Tropospheric delay significantly impacts radio wave propagation, affecting high-precision geodetic observations, deep space exploration, and radio navigation. Collecting high-precision tropospheric information in marine areas faces challenges such as limited observation stations, environmental noise interference, and sparsity of space-based measurements. However, the increase in global GNSS devices and the enhancement of GNSS real-time services offer opportunities for obtaining high-precision tropospheric data at sea. To extract accurate Zenith Tropospheric Delay (ZTD) information in the complex dynamic environment of ocean vessels, we propose a method for estimating Common Zenith Tropospheric Delay (CZTD) parameters based on Baseline-Constrained Precise Point Positioning (BC-PPP) using four GNSS receiver antennas distributed at different locations on a research vessel. This method improves the accuracy and robustness of real-time positioning and ZTD estimation, effectively addressing the instability of satellite geometry in single-station observations. When the satellite geometry at the single-station observation platform is unstable, this method achieves improvements in positioning accuracy of above 60.8

Spatiotemporal filtering is an effective approach for extracting common mode errors (CMEs) from regional continuous GNSS coordinate time series. However, the covariance matrix formed from least–squares (LS) residuals in conventional principal component analysis (PCA) is easily contaminated by complex trends, anharmonic or multi–frequency seasonal signals, and other non–stationary components. While Multichannel Singular Spectrum Analysis (MSSA) effectively isolates structured signals, it often suffers from severe energy dispersion when handling high-frequency spatial white noise in low signal-to-noise ratio (SNR) environments. To address the limitation, this study proposes an integrated MSSA and PCA approach (MSSA–PCA) for CME extraction. First, MSSA is employed as a non-parametric pre-filter to adaptively remove trends and seasonal signals, and then computes residuals. The residuals are subsequently filtered via PCA to extract the CME. This approach was validated using continuous GNSS data from two geophysically distinct regions. The results demonstrate that in the high-density and high-SNR environment of Southern California, both MSSA and MSSA-PCA successfully isolate highly concentrated CMEs. Conversely, in the highly dispersed energy environment of the Australian East Coast Network, MSSA suffers from severe mode mixing. MSSA-PCA reliably extracts the CME across all coordinate components and significantly outperforms traditional PCA. Specifically, the proposed method achieves average residual Root Mean Square (RMS) improvements of 35.76%, 31.91%, and 28.82% for the East, North, and Up components, respectively. Furthermore, removing the CME via MSSA-PCA reduces the parameter estimation uncertainties of seasonal signals and improves the overall SNR. The proposed MSSA-PCA method provides a versatile and robust processing pipeline for CME extraction across diverse geophysical environments.

Quantifying ionospheric variability under quiet geomagnetic and low solar forcing is required to establish a robust baseline for space-weather monitoring and GNSS performance in North-West Africa. We analyze dual-frequency GNSS observations from Oukaïmeden (OUCA; 31.206°N, 7.866°W) collected between 1 October 2015 and 26 September 2025 to build a quiet-time climatology of vertical total electron content (VTEC) at the poleward flank of the Equatorial Ionization Anomaly. VTEC is retrieved from the geometry-free carrier-phase combination leveled to code, with satellite DCB corrections from SINEX-BIAS products and a single daily receiver bias estimated using the minimum-scalloping (MS) method; an independent geometry-weighted least-squares (WLS) solution is used for consistency checks. Quiet–Solar–Low–coherent (QSL–GIM20) days are defined by the intersection of (i) geomagnetic quietness from the GFZ/ISGI International Quiet Days label (Q), (ii) low solar forcing using F10.7eff=(F10.7+F10.7A)/2⩽125 sfu (with F10.7A a trailing 81-day mean), and (iii) external coherence with CODE GIM through the daily median offset gate |median(VTEClocal-VTECGIM)|⩽20 TECU. The resulting climatology exhibits a systematic afternoon maximum with strong seasonal modulation and a robust seasonal delay of peak time from winter to summer. Yearly diurnal anomalies within the QSL–GIM20 subset show modest negative departures during the extended Solar Cycle 24 minimum and positive afternoon enhancements during the early rise of Solar Cycle 25. This work provides the first long-term quiet-condition VTEC baseline for Morocco and a regional benchmark for anomaly detection and ionospheric model validation over North-West Africa.

