS) Civil Navigation Message (CNAV) has been transmitted by Block IIR-M and Block IIF satellites since April 2014, both on the L2C and L5 signals. Compared to the Legacy Navigation Message (LNAV), the CNAV message provides six additional parameters (two orbit parameters and four Inter-Signal Correction (ISC) parameters) for prospective civil users. Using the precise products of the International Global Navigation Satellite System Service (IGS), we evaluate the precision of satellite orbit, clock and ISCs of the CNAV. Additionally, the contribution of the six new parameters to GPS Single Point Positioning (SPP) is analysed using data from 22 selected Multi-Global Navigation Satellite System Experiment (MGEX) stations from a 30-day period. The results indicate that the CNAV/LNAV Signal-In-Space Range Error (SISRE) and orbit-only SISRE from January 2016 to March 2018 is of 0·5 m and 0·3 m respectively, which is improved in comparison with the results from an earlier period. The ISC precision of L1 Coarse/Acquisition (C/A) is better than 0·1 ns, and those of L2C and L5Q5 are about 0·4 ns. Remarkably, ISC correction has little effect on the single-frequency SPP for GPS users using civil signals (for example, L1C, L2C), whereas dual-frequency SPP with the consideration of ISCs results have an accuracy improvement of 18·6%, which is comparable with positioning accuracy based on an ionosphere-free combination of the L1P (Y) and L2P (Y) signals.

Performance analysis of quiet and disturbed time ionospheric TEC responses from GPS-based observations, IGS-GIM, IRI-2016 and SPIM/IRI-Plas 2017 models over the low latitude Indian region

This paper focuses on the variability of ionospheric Total Electron Content (TEC) over low latitude Indian sub-continental region during the geomagnetically quiet and disturbed periods under the high solar activity phase (years 2012–2015) of the 24th solar cycle. The study is carried out with Global Positioning System (GPS) observations from four International Global Navigation Satellite System Service (IGS) stations, aligned in a longitudinal fashion from magnetic equatorial location to beyond Equatorial Ionization Anomaly (EIA) crest latitude across Indian longitude. The corresponding values are extracted by four-point Inverse Distance Weighted (IDW) interpolation of TEC from IGS-Global Ionosphere Maps (IGS-GIMs) and by running the globally acceptable empirical ionosphere models: International Reference Ionosphere (IRI-2016) and Standard Plasmasphere Ionosphere Model (SPIM/IRI-Plas 2017). Apart from the manifestations of broader daytime diurnal peak TEC, its double-humped structure, EIA, winter anomaly/seasonal anomaly, and storm-time alterations, the study tried to probe the model performances with respect to the GPS based TEC observations. While GIM-TEC portrays a systematically varying magnitude for a particular location, the underestimation (equatorial latitude) and overestimation (higher latitude) is being witnessed by IRI model in the diurnal and seasonal variations. However, SPIM-2017 manifests an all-time overestimated TEC irrespective of time and season though the variation pattern replicates the GPS-TEC observations. Concerning storm-time response, the sub-models embedded in IRI/SPIM hardly reveal a remarkable alteration in the regular TEC variation except for trivial divergences in the IRI outcomes. In spite of compelling timely improvements in climatological representations, the limited storm-time response in IRI/SPIM models attracts the attention for further improvements in the existing primitive storm model specifications. Moreover, the intentional ingestion of external GPS-TEC into the SPIM-2017 model resulted in an exceptional improvement (about 75%) in the model prediction with improved correlation coefficients. The results from this study would complement a realistic global climatological representation of ionosphere for a faithful estimation of ionospheric delay error in radio signal applications. Finally, our results emphasize the flexibility of scopes in SPIM-2017 model towards external ingestions of observed ionospheric parameters. The ingestion of optional inputs convolved with rescaling and optimization would significantly improve the model performances for global climatological as well as storm-time ionospheric representation.

