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22 pages, 6054 KiB  
Article
Evaluation and Adjustment of Precipitable Water Vapor Products from FY-4A Using Radiosonde and GNSS Data from China
by Xiangping Chen, Yifei Yang, Wen Liu, Changzeng Tang, Congcong Ling, Liangke Huang, Shaofeng Xie and Lilong Liu
Atmosphere 2025, 16(1), 99; https://doi.org/10.3390/atmos16010099 (registering DOI) - 17 Jan 2025
Viewed by 247
Abstract
The geostationary meteorological satellite Fengyun-4A (FY-4A) has rapidly advanced, generating abundant high spatiotemporal resolution atmospheric precipitable water vapor (PWV) products. However, remote sensing satellites are vulnerable to weather conditions, and these latest operational PWV products still require systematic validation. This study presents a [...] Read more.
The geostationary meteorological satellite Fengyun-4A (FY-4A) has rapidly advanced, generating abundant high spatiotemporal resolution atmospheric precipitable water vapor (PWV) products. However, remote sensing satellites are vulnerable to weather conditions, and these latest operational PWV products still require systematic validation. This study presents a comprehensive evaluation of FY-4A PWV products by separately using PWV data retrieved from radiosondes (RS) and the Global Navigation Satellite System (GNSS) from 2019 to 2022 in China and the surrounding regions. The overall results indicate a significant consistency between FY-4A PWV and RS PWV as well as GNSS PWV, with mean biases of 7.21 mm and −8.85 mm, and root mean square errors (RMSEs) of 7.03 mm and 3.76 mm, respectively. In terms of spatial variability, the significant differences in mean bias and RMSE were 6.50 mm and 2.60 mm between FY-4A PWV and RS PWV in the northern and southern subregions, respectively, and 5.36 mm and 1.73 mm between FY-4A PWV and GNSS PWV in the northwestern and southern subregions, respectively. The RMSE of FY-4A PWV generally increases with decreasing latitude, and the bias is predominantly negative, indicating an underestimation of water vapor. Regarding temporal differences, both the monthly and daily biases and RMSEs of FY-4A PWV are significantly higher in summer than in winter, with daily precision metrics in summer displaying pronounced peaks and irregular fluctuations. The classic seasonal, regional adjustment model effectively reduced FY-4A PWV deviations across all regions, especially in the NWC subregion with low water vapor distribution. In summary, the accuracy metrics of FY-4A PWV show distinct spatiotemporal variations compared to RS PWV and GNSS PWV, and these variations should be considered to fully realize the potential of multi-source water vapor applications. Full article
(This article belongs to the Special Issue GNSS Remote Sensing in Atmosphere and Environment (2nd Edition))
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<p>Distribution of RS sites and GNSS sites from 2019–2022 in the research area.</p>
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<p>Observation mode of the AGRI on FY-4A satellite. The vertical axis represents UTC time in hours, while the horizontal axis represents the minutes within each hour.</p>
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<p>Fitting plots between RS PWV and FY-4A PWV from 2019 to 2022 for different regions, with correlation, annual mean bias, and RMSE values.</p>
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<p>Site distribution maps of the mean bias and mean RMSE between FY-4A PWV and RS PWV from 2019 to 2022.</p>
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<p>Histograms of annual mean bias and RMSE between FY-4A PWV and RS PWV in different regions.</p>
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<p>Seasonal average distribution of FY-4A PWV and GNSS PWV for 2022.</p>
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<p>Fitting plots between FY-4A PWV and GNSS PWV from 2019 to 2022 for different regions, with correlation, annual mean bias, and RMSE values.</p>
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<p>Site distribution maps of the mean bias and mean RMSE between FY-4A PWV and GNSS PWV from 2019 to 2022.</p>
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<p>Bar charts of monthly mean bias and RMSE for four seasons between FY-4A PWV and GNSS PWV from 2019–2022.</p>
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<p>Box plots of monthly mean bias and RMSE between FY-4A PWV and GNSS PWV from 2019–2022 in different regions. Q1 and Q3 of the box are the first and third quartiles, respectively. The distance between Q1 and Q3 reflects the degree of fluctuation of the data; Q2 is the median value, which reflects the average level of the data; Q4 is the outlier.</p>
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<p>Time series of daily mean bias and RMSE between FY-4A PWV and GNSS PWV in different regions from 2019 to 2022.</p>
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<p>Bar charts of the mean MAE and RMSE between FY-4A PWV and GNSS PWV before and after adjustment in different regions and seasons for 2022. The length of the arrows represents the degree of improvement in mean MAE and RMSE.</p>
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<p>Site-level distribution of seasonal average improvements in MAE and RMSE between corrected and uncorrected FY-4A PWV and GNSS PWV for 2022. IMAE and IRMSE represent the improved MAE and RMSE values, respectively.</p>
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21 pages, 4420 KiB  
Article
Multi-Layer Perceptron Model Integrating Multi-Head Attention and Gating Mechanism for Global Navigation Satellite System Positioning Error Estimation
by Xiuxun Liu, Zuping Tang and Jiaolong Wei
Remote Sens. 2025, 17(2), 301; https://doi.org/10.3390/rs17020301 - 16 Jan 2025
Viewed by 271
Abstract
To better understand and evaluate the GNSS positioning performance, it is convenient to adopt corresponding measures to reduce the impact of errors on positioning. A GNSS positioning error estimation scheme based on an improved multi-layer perceptron model is proposed. The multi-head attention mechanism [...] Read more.