On 3 October 2024, an X9.0 solar flare erupted in solar active region 13842, representing the strongest flare event observed to date in Solar Cycle 25. This study conducted coordinated multi-spectral observations of the flare using X-ray flux from GOES 16/18, extreme ultraviolet (EUV) flux from the Solar and Heliospheric Observatory, and very low frequency (VLF) signal amplitudes. The Kp, Dst, sunspot number, and the F10.7 index were integrated to characterize space environment variations during the event. Ionospheric total electron content (TEC) and the rate of TEC index (ROTI) were derived from global International GNSS Service observations to investigate spatiotemporal disturbances during the flare. An error analysis of kinematic precise point positioning (PPP) was conducted. The results show rapid surges in both X-ray and EUV fluxes during the flare, and the VLF signal amplitude increased by about 24.35 dB relative to quiet-day levels, indicating a modification of the ionospheric waveguide. Dayside TEC exhibited instantaneous increases up to 1 TECU (1 TECU = 1016 electron m 2), while the nightside showed no response. The disturbances displayed an approximately symmetric longitudinal-latitudinal pattern strongly correlated with the solar zenith angle. Following flare onset, dayside ROTI rapidly exceeded 0.5 TECU/min, inducing ionospheric scintillation lasting about 10 min. PPP performance decreased significantly after the flare onset, with the three-dimensional root mean square of PPP errors exceeding 1 mat most dayside stations. These findings indicate that an intense X9.0 flare can markedly perturb dayside ionospheric electron content and irregularity activity within minutes, thereby substantially degrading GNSS positioning performance. The combined TEC and ROTI diagnostics effectively reveal ionospheric spatiotemporal disturbances, providing valuable references for space weather monitoring and GNSS service. (c) 2026 COSPAR. Published by Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Electron density irregularities within the ionosphere pose significant challenges to the detection of cycle slips in Global Navigation Satellite System (GNSS) carrier phase observations, compromising their reliability and affecting the performance of applications that rely on these observations, such as precise point positioning (PPP). In this paper, we propose a novel strategy to demonstrate that traditional threshold-based cycle slip detection methods often produce a large number of false positives in low-sampling-rate (30 s) data due to ionospheric variations exceeding small cycle slips. To overcome this limitation, we further propose two improved thresholds incorporating ionospheric variation magnitudes. The effectiveness of the new thresholds is validated through a two-year kinematic PPP analysis involving 47 globally distributed GNSS stations from 2014 to 2015. Results demonstrate that the new thresholds reduce false positives of cycle slip and enhance PPP accuracy by up to 20

The vigorous development of Low Earth Orbit (LEO) satellite constellation programs imposes higher requirements for the accuracy of satellite orbit determination. Significant variations in atmospheric density within the operational region of LEO satellites are primary factors influencing their orbital decay and operational lifespan. This article first summarizes the research advancements in atmospheric density inversion utilizing LEO satellites, comparing and analyzing the principles of various algorithms, factors affecting accuracy, as well as the advantages and disadvantages associated with different acquisition methods. Subsequently, we introduce recent progress in enhancing atmospheric density inversion algorithms and data analysis applications based on LEO satellites. The SWARM-A satellite, equipped with a high-precision GPS receiver and accelerometer, was employed to invert atmospheric density using both semi-long axis attenuation and accelerometer methodologies. The inversion results were compared against empirical models to validate their reliability; specifically, the correlation coefficient between the semi-long axis attenuation method and nrlmsise00 reached 0.9158, while that between the accelerometer method and nrlmsise00 attained 0.9204. Notably, the inversion accuracy achieved by the accelerometer slightly surpasses that of the semi-long axis attenuation method. These findings provide valuable support for predicting large air tightness based on LEO satellite orbit data inversions and for adjusting operational orbits to ensure successful execution of satellite missions.

Precise point positioning (PPP) technology is capable of providing global high-precision positioning services, but its main application bottleneck is the long convergence time. Accurate and reliable carrier phase ambiguity resolution (AR) is a primary approach to accelerate PPP convergence and improve its accuracy. The best integer equivariant (BIE) method, known for its superior performance in minimizing mean square error, is gradually being adopted for PPP-AR. This study examines key aspects of the BIE algorithm, including the determination of the optimal number of candidate sets and how the number of candidates evolves during convergence. The performance of the BIE algorithm is evaluated by utilizing both post-processing products and real-time products generated at the French CNES (Centre National D’Etudes Spatiales) with static station data. The experimental results unequivocally demonstrate that the BIE algorithm significantly improves both positioning accuracy and convergence speed compared to the least-squares ambiguity decorrelation adjustment algorithm in PPP-AR. Furthermore, a verification experiment using real ship-borne kinematic data confirms the exceptional robustness of the BIE algorithm.