One‐ to 10‐Day Forecasts of Ionospheric Total Electron Content Using a Statistical Model

AbstractA new, rapid, nonassimilative technique is demonstrated for forecasting the ionosphere's vertical total electron content (TEC) on time scales longer than 1 day. The approach uses a statistical model constructed by regressing solar extreme ultraviolet irradiance and seasonal, diurnal, and geomagnetic predictors at multiple lags against the 2‐hourly International Global Navigation Satellite Systems Service observations, with a formulation that accounts for solar modulation of the seasonal oscillations and solar and seasonal modulation of the diurnal oscillations. Solar irradiance inputs to the statistical model are forecast at successive 2‐hr intervals from 1999 to 2015 using an autoregressive model of irradiance variations during the prior 100 days. As the forecast time increment increases from 1 to 10 days, the average over the globe of the mean absolute error of TEC observations and the forecasts increases from 2.5 to 3.2 TECU (total electron content unit, 1 TECU = 1016 el/m2); the root‐mean‐square error increases from 3.7 to 4.8 TECU. Averaged over the equatorial ionization anomaly region (30°S–30°N) the mean absolute error of the forecasts increases from 3.2 to 4.3 TECU and the root‐mean‐square error increases from 4.6 to 6.4 TECU. The skill of the TEC forecasts at time increments of 3, 5, and 8 days ahead exceeds persistence by 9%, 13%, and 15% and climatology by 9%, 12%, and 10%, respectively. Forecast skill is higher in April than in July. Long‐range, multiyear forecasts from 2018 to 2030 are demonstrated based on current expectations that solar activity in cycle 25 will be comparable to that in cycle 24.

The BeiDou global broadcast ionospheric delay correction model (BDGIM) and its preliminary performance evaluation results

A global ionospheric delay correction model (BeiDou global broadcast ionospheric delay correction model [BDGIM]) is proposed for the single-frequency ionospheric delay correction of the third phase of the BeiDou navigation satellite system (BDS-3). An initial performance assessment of BDGIM was conducted with data collected in China and worldwide. For regional analysis, the broadcast coefficients of BDGIM were provided by the operational control system of BDS, while for global analysis, the coefficients of BDGIM were estimated using global positioning system (GPS)-derived total electron contents (TECs) obtained from 19 globally distributed monitoring sites. In China, the performance of BDGIM was evaluated by GPS-TEC derived from 40 test sites during day of year (DOY) 060 to 181, 2015. The ionospheric errors can be mitigated by 80.9% for BDGIM. On the global scale, the ionospheric TECs derived from 50 sites of the International Global Navigation Satellite System (GNSS) Services (IGS) were used as references during DOY 220 to 365, 2014, and BDGIM can correct for 77.6% of the ionospheric delay.

Improvement of a Deep Learning Algorithm for Total Electron Content Maps: Image Completion

AbstractObservations with a global coverage are very important for space physics research and space weather monitoring. However, due to the technical limitations, it would be very expensive or even impossible to achieve a seamless global coverage even with advanced observational devices. It would be useful to fill missing data gaps to create a global map from the available data, but up until now this has been very challenging. Fortunately, the deep learning method, a recent breakthrough in artificial intelligence, may provide an effective way to solve this problem by making full use of data from reliable observations. In this paper, a promising deep learning algorithm, deep convolutional generative adversarial network (DCGAN), is investigated to fill the missing data of total electron content (TEC) map images. The direct use of DCGAN fails to fill missing data for the completion of TEC maps because there are always missing TEC data in some regions, such as oceans, where the features vary with time and geophysical conditions. Thus, no useful information can be utilized by DCGAN to achieve a meaningful image completion. In order to overcome this shortcoming of the original DCGAN method, a novel regularized DCGAN (R‐DCGAN) is proposed by adding an extra discriminator and some widely used reference TEC maps from the International Global Navigation Satellite Systems Service Ionosphere Working Group. The proposed R‐DCGAN method generates satisfactory ionospheric peak structures at different times and geomagnetic conditions, which demonstrate its effectiveness on filling the missing data in TEC maps. The proposed R‐DCGAN framework can be readily extended to a broad application in other fields of space sciences, particularly for addressing the missing observation data issues.

