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18 pages, 14698 KiB  
Article
Analysis on GNSS Common View and Precise Point Positioning Time Transfer: BDS-3/Galileo/GPS
by Meng Wang, Chunlei Pang, Dong Guo, Shize Wang, Yang Zhang, Jinglong Gao and Xiubin Zhao
Remote Sens. 2025, 17(10), 1725; https://doi.org/10.3390/rs17101725 - 15 May 2025
Viewed by 433
Abstract
The International Bureau of Weights and Measures (BIPM) currently mainly uses GPS time transfer for the calculation of UTC. In order to enhance the reliability of the time links, the common-view (CV) and Precise Point Positioning (PPP) time transfer performance of the dual-frequency [...] Read more.
The International Bureau of Weights and Measures (BIPM) currently mainly uses GPS time transfer for the calculation of UTC. In order to enhance the reliability of the time links, the common-view (CV) and Precise Point Positioning (PPP) time transfer performance of the dual-frequency ionosphere-free combination for BRUX-SPT0, NIST-USN7, and BRUX-USN7 links was evaluated, including GPS (P1 & P2), Galileo (E1 & E5a), and BDS-3 (B1I & B3I, B1I & B2a, B1C & B3I, B1C & B2a). The experimental results show that the precision and average frequency stability (AFT) of BDS-3 B1C & B2a CV and PPP links are better than those of BDS-3 B1I & B3I, B1I & B2a, and B1C & B3I links. Compared to the GPS P1 & P2 and BDS-3 B1C & B2a CV links, the Galileo E1 & E5a links have the highest precision. In addition, the precision of GPS PPP links outperforms the BDS-3 and Galileo links. The short-term FT (frequency stability) of GPS PPP links is better than that of BDS-3 B1C & B2a PPP links. When the average time is greater than 4.3 h, however, the BDS-3 B1C & B2a PPP link’s AFT is significantly improved compared with the Galileo PPP links. Full article
(This article belongs to the Special Issue Advances in GNSS for Time Series Analysis)
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11 pages, 3058 KiB  
Proceeding Paper
Establishing Large-Scale Network PPP-RTK Through a Decentralized Architecture with a Common Pivot Station
by Cheolmin Lee, Sulgee Park and Sanghyun Park
Eng. Proc. 2025, 88(1), 37; https://doi.org/10.3390/engproc2025088037 - 30 Apr 2025
Viewed by 259
Abstract
In this study, we introduce a decentralized architecture aimed at enhancing the efficiency of precise point positioning real-time kinematics (PPP-RTK) in large-scale networks with a common pivot station. Initially, we partition the extensive network into multiple smaller subnetworks (SNs), each with a common [...] Read more.
In this study, we introduce a decentralized architecture aimed at enhancing the efficiency of precise point positioning real-time kinematics (PPP-RTK) in large-scale networks with a common pivot station. Initially, we partition the extensive network into multiple smaller subnetworks (SNs), each with a common pivot station. The augmentation parameters for each SN are then computed using the precise orbit corrections and ionosphere-weighted constraints. However, directly applying the estimated augmentation parameters to users across subnetworks poses challenges due to inter-subnetwork discontinuities. These discontinuities arise from variations in the network configurations and the time correlation of the Kalman filters, despite the use of the same pivot station. To address this, common augmentation parameters, such as the satellite clocks and phase biases from each SN, are integrated into a unified set of parameters and broadcast to users. The aligned common augmentation parameters are then fed back into each SN, and the Kalman filter is re-updated to mitigate the inter-subnetwork discontinuities. The proposed architecture offers a reduced computational burden compared to the centralized PPP-RTK architecture, which handles a full-scale network simultaneously. Unlike previous research on decentralized PPP-RTK, the use of a common pivot station ensures a consistent basis for the common augmentation parameters. This approach enables seamless user positioning during transitions between SNs, eliminating the need to reset the user navigation filter during handover operations and simplifying the integration process. To evaluate the effectiveness of our proposed architecture, we gather dual-frequency global positioning system (GPS) observation data from over 40 continuously observed reference stations (CORSs) in Korea. These data are then partitioned into four SNs, each sharing a common pivot station. Subsequently, we compare the static positioning error and processing time of our proposed architecture with those of the centralized architecture. Additionally, the mitigation performance of the inter-network discontinuities is shown. Full article
(This article belongs to the Proceedings of European Navigation Conference 2024)
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21 pages, 7328 KiB  
Article
Backpropagation Neural Network-Assisted Helmert Variance Model for Weighted Global Navigation Satellite System Localization in High Orbit
by Zhipu Wang, Xialan Chen, Zimin Huo, Zhibo Fang and Zhenting Xu
Electronics 2025, 14(8), 1529; https://doi.org/10.3390/electronics14081529 - 10 Apr 2025
Viewed by 354
Abstract
In high-orbit space missions, the significant attenuation of Global Navigation Satellite System (GNSS) signals due to long transmission distances and complex environmental interferences has led to a drastic degradation in the accuracy of traditional positioning models, which has attracted great attention in recent [...] Read more.