Ionospheric delay, as one of the largest error sources in radio propagation, can only be corrected for this error using the ionospheric delay correction model for Global Navigation Satellite System (GNSS) single-frequency users. In this paper, the 2021 geomagnetic storm event is selected, and based on the measured ionospheric data from the GNSS observatory, the perturbation of the ionosphere by the geomagnetic storm event is analyzed, and it is found that the response of the ionosphere to the geomagnetic storm has obvious differences in the response characteristics and response time in different latitude regions. The performance of the global ionospheric map (GIM), the empirical model, and the broadcast ionospheric model during the geomagnetic storm-induced ionospheric perturbation is analyzed and the change in the accuracy of each ionospheric model during the geomagnetic storm-induced ionospheric perturbation is investigated, using the measured electron content of the GNSS as a benchmark. The results show that there is good agreement between the GIM products and the measured electron content during the period of ionospheric calm and the period of ionospheric perturbation. It is worth noting that geomagnetic storms do not necessarily lead to a decrease in the accuracy of ionospheric delay-correction models, and in some cases, the models that were originally under-accurate show a tendency to improve their accuracy during the period of perturbation instead. Neither the broadcast ionospheric model nor the electron content of the empirical model output responds to geomagnetic storm-induced ionospheric perturbations.

The national Beidou Navigation Satellite System (BDS) ground-based augmentation network (BGAN) of China is constructed with the existing GNSS observation resources of industrial sectors and local governments, based on the concept of joint building and sharing with sustainable development. This study provides a detailed introduction to the design, construction and operation of a meteorological application system based on BGAN, and validation of its water vapor products. BDS and GPS real-time observation of atmospheric water vapor is achieved nationwide in China and multi-GNSS applications. Through the application of multi-GNSS data and validation of the water vapor products from 2018 to 2020, the accuracy of precipitable water vapor (PWV) derived from BDS only is equivalent to that from GPS only. The root mean square error (RMSE) between them is about 2 mm with high correlation coefficient. Based on radiosonde data, the validation is conducted with the products of BDS-PWV, GPS-PWV, and Combined-PWV derived with multi-GNSS of BDS and GPS. The error characteristics of the three products show a consistent trend over the months. The bias is relatively small. The RMSE of the three products is in the range of 2.18–2.73 mm. The BDS-PWV has the largest RMSE, followed by GPS-PWV, and Combined-PWV has the smallest RMSE.

Tropospheric delay is a significant source of error in various microwave measurement technologies. As the tropospheric delay differences associated with the signal frequency can be neglected for signals near the L band, the Global Navigation Satellite System (GNSS) is frequently used to assist other microwave measurements on tropospheric delay correction for its high precision and all-weather capabilities. However, when the signal frequency differences are significant, further analysis of tropospheric delay related to signal frequency is required for higher accuracy in long-distance propagation. This study quantitatively analyzed the tropospheric delay differences from L-band to millimeter band (1-300 GHz) affected by dry air, water vapor, and liquid water, based on Microwave Radiometer (MWR) measurement profiles and the Millimeter-wave Propagation Model93 (MPM93) at Shanghai. Relative to the GNSS L-band signal of 1.2 GHz, the RMS of tropospheric delay differences over 1-300 GHz varies from 0.033 mm to 9.436 mm, with the maximum tropospheric delay differences up to 18.03 mm at 300 GHz. Tropospheric delay differences strongly correlate with surface temperature and surface pressure, except for some of the atmosphere absorption bands. These quantitative analyses are helpful for the comprehensive application of GNSS to assist other microwave measurement techniques.

深空探测中探测器轨道主要采用地面跟踪站进行测量,无线电信号在探测器与地面跟踪站间传输时会受到地球传播介质误差的影响.传播介质误差主要包括地球的中性大气时延误差和电离层时延误差等.针对传播介质误差修正在深空探测中的应用需求,调研了国内外地基测量数据传播介质误差研究进展,重点阐述了深空探测中VLBI地基测量数据中性大气和电离层时延产生的机理和修正方法.针对关键技术及未来发展趋势进行了分析,以提高传播介质误差修正精度及时效性.