Early analysis of precise orbit and clock offset determination for the satellites of the global BeiDou-3 system

Eight new-generation BeiDou satellites (BeiDou-3) have been launched into Medium Earth Orbit (MEO), allowing for global coverage since March 2018, and they are equipped with new hydrogen atomic clocks and updated rubidium clocks. Firstly, we analyzed the signals for the carrier-to-noise-density ratio (C/N0) and pseudorange multipath (MP) by using international GNSS (Global Navigation Satellite System) Monitoring and Assessment System (iGMAS) station data, and found that B1C has a lower C/N0, and B2a has the same level of C/N0 as the B1I and B3I signals. For pseudorange multipath, compared with the BeiDou-2 satellites, the obvious systematic variation of MP scatters related to the elevation angle is greatly improved for the BeiDou-3 and BeiDou-3e satellites signals. For the signals of the BeiDou-3 satellites, the order of the Root Mean Square (RMS) values of multipath and noise is B3I < B1I < B2a < B1C. Then, the comparison of the precise orbit determination and clock offset determination for the BeiDou-2, BeiDou-3, and BeiDou-3 experimental (BeiDou-3e) satellites was done by using 10 stations from iGMAS. The 3D precision of the 24 h orbit overlap is 24.55, 25.61, and 23.35 cm for the BeiDou-3, BeiDou-3e, and BeiDou-2 satellites, respectively. BeiDou-3 satellite has a comparable precision to that of the BeiDou-2 satellite. For the precision of clock offset estimation, the Standard Deviation (STD) of the BeiDou-3 MEO satellite is 0.350 ns, which is an improvement of 0.042 ns over that of the BeiDou-2 MEO satellite. The stabilities of the BeiDou-3 and BeiDou-3e onboard clocks are better than those of BeiDou-2 by factors of 2.84 and 1.61 at an averaging time of 1000 and 10,000 s, respectively.

Analysis of the data processing strategies of spherical harmonic expansion model on global ionosphere mapping for moderate solar activity

Spherical harmonic (SH) expansion is widely used to model the global ionosphere map (GIM) of vertical total electron content (VTEC). According to the impact of different data processing methods of the SH expansion model on the VTEC maps, we specifically performed comprehensive analysis in terms of the data sampling rate, the time resolution, the spherical harmonic degree, and the relative constraint. One month of GPS data (January in 2016) from the International GNSS (Global Navigation Satellite System) Service (IGS) network in a moderate ionospheric activity period at the descending phase of Solar Cycle 24 was processed. To improve the computational efficiency of the daily GIM generation, the data sampling rate of 5 min was recommended allowing the GIM precision loss within 0.10 TECU (total electron content unit). The global VTEC map could be better represented in temporal and spatial domains with higher time resolution and higher spherical harmonic degree, especially at low latitude bands and in the southern hemisphere. The GIM precision improvement was about 10.91% for 1-h and about 15.15% for 0.5-h compared with the commonly used 2-h time resolution. The use of spherical harmonic degree 17 or 20 instead of 15 could improve the precision by 3.19% or 6.06%. We also found that an optimal relative constraint had to be found experimentally considering both the GIM precision and the GIM root mean square (RMS) map.

Global positioning systems meteorology over Morocco: accuracy assessment and comparison of zenith tropospheric delay from global positioning systems and radiosondes

Global positioning systems (GPSs) have become a powerful remote sensing tool to estimate the water vapour in the troposphere. This study describes the operational processing of the Moroccan ground‐based GPS meteorology stations. It presents the evaluation of the accuracy of zenith tropospheric delay (ZTD). The accuracy is evaluated first in relation to the International Global Navigation Satellite System Service (IGS) final products, and second by comparison to equivalent values derived from radiosonde profiles. The comparison of near‐real‐time ZTD with the IGS final product shows a bias of −1 mm with a standard deviation of 6 mm. The comparison with radiosondes shows a bias of −2.82 mm and a standard deviation of 14.01 mm. Also, the comparison of GPS ZTD and radiosonde ZTD time series over almost 1 year (2016) shows good agreement and a seasonal signal with higher values of ZTD in summer.