In high-orbit space missions, the significant attenuation of Global Navigation Satellite System (GNSS) signals due to long transmission distances and complex environmental interferences has led to a drastic degradation in the accuracy of traditional positioning models, which has attracted great attention in recent years. Although multi-system GNSS fusion positioning can alleviate the problem of insufficient satellite visibility, the existing methods are difficult to effectively cope with the challenges of multi-source noise coupling and inter-system error differences unique to high orbit. In this paper, we propose an adaptive GNSS positioning optimization framework for a high-orbit environment, which improves the orbiting reliability under complex signal conditions through dynamic weight allocation and a multi-system cooperative strategy. Different from the traditional weighting model, this method innovatively constructs a two-layer optimization mechanism: (1) Based on BP neural network, it evaluates the noise characteristics of pseudo-range observations in real time and realizes the adaptive suppression of receiver thermal noise, ionospheric delay, etc.; (2) it introduces Helmert variance component estimation to optimize the weighting ratio of GPS, GLONASS, BeiDou, and Galileo and reduces the impact of signal heterogeneity on the positioning solution of the multi-system. Simulation results show that the new method reduces the root-mean-square error of positioning by 32.8% compared with the traditional algorithm to 97.72 m in typical high-orbit scenarios and significantly improves the accuracy loss caused by the defective satellite geometrical configurations under multi-system synergy. Full article
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20 pages, 12169 KiB  
Article
Exploring the Advantages of Multi-GNSS Ionosphere-Weighted Single-Frequency Precise Point Positioning in Regional Ionospheric VTEC Modeling
by Ahao Wang, Yize Zhang, Junping Chen, Hu Wang, Xuexi Liu, Yihang Xu, Jing Li and Yuyan Yan
Remote Sens. 2025, 17(6), 1104; https://doi.org/10.3390/rs17061104 - 20 Mar 2025
Cited by 1 | Viewed by 443
Abstract
Although the traditional Carrier-to-Code Leveling (CCL) method can provide ideal slant total electron content (STEC) observables for establishing ionospheric models, it must rely on dual-frequency (DF) receivers, which results in high hardware costs. In this study, an ionosphere-weight (IW) single-frequency (SF) precise point [...] Read more.
Although the traditional Carrier-to-Code Leveling (CCL) method can provide ideal slant total electron content (STEC) observables for establishing ionospheric models, it must rely on dual-frequency (DF) receivers, which results in high hardware costs. In this study, an ionosphere-weight (IW) single-frequency (SF) precise point positioning (PPP) method for extracting STEC observables is proposed, and multi-global navigation satellite system (GNSS)-integrated processing is adopted to improve the spatial resolution of the ionospheric model. To investigate the advantages of this novel method, 41 European stations are used to establish the regional ionospheric model, and both low- and high-solar-activity conditions are considered. The results show that the IW SFPPP-derived regional ionospheric model has a significantly better quality of vertical total electron content (VTEC) than the CCL method when using the final global ionospheric map (GIM) as a reference, especially in areas with sparse monitoring stations. Compared with the CCL method, the RMS VTEC accuracy of the IW SFPPP method can be improved by 17.4% and 12.7% to 1.09 and 2.83 total electron content unit (TECU) in low- and high-solar-activity periods, respectively. Regarding GNSS carrier-phase-derived STEC variation (dSTEC) as the reference, the dSTEC accuracy of the IW SFPPP method is comparable to that of the CCL method, and its RMS values are about 1.5 and 2.8 TECU in low- and high-solar-activity conditions, respectively. This indicates that the proposed method using SF-only observations can achieve the same external accord accuracy as the CCL method in regional ionospheric modeling. Full article
(This article belongs to the Special Issue Advanced Multi-GNSS Positioning and Its Applications in Geoscience)
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23 pages, 7822 KiB  
Article
Crowdsourcing User-Enhanced PPP-RTK with Weighted Ionospheric Modeling
by Qing Zhao, Shuguo Pan, Wang Gao, Xianlu Tao, Hao Liu and Zeyu Zhang
Remote Sens. 2025, 17(6), 1099; https://doi.org/10.3390/rs17061099 - 20 Mar 2025
Viewed by 533
Abstract
In the conventional PPP-RTK mode, the platform and users act only as the generator and the utilizer of ionospheric corrections, respectively. In sparse reference station networks or regions with an active ionosphere, high-precision modeling still faces challenges. This study utilizes the concept of [...] Read more.