Within the Multi-GNSS Pilot Project (MGEX) of the International GNSS Service (IGS), precise orbit and clock products for the BeiDou-3 global navigation satellite system (BDS-3) are routinely generated by a total of five analysis centers. The processing standards and specific properties of the individual products are reviewed and the BDS-3 orbit and clock product performance is assessed through direct inter-comparison, satellite laser ranging (SLR) residuals, clock stability analysis, and precise point positioning solutions. The orbit consistency evaluated by the signal-in-space range error is on the level of 4-8 cm for the medium Earth orbit satellites whereas SLR residuals have RMS values between 3 and 9 cm. The clock analysis reveals sytematic effects related to the elevation of the Sun above the orbital plane for all ACs pointing to deficiencies in solar radiation pressure modeling. Nevertheless, precise point positioning with the BDS-3 MGEX orbit and clock products results in 3D RMS values between 7 and 8 mm.

不同导航系统中卫星的形状、材料、轨道设计和姿态控制模式等都不相同,在进行多系统数据联合处理时,要获得高精度的卫星轨道,需要区别对待不同类型卫星的姿态模型和光压模型.作为导航卫星所受量级最大的非保守力,国内外许多研究是围绕光压模型的建立与精化等方面来开展,以便建立最合适的模型,从而获取更高的定轨精度.目前的研究表明,新的Galileo以及北斗卫星采用与之前不同的姿态控制模式,适用的光压模型也不同.总结了目前比较通用的导航卫星姿态模型,尤其是官方最新公布的北斗卫星的姿态模型,详细介绍了卫星光压模型研究进展和近几年来新发射卫星光压模型以及其先验模型的构建方法,并分析了各个模型的优缺点和适应性.通过对目前导航卫星姿态以及光压模型的分析,提出在更高精度的定轨任务中有待改进的问题,为导航卫星尤其是新发射导航卫星精密定轨中的光压和姿态模型的选择和建立提供参考.

The tropospheric delay acquired by the Global Navigation Position System (GPS) Precise Point Positioning (PPP) is continuous and steady, less affected by rainfall. The Water Vapor Radiometer (WVR) can provide real-time meteorological parameters but is more sensitive to high-frequency information in troposphere. To explore the use of WVR-retrieved tropospheric delay and assist other geodetic techniques for atmospheric correction, the tropospheric delay from WVR and co-located GPS at Shanghai, Beijing, Kunming, and Urumqi stations in China are compared. For the inconsistent values of WVR-PPP zenith wet delay, the variations of the tropospheric delay from WVR and GPS before and after the rainfall were statistically analyzed. The results suggest that, for the rain rate ranging from 0.1 to 50 mm/hr, the impact of rainfall on WVR could last from 10 min before to 30 min after the rainfall. With filtering WVR data based on meteorological parameters and rain rate, the zenith wet delay between WVR and PPP at Shanghai shows good consistency, the root mean square (RMS) is 6.11 mm, correlation is 0.997, and the RMS in the other three stations ranges from 16.35 to 25.16 mm (correlation ranges in 0.794-0.951). The analysis indicates that the tropospheric delay of WVR is reliable to be applied to space geodetic techniques correction in real-time with filtering to reduce the effect of rainfall, water vapor, and liquid water variability. Comparison of zenith wet delay(ZWD) from water vapor radiometer, co-located GPS station observations in high temporal resolutionQuantitative analysis of the magnitude and duration of rainfall effects on the zenith wet delay from water vapor radiometer and GPSSuch data analysis and processing might be valuable for assimilating multi-source data on tropospheric wet delay

For the purposes of routinely providing reliable and low-latency Global Ionosphere Maps (GIMs), a method of estimating hourly updated near real-time GIM with a time latency of about 1–2 h based on a 24-h data sliding window of Global Navigation Satellite System (GNSS) near real-time observations and real-time data streams was presented. On the basis of the implementation of near real-time GIM estimation, an hourly updated GIM nowcasting method was further proposed to improve the accurate of short-term total electron content (TEC) prediction. We estimated the Shanghai Astronomical Observatory near real-time GIM (SHUG) and nowcasting GIM (SHPG) in the solar relatively active year (2014) and quiet year (2021), and employed GIMs provided by the International GNSS Service, the Global Positioning System (GPS) differential slant TECs (dSTECs) extracted from global independent GNSS stations, and the vertical TECs (VTECs) inverted from satellite altimetry as the references to validate the estimated results. The GPS dSTECs evaluation results show that SHUG behaves fairly consistent with the rapid GIMs, with a discrepancy of less than 1 TEC unit (TECu) overall. The standard deviations (STDs) of SHUG with respect to Jason-2/-3 VTECs are no more than 10% over the majority of rapid GIMs due to the instability of observations. The performance of 1-h nowcasting SHPG is significantlybetter than the Center for Orbit Determination in Europe (CODE) 1-day predicted GIM (C1PG). GPS dSTEC validation results indicate that 1-h nowcasting SHPG is 1 to 2 TECu more reliable than C1PG in eventful ionospheric electron activity regions, and it outperforms the C1PG by 10% overall versus Jason-2/-3 VTECs. The hourly updated SHUG and SHPG have relatively high reliability and low time latency, and thus can provide excellent service for (near) real-time users and offer more accurate TEC background information than daily predicted GIM for real-time GIM estimation.