IGGtrop_SH and IGGtrop_rH: Two Improved Empirical Tropospheric Delay Models Based on Vertical Reduction Functions

IGGtrop_SH and IGGtrop_rH are two improved tropospheric delay models that are established based on empirical vertical reduction functions and capable of providing zenith tropospheric delay (ZTD) correction for radio space geodetic analysis without meteorological measurements. The vertical dependence of ZTD mean values is represented by an exponential function (four coefficients in the high latitudes and six coefficients in other regions) and the vertical dependence of ZTD seasonal variation amplitudes is represented by a fifth degree polynomial. IGGtrop_SH considers both annual and semiannual variations of ZTD, while IGGtrop_rH only considers the annual variation of ZTD, which is suitable for applications more concerned about time and data storage space. The new models are validated by international Global Navigation Satellite System service tropospheric products at 292 globally distributed tracking stations between January 2010 and December 2013. The average bias values over the four years are around −0.46 cm for both models; the globally averaged root-mean-square error of IGGtrop_SH is about 3.86 cm and the value of IGGtrop_rH is about 3.97 cm. Comparison between IGGtrop_SH and the previous IGGtrop model suggests that the inclusion of semiannual variation leads to an apparent improvement of ZTD correction performance in the Northern Hemisphere, especially for middle latitudes, while no obvious change is seen in the Southern Hemisphere.

An Ionosphere Specification Technique Based on Data Ingestion Algorithm and Empirical Orthogonal Function Analysis Method

AbstractA data ingestion method in reproducing ionospheric electron density and total electron content (TEC) was developed to incorporate TEC products from the Madrigal Database into the NeQuick 2 model. The method is based on retrieving an appropriate global distribution of effective ionization parameter (Az) to drive the NeQuick 2 model, which can be implemented through minimizing the difference between the measured and modeled TEC at each grid in the local time‐modified dip latitude coordinates. The performance of this Madrigal TEC‐driven‐NeQuick 2 result is validated through the comparison with various International Global Navigation Satellite Systems Services global ionospheric maps and ionosonde data. The validation results show that a general accuracy improvement of 30–50% can be achieved after data ingestion. In addition, the empirical orthogonal function (EOF) analysis technique is used to construct a parameterized time‐varying global Az model. The quick convergence of EOF decomposition makes it possible to use the first six EOF series to represent over 90% of the total variances. The intrinsic diurnal variation and spatial distribution in the original data set can be well reflected by the constructed EOF base functions. The associated EOF coefficients can be expressed as a set of linear functions of F10.7 and Ap indices, combined with a series of trigonometric functions with annual/seasonal variation components. The NeQuick TEC driven by EOF‐modeled Az shows 10–15% improvement in accuracy over the standard ionosphere correction algorithm in the Galileo navigation system. These preliminary results demonstrate the effectiveness of the combined data ingestion and EOF modeling technique in improving the specifications of ionospheric density variations.

Studies of precipitable water vapour characteristics on a global scale

ABSTRACTAtmospheric water vapour plays an important role in hydrological, global climate change, atmospheric, and meteorological processes. In this study, precipitable water vapour (PWV) data set for 2004–2017 was first estimated with an average accuracy of about 1.28 mm globally using the products provided by the International Global Navigation Satellite System Service and Global Geodetic Observation System Atmosphere and then the spatio-temporal trends of PWV variation were characterized. Periodic signals of the annual, semi-annual, and seasonal variations of PWV time series were detected based on the Lomb–Scargle periodogram and analysed by dividing the whole world into five geographical zones. From a global perspective, the average PWV has an increasing trend, which may be caused by global warming effects and anthropogenic activities. Analysis of different PWV amplitudes also shows that the main component of the PWV is annual amplitude except in low latitude zones. In addition, the PWV differences between weekends and weekdays for four seasons are also analysed globally, and the result indicates that the weekend effects caused by anthropogenic activity depend on season and region