In the conventional PPP-RTK mode, the platform and users act only as the generator and the utilizer of ionospheric corrections, respectively. In sparse reference station networks or regions with an active ionosphere, high-precision modeling still faces challenges. This study utilizes the concept of crowdsourcing and treats users as dynamic reference stations. By continuously feeding back ionospheric information to the platform, high-spatial-resolution modeling is achieved. Additionally, weight factors related to user positions are incorporated into conventional polynomial models to transform the regional ionosphere model from a common model into customized models, thereby providing more personalized services for different users. Validation was conducted with a sparse reference network with an average inter-station distance of approximately 391 km. While increasing the number of crowdsourcing users generally improves modeling performance, the enhancement also depends on their spatial distribution; that is, crowdsourcing users primarily provide localized improvements in their vicinity. Therefore, crowdsourcing users should ideally be uniformly distributed across the whole network. Compared with the conventional common model, the proposed customized model can more effectively characterize the irregular physical characteristics of the ionosphere, and the modeling accuracy is improved by about 12% to 41% in different scenarios. Furthermore, the performance of single-frequency PPP-RTK was verified on the terminal. In general, both crowdsourcing enhancement and the customized model can accelerate the convergence speed of the float solutions and improve positioning accuracy to varying degrees, and the epoch fix rate of the fixed solutions is also significantly improved. Full article
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23 pages, 10008 KiB  
Review
Multi-Global Navigation Satellite System for Earth Observation: Recent Developments and New Progress
by Shuanggen Jin, Xuyang Meng, Gino Dardanelli and Yunlong Zhu
Remote Sens. 2024, 16(24), 4800; https://doi.org/10.3390/rs16244800 - 23 Dec 2024
Viewed by 2056
Abstract
The Global Navigation Satellite System (GNSS) has made important progress in Earth observation and applications. With the successful design of the BeiDou Navigation Satellite System (BDS), four global navigation satellite systems are available worldwide, together with Galileo, GLONASS, and GPS. These systems have [...] Read more.
The Global Navigation Satellite System (GNSS) has made important progress in Earth observation and applications. With the successful design of the BeiDou Navigation Satellite System (BDS), four global navigation satellite systems are available worldwide, together with Galileo, GLONASS, and GPS. These systems have been widely employed in positioning, navigation, and timing (PNT). Furthermore, GNSS refraction, reflection, and scattering signals can remotely sense the Earth’s surface and atmosphere with powerful implications for environmental remote sensing. In this paper, the recent developments and new application progress of multi-GNSS in Earth observation are presented and reviewed, including the methods of BDS/GNSS for Earth observations, GNSS navigation and positioning performance (e.g., GNSS-PPP and GNSS-NRTK), GNSS ionospheric modelling and space weather monitoring, GNSS meteorology, and GNSS-reflectometry and its applications. For instance, the static Precise Point Positioning (PPP) precision of most MGEX stations was improved by 35.1%, 18.7%, and 8.7% in the east, north, and upward directions, respectively, with PPP ambiguity resolution (AR) based on factor graph optimization. A two-layer ionospheric model was constructed using IGS station data through three-dimensional ionospheric model constraints and TEC accuracy was increased by about 20–27% with the GIM model. Ten-minute water level change with centimeter-level accuracy was estimated with ground-based multiple GNSS-R data based on a weighted iterative least-squares method. Furthermore, a cyclone and its positions were detected by utilizing the GNSS-reflectometry from the space-borne Cyclone GNSS (CYGNSS) mission. Over the years, GNSS has become a dominant technology among Earth observation with powerful applications, not only for conventional positioning, navigation and timing techniques, but also for integrated remote sensing solutions, such as monitoring typhoons, river water level changes, geological geohazard warnings, low-altitude UAV navigation, etc., due to its high performance, low cost, all time and all weather. Full article
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19 pages, 4394 KiB  
Article
Ionosphere-Weighted Network Real-Time Kinematic Server-Side Approach Combined with Single-Differenced Observations of GPS, GAL, and BDS
by Yi Ma, Hongjin Xu, Yifan Wang, Yunbin Yuan, Xingyu Chen, Zelin Dai and Qingsong Ai
Remote Sens. 2024, 16(13), 2269; https://doi.org/10.3390/rs16132269 - 21 Jun 2024
Viewed by 1140
Abstract
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 [...] Read more.