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/ E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) appli-cations. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8-12% for triple-frequency models, and 19-27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi -frequency satellite clock offsets can be improved by 7-18% for dual-frequency PPP, 8-15% for triple-frequency PPP, 4-16% for five-frequency PPP. The positioning accuracy can be further improved by 11-28% for triple -frequency PPP and 7-20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.

Evaluation for Global Navigation Satellite System (GNSS) Position Dilution Of Precision (PDOP) is generally based on a simulated global grid with a specific Temporal–Spatial (T–S) resolution. However, the lack of a unified evaluation standard regarding the grid model, T–S resolution and evaluation period leads to inaccurate PDOP evaluation results and unreasonable comparisons among multi-GNSS. We propose the Equal-Arc-Length Grid (GRID_EAL) for PDOP evaluation, which can avoid the bias caused by uneven point distribution present in the commonly used Equal-Interval of Longitude and Latitude Grid (GRID_ELL) and provide more accurate results. Based on GRID_EAL, we thoroughly analyze the varying characteristics and convergence of PDOP metrics with different T–S resolutions. The results indicate that the optimal T–S resolution is 300 s and 3 degrees, reducing time and memory costs by 90

北斗三号全球卫星导航系统(BDS-3)开通了全球服务,BDS Klobuchar(BDSklob)模型的服务区域也拓展至全球范围,BDSklob模型全球化后的性能引起了极大的关注.针对北斗二号卫星导航系统(BDS-2)播发的BDSklob模型在服务区域外精度不高、两极地区改正异常情况,本文基于参数精化方法,利用经验模型IRI-Plas-2017、北斗全球广播电离层延迟修正模型(BDGIM),以及欧洲定轨中心(CODE)的全球电离层格网(GIM)产品多源数据提出新的BDSklob模型精细化方案多源数据精细化法.结果表明:各个数据源精细化方法对BDSklob模型性能都有明显提升,尤其是在极地区域;BDSklob_C(数据源为CODE的GIM产品)处理结果精度最高;BDSklob_B(数据源为BDGIM)精度次之,但不借助外部数据源,在北斗系统中即可完成精化处理;BDSklob_I(数据源为IRI模型)精度稍差,但基于经验模型的预测性,可以满足实时精化处理的需要.

Accurate satellite phase center offsets (PCOs) are essential for GNSS data processing, and their calibration before launch and estimation in orbit have been crucial tasks since decades. However, for the third-generation BeiDou navigation satellite system (BDS-3), the results in most recent studies are derived from precise orbit determination (POD) by wholly or partly employing GPS L1/L2 antenna calibrations for receivers and the adjustable box-wing model for solar radiation pressure (SRP) modeling. Since the strategy usages are different, the estimated BDS-3 PCOs are also varied from studies. With the help of BDS-3 satellite metadata and the receiver antenna calibration of BDS signals, this study estimated BDS-3 satellite PCOs in orbit with long-term data. The results show that the X-offset estimated using the empirical SRP model with the BDS-3 metadata is the most stable. Further analyses of PCO estimation using GPS and BDS receiver antenna calibrations for BDS signals show that the Z-offset is strongly affected by the receiver antenna calibration model types. The correlation can be approximately determined by giving a change to receiver antenna calibration and expressed as: A network averaged bias in the Up-direction of receiver antenna results in a − 22.7 times change of MEO Z-offset for single BDS-3 POD as well as − 28.6 for the joint processing with GPS. This is consistent with the result derived from other studies although different method was applied. Therefore, receiver antenna calibrations need to be carried out precisely. Validation experiments are carried out for comparison between the manufacture and the newly SHAPCO models. Compared with the manufacture model, the average improvement of the root mean square of the overlapping orbit differences is close to 3