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. Full article
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25 pages, 30172 KiB  
Article
Comprehensive Analysis on GPS Carrier Phase under Various Cutoff Elevation Angles and Its Impact on Station Coordinates’ Repeatability
by Sorin Nistor, Norbert-Szabolcs Suba, Aurelian Stelian Buda, Kamil Maciuk and Ahmed El-Mowafy
Remote Sens. 2024, 16(10), 1691; https://doi.org/10.3390/rs16101691 - 9 May 2024
Viewed by 2111
Abstract
When processing the carrier phase, the global navigation satellite system (GNSS) grants the highest precision for geodetic measurements. The analysis centers (ACs) from the International GNSS Service (IGS) provide different data such as precise clock data, precise orbits, reference frame, ionosphere and troposphere [...] Read more.
When processing the carrier phase, the global navigation satellite system (GNSS) grants the highest precision for geodetic measurements. The analysis centers (ACs) from the International GNSS Service (IGS) provide different data such as precise clock data, precise orbits, reference frame, ionosphere and troposphere data, as well as other geodetic products. Each individual AC has its own strategy for delivering the abovementioned products, with one of the key elements being the cutoff elevation angle. Typically, this angle is arbitrarily chosen using generic values without studying the impact of this choice on the obtained results, in particular when very precise positions are considered. This article addresses this issue. To this end, the article has two key sections, and the first is to evaluate the impact of using the two different cutoff elevation angles that are most widely used: (a) 3 degrees cutoff and (b) 10 degrees cutoff elevation angle. This analysis is completed in two major parts: (i) the analysis of the root mean square (RMS) for the carrier phase and (ii) the analysis of the station position in terms of repeatability. The second key section of the paper is a comprehensive carrier phase analysis conducted by adopting a new approach using a mean of the 25-point average RMS (A-RMS) and the single-point RMS and using an ionosphere-free linear combination. By using the ratio between the 25-point average RMS and the single-point RMS we can define the type of scatter that dominates the phase solution. The analyzed data span a one-year period. The tested GNSS stations belong to the EUREF Permanent Network (EPN) and the International GNSS Service (IGS). These comprise 55 GNSS stations, of which only 23 GNSS stations had more than 95% data availability for the entire year. The RMS and A-RMS are analyzed in conjunction with the precipitable water vapor (PWV), which shows clear signs of temporal correlation. Of the 23 GNSS stations, three stations show an increase of around 50% of the phase RMS when using a 3° cutoff elevation angle, and only four stations have a difference of 5% between the phase RMS when using both cutoff elevation angles. When using the A-RMS, there is an average improvement of 37% of the phase scatter for the 10° cutoff elevation angle, whereas for the 3° cutoff elevation angle, the improvement is around 33%. Based on studying this ratio, four stations indicate that the scatter is dominated by the stronger-than-usual dominance of long-period variations, whereas the others show short-term noise. In terms of station position repeatability, the weighted root mean square (WRMS) is used as an indicator, and the results between the differences of using a 3° and 10° cutoff elevation angle strategy show a difference of −0.16 mm for the North component, −0.21 mm for the East component and a value of −0.75 mm for the Up component, indicating the importance of using optimal cutoff angles. Full article
(This article belongs to the Special Issue Advanced Remote Sensing Technology in Modern Geodesy)
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22 pages, 9742 KiB  
Article
Fusion of Land-Based and Satellite-Based Localization Using Constrained Weighted Least Squares
by Paihang Zhao, Linqiang Jiang, Tao Tang, Zhidong Wu and Ding Wang
Sensors 2024, 24(8), 2628; https://doi.org/10.3390/s24082628 - 20 Apr 2024
Cited by 1 | Viewed by 1133
Abstract
Combining multiple devices for localization has important applications in the military field. This paper exploits the land-based short-wave platforms and satellites for fusion localization. The ionospheric reflection height error and satellite position errors have a great impact on the short-wave localization and satellite [...] Read more.
Combining multiple devices for localization has important applications in the military field. This paper exploits the land-based short-wave platforms and satellites for fusion localization. The ionospheric reflection height error and satellite position errors have a great impact on the short-wave localization and satellite localization accuracy, respectively. In this paper, an iterative constrained weighted least squares (ICWLS) algorithm is proposed for these two kinds of errors. The algorithm converts the nonconvex equation constraints to linear constraints using the results of the previous iteration, thus ensuring convergence to the globally optimal solution. Simulation results show that the localization accuracy of the algorithm can reach the corresponding Constrained Cramér–Rao Lower Bound (CCRLB). Finally, the localization results of the two methods are fused using Kalman filtering. Simulations show that the fused localization accuracy is improved compared to the single-means localization. Full article
(This article belongs to the Section Navigation and Positioning)
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15 pages, 6296 KiB  
Article
A Two-Step Regional Ionospheric Modeling Approach for PPP-RTK
by Zhenyu Xu, Changsheng Cai, Lin Pan, Wujiao Dai and Bei He
Sensors 2024, 24(7), 2307; https://doi.org/10.3390/s24072307 - 5 Apr 2024
Cited by 1 | Viewed by 1622
Abstract
In the precise point positioning/real-time kinematic (PPP-RTK) technique, high-precision ionospheric delay correction information is an important prerequisite for rapid PPP convergence. The commonly used ionospheric modeling approaches in the PPP-RTKs only take the trend term of the ionospheric total electron content (TEC) variations [...] Read more.
In the precise point positioning/real-time kinematic (PPP-RTK) technique, high-precision ionospheric delay correction information is an important prerequisite for rapid PPP convergence. The commonly used ionospheric modeling approaches in the PPP-RTKs only take the trend term of the ionospheric total electron content (TEC) variations into account. As a result, the residual ionospheric delay still affects the positioning solutions. In this study, we propose a two-step regional ionospheric modeling approach that involves combining a polynomial fitting model (PFM) and a Kriging interpolation (KI) model. In the first step, a polynomial fitting method is used to model the trend term of the ionospheric TEC variations. In the second step, a KI method is used to compensate for the residual term of the ionospheric TEC variations. Datasets collected from continuously operating reference stations (CORSs) in Hunan Province, China, are used to validate the PFM/KI method by comparing with a single PFM method and a combined PFM and inverse distance weighting interpolation (IDWI) method. The experimental results show that the two-step PFM/KI modeled ionospheric delay achieves an average root mean square (RMS) error of 1.8 cm, which is improved by about 48% and 23% when compared with the PFM and PFM/IDWI methods, respectively. Regarding the positioning performance, the PPP-RTK with the PFM/KI method takes an average of 1.8 min or 4.0 min to converge to a positioning accuracy of 1.3 cm or 2.5 cm in the horizontal and vertical directions, respectively. The convergence times are decreased by about 18% and 14% in the horizontal direction and 9% and 5% in the vertical direction over the PFM and the PFM/IDWI methods, respectively. Full article
(This article belongs to the Special Issue GNSS Signals and Precise Point Positioning)
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22 pages, 8969 KiB  
Article
Research on Reliable Long-Baseline NRTK Positioning Method Considering Ionospheric Residual Interpolation Uncertainty
by Hao Liu, Wang Gao, Weiwei Miao, Shuguo Pan, Xiaolin Meng and Longlei Qiao
Remote Sens. 2023, 15(22), 5353; https://doi.org/10.3390/rs15225353 - 14 Nov 2023
Cited by 2 | Viewed by 1570
Abstract
In the past few decades, network real-time kinematic (NRTK) positioning technology has developed rapidly. Generally, in the continuously operating reference stations (CORS) network, within a moderate baseline length, e.g., 80–100 km, atmospheric delay can be effectively processed through regional modeling and, thus, can [...] Read more.
In the past few decades, network real-time kinematic (NRTK) positioning technology has developed rapidly. Generally, in the continuously operating reference stations (CORS) network, within a moderate baseline length, e.g., 80–100 km, atmospheric delay can be effectively processed through regional modeling and, thus, can support almost instantaneous centimeter-level NRTK positioning. However, in long-baseline CORS networks, especially during the active period of the ionosphere, ionospheric delays cannot be fully eliminated through modeling, leading to decreased NRTK positioning accuracy. To address this issue, this study proposes a long-baseline NRTK positioning method considering ionospheric residual interpolation uncertainty (IRIU). The method utilizes the ionospheric residual interpolation standard deviation (IRISTD) calculated during atmospheric delay modeling, then fits an IRISTD-related stochastic model through the fitting of the absolute values of the ionospheric delay modeling residuals and IRISTD. Finally, based on the ionosphere-weighted model, the IRISTD processed by the stochastic model is used to constrain the ionospheric pseudo-observations. This method achieves good comprehensive performance in handling ionospheric delay and model strength, and the advantage is validated through experiments using CORS data with baseline lengths ranging from 54 km to 106 km in western China and from 84 km to 180 km in AUSCORS data. Quantitative results demonstrate that, across the three sets of experiments, the proposed ionosphere-weighted model achieves an average increase in the fixed rate of 16.9% compared to the ionosphere-fixed model and 25.6% compared to the ionosphere-float model. In terms of positioning accuracy, the proposed model yields average improvements of 67.4%, 76.4%, and 66.0% in the N/E/U directions, respectively, compared to the ionosphere-fixed model, and average improvements of 21.0%, 32.0%, and 24.4%, respectively, compared to the ionosphere-float model. Overall, the proposed method can achieve better NRTK positioning performance in situations where ionospheric delay modeling is inaccurate, such as long baselines and ionospheric activity. Full article
(This article belongs to the Special Issue GNSS CORS Application)
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19 pages, 14133 KiB  
Article
An Improved Carrier-Smoothing Code Algorithm for BDS Satellites with SICB
by Qichao Zhang, Xiaping Ma, Yuting Gao, Gongwen Huang and Qingzhi Zhao
Remote Sens. 2023, 15(21), 5253; https://doi.org/10.3390/rs15215253 - 6 Nov 2023
Cited by 4 | Viewed by 1897
Abstract
Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as [...] Read more.
Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as Satellite-induced Code Bias (SICB). SICB has been identified in the BDS-2 and the bias will reduce the accuracy or reliability of the CSC. To confront bias, an improved CSC algorithm is proposed by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. The correction model of SICB for IGSO/MEO satellites is established by using a 0.1-degree interval piecewise weighted least squares Third-order Curve Fitting Method (TOCFM). The Variational Mode Decomposition combined with Wavelet Transform (VMD-WT) is proposed to establish the correction model of SICB for the GEO satellite. To verify the proposed method, the SICB model was established by collecting 30 Multi-GNSS Experiment (MGEX) BDS stations in different seasons of a year, in which the BDS data of ALIC, KRGG, KOUR, GCGO, GAMG, and SGOC stations were selected for 11 consecutive days to verify the effectiveness of the algorithm. The results show that there is obvious SICB in the BDS-2 Multipath (MP) combination, but the SICB in the BDS-3 MP is smaller and can be ignored. Compared with the modeling in the references, TOCFM is more suitable for IGSO/MEO SICB modeling, especially for the SICB correction at low elevation angles. After the VMD-WT correction, the Root Mean Square Error (RMSE) of SICB of B1I, B2I, and B3I in GEO satellites is reduced by 53.35%, 63.50%, and 64.71% respectively. Moreover, we carried out ionosphere-free Single Point Positioning (IF SPP), Ionosphere-free CSC SPP (IF CSC SPP), CSC single point positioning with the IGSO/MEO SICB Correction based on the TOCFA Method (IGSO/MEO SICB CSC), and CSC single point positioning with the IGSO/MEO/GEO SICB correction based on VMD-WT and TOCFA (IGSO/MEO/GEO SICB CSC), respectively. Compared to IF SPP, the average improvement of the IGSO/MEO/GEO SICB CSC algorithm in the north, east, and up directions was 24.42%, 27.94%, and 24.98%, respectively, and the average reduction in 3D RMSE is 24.54%. Compared with IF CSC SPP, the average improvement of IGSO/MEO/GEO SICB CSC is 7.03%, 6.50%, and 10.48% in the north, east, and up directions, respectively, while the average reduction in 3D RMSE was 9.86%. IGSO/MEO SICB mainly improves the U direction positioning accuracy, and GEO SICB mainly improves the E and U direction positioning accuracy. After the IGSO/MEO/GEO SICB correction, the overall improvement was about 10% and positioning improved to a certain extent. Full article
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25 pages, 6214 KiB  
Article
Research on Soil Moisture Estimation of Multiple-Track-GNSS Dual-Frequency Combination Observations Considering the Detection and Correction of Phase Outliers
by Xudong Zhang, Chao Ren, Yueji Liang, Jieyu Liang, Anchao Yin and Zhenkui Wei
Sensors 2023, 23(18), 7944; https://doi.org/10.3390/s23187944 - 17 Sep 2023
Cited by 1 | Viewed by 1730
Abstract
Soil moisture (SM), as one of the crucial environmental factors, has traditionally been estimated using global navigation satellite system interferometric reflectometry (GNSS-IR) microwave remote sensing technology. This approach relies on the signal-to-noise ratio (SNR) reflection component, and its accuracy hinges on the successful [...] Read more.
Soil moisture (SM), as one of the crucial environmental factors, has traditionally been estimated using global navigation satellite system interferometric reflectometry (GNSS-IR) microwave remote sensing technology. This approach relies on the signal-to-noise ratio (SNR) reflection component, and its accuracy hinges on the successful separation of the reflection component from the direct component. In contrast, the presence of carrier phase and pseudorange multipath errors enables soil moisture retrieval without the requirement for separating the direct component of the signal. To acquire high-quality combined multipath errors and diversify GNSS-IR data sources, this study establishes the dual-frequency pseudorange combination (DFPC) and dual-frequency carrier phase combination (L4) that exclude geometrical factors, ionospheric delay, and tropospheric delay. Simultaneously, we propose two methods for estimating soil moisture: the DFPC method and the L4 method. Initially, the equal-weight least squares method is employed to calculate the initial delay phase. Subsequently, anomalous delay phases are detected and corrected through a combination of the minimum covariance determinant robust estimation (MCD) and the moving average filter (MAF). Finally, we utilize the multivariate linear regression (MLR) and extreme learning machine (ELM) to construct multi-satellite linear regression models (MSLRs) and multi-satellite nonlinear regression models (MSNRs) for soil moisture prediction, and compare the accuracy of each model. To validate the feasibility of these methods, data from site P031 of the Plate Boundary Observatory (PBO) H2O project are utilized. Experimental results demonstrate that combining MCD and MAF can effectively detect and correct outliers, yielding single-satellite delay phase sequences with a high quality. This improvement contributes to varying degrees of enhanced correlation between the single-satellite delay phase and soil moisture. When fusing the corrected delay phases from multiple satellite orbits using the DFPC method for soil moisture estimation, the correlations between the true soil moisture values and the predicted values obtained through MLR and ELM reach 0.81 and 0.88, respectively, while the correlations of the L4 method can reach 0.84 and 0.90, respectively. These findings indicate a substantial achievement in high-precision soil moisture estimation within a small satellite-elevation angle range. Full article
(This article belongs to the Special Issue GNSS Sensing and Imaging Based on Monitoring Applications)
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25 pages, 3595 KiB  
Article
Optimal Estimation Inversion of Ionospheric Electron Density from GNSS-POD Limb Measurements: Part II-Validation and Comparison Using NmF2 and hmF2
by Nimalan Swarnalingam, Dong L. Wu, Daniel J. Emmons and Robert Gardiner-Garden
Remote Sens. 2023, 15(16), 4048; https://doi.org/10.3390/rs15164048 - 16 Aug 2023
Cited by 6 | Viewed by 1872
Abstract
A growing number of SmallSat/CubeSat constellations with high-rate (50–100 Hz) global navigation satellite system radio occultations (GNSS-RO) as well as low-rate (1 Hz) precise orbit determination (GNSS-POD) limb-viewing capabilities provide unprecedented spatial and temporal sampling rates for ionospheric studies. In the F-region electron [...] Read more.
A growing number of SmallSat/CubeSat constellations with high-rate (50–100 Hz) global navigation satellite system radio occultations (GNSS-RO) as well as low-rate (1 Hz) precise orbit determination (GNSS-POD) limb-viewing capabilities provide unprecedented spatial and temporal sampling rates for ionospheric studies. In the F-region electron density (Ne) retrieval process, instead of the conventional onion-peeling (OP) inversion, an optimal estimation (OE) inversion technique was recently developed using total electron content measurements acquired by GNSS-POD link. The new technique is applied to data acquired from the COSMIC-1, COSMIC-2, and Spire constellations. Although both OE and OP techniques use the Abel weighting function in Ne inversion, OE significantly differs in its performance, especially in the lower F- and E-regions. In this work, we evaluate and compare newly derived data sets using F2 peak properties with other space-based and ground-based observations. We determine the F2 peak Ne (NmF2) and its altitude (hmF2), and compare them with the OP-retrieved values. Good agreement is observed between the two techniques for both NmF2 and hmF2. In addition, we also utilize autoscaled F2 peak measurements from a number of worldwide Digisonde stations (∼30). The diurnal sensitivity and latitudinal variability of the F2 peak between the two techniques are carefully studied at these locations. Good agreement is observed between OE-retrieved NmF2 and Digisonde-measured NmF2. However, significant differences appear between OE-retrieved hmF2 and Digisonde-measured hmF2. During the daytime, Digisonde-measured hmF2 remains ∼25–45 km below the OE-retrieved hmF2, especially at mid and high latitudes. We also incorporate F-region Ne measurements from two incoherent scatter radar observations at high latitudes, located in the North American (Millstone Hill) and European (EISCAT at Tromso) sectors. The radar measurements show good agreement with OE-retrieved values. Although there are several possible sources of error in the ionogram-derived Ne profiles, our further analysis on F1 and F2 layers indicates that the low Digisonde hmF2 is caused by the autoscaled method, which tends to detect a height systematically below the F2 peak when the F1 layer is present. Full article
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28 pages, 7429 KiB  
Article
Spire RO Thermal Profiles for Climate Studies: Initial Comparisons of the Measurements from Spire, NOAA-20 ATMS, Radiosonde, and COSMIC-2
by Xin Jing, Shu-Peng Ho, Xi Shao, Tung-Chang Liu, Yong Chen and Xinjia Zhou
Remote Sens. 2023, 15(15), 3710; https://doi.org/10.3390/rs15153710 - 25 Jul 2023
Cited by 12 | Viewed by 2953
Abstract
Global Navigation Satellite System (GNSS) Radio Occultation (RO) data play an essential role in improving numerical weather prediction (NWP) and monitoring climate change. The NOAA Commercial RO Purchase Program (CDP) purchased RO data provided by Spire Global Inc. To ensure the data quality [...] Read more.
Global Navigation Satellite System (GNSS) Radio Occultation (RO) data play an essential role in improving numerical weather prediction (NWP) and monitoring climate change. The NOAA Commercial RO Purchase Program (CDP) purchased RO data provided by Spire Global Inc. To ensure the data quality from Spire Global Inc. is consistent with other RO missions, we need to quantify their accuracy and retrieval uncertainty carefully. In this work, Spire Wet Profile (wet temperature profile) data from 7 September 2021 to 31 October 2022, processed by the University Corporation for Atmospheric Research (UCAR), and COSMIC-2 (Constellation Observing System for Meteorology, Ionosphere, and Climate-2/Formosa Satellite Mission 7) data are evaluated through comparison with NOAA-20 Advanced Technology Microwave Sounder (ATMS) microwave sounder measurements and collocated RS41 radiosonde measurements. Through the Community Radiative Transfer Model (CRTM) simulation, we convert the Spire and COSMIC-2 RO retrievals to ATMS brightness temperature (BT) at sounding channels CH07 to CH14 (temperature channels), with weighting function peak heights from 8 km to 35 km, and CH19 to CH22 (water vapor channels), with weighting function peak heights ranging from 3.2 km to 6.7 km, and compare the simulations with the collocated NOAA-20 ATMS measurements over ocean. Using ATMS observations as references, Spire and COSMIC-2 BTs agree well with ATMS within 0.07 K for CH07-14 and 0.20 K for CH19-22. The trends between Spire and COSMIC-2 are consistent within 0.07 K/year over the oceans for ATMS CH07-CH13 and CH19-22, indicating that Spire/COSMIC-2 wet profiles are, in general, compatible with each other over oceans. The RO retrievals and RS41 radiosonde observation (RAOB) comparison shows that above 0.2 km altitude, RS41 RAOB matches Spire/COSMIC-2 temperature profiles well with a temperature difference of <0.13 K, and the trends between Spire and COSMIC-2 are consistent within 0.08 K/year over land, indicating that Spire/COSMIC-2 wet profiles are overall compatible with each other through RS41 RAOB measurements over land. In addition, the consistency of Spire and COSMIC-2 based on different latitude intervals, local times, and signal-to-noise ratios (SNRs) through ATMS was evaluated. The results show that the performance of Spire is comparable to COSMIC-2, even though COSMIC-2 has a higher SNR. The high quality of RO profiles from Spire is expected to improve short- and medium-range global numerical weather predictions and help construct consistent climate temperature records. Full article
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