To better understand and evaluate the GNSS positioning performance, it is convenient to adopt corresponding measures to reduce the impact of errors on positioning. A GNSS positioning error estimation scheme based on an improved multi-layer perceptron model is proposed. The multi-head attention mechanism and gating operation are integrated into the multi-layer perceptron model to adaptively select and filter features, enhancing the model’s ability to understand input features. First, the original positioning error of the satellite is obtained through the Kalman filter positioning method. The data are then preprocessed to extract available features. Finally, the features are input into the constructed model for training and testing to obtain the estimated positioning error value. Two types of comparative experiments were completed. The performance of the presented model is evaluated by the root mean square error. Experimental results show that the proposed method performs well in terms of performance indicators, and has obvious advantages over other state-of-the-art methods. In particular, the root mean square error of the presented method in the first dataset is 0.239 m, which is 39.2% and 17% lower than the current state-of-the-art long short-term memory network and convolutional neural network, respectively. The presented method can provide higher-precision estimated values for studying the GNSS positioning error estimation problem. Full article
(This article belongs to the Special Issue Advances in Multi-GNSS Technology and Applications)
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<p>Schematic diagram of positioning error estimation.</p>
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<p>Overall flow chart of the presented scheme.</p>
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<p>The overall network structure of the improved MLP model.</p>
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<p>Network structure diagram of the multi-head attention gating unit.</p>
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<p>Structure diagram of the multi-head attention mechanism. Q, K, V represent the query, key, and value of the attention head, respectively.</p>
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<p>Positioning error results are obtained through the Kalman filter method.</p>
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<p>Image of the loss function of the presented model during training.</p>
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<p>Experimental results of the proposed model on the three components of East, North, and Up.</p>
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<p>Comparison of the estimated and true values of the presented method (<b>left</b>) and the random forest algorithm (<b>right</b>).</p>
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<p>Comparison of the estimation error distributions between the presented method and the RF algorithm.</p>
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<p>Stanford diagram with the presented method and the RF algorithm. The red dotted line indicates the diagonal line.</p>
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<p>Residual histogram with the presented method and the RF algorithm.</p>
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29 pages, 4271 KiB  
Article
Maximum Mixture Correntropy Criterion-Based Variational Bayesian Adaptive Kalman Filter for INS/UWB/GNSS-RTK Integrated Positioning
by Sen Wang, Peipei Dai, Tianhe Xu, Wenfeng Nie, Yangzi Cong, Jianping Xing and Fan Gao
Remote Sens. 2025, 17(2), 207; https://doi.org/10.3390/rs17020207 - 8 Jan 2025
Viewed by 340
Abstract
The safe operation of unmanned ground vehicles (UGVs) demands fundamental and essential requirements for continuous and reliable positioning performance. Traditional coupled navigation systems, combining the global navigation satellite system (GNSS) with an inertial navigation system (INS), provide continuous, drift-free position estimation. However, challenges [...] Read more.
The safe operation of unmanned ground vehicles (UGVs) demands fundamental and essential requirements for continuous and reliable positioning performance. Traditional coupled navigation systems, combining the global navigation satellite system (GNSS) with an inertial navigation system (INS), provide continuous, drift-free position estimation. However, challenges like GNSS signal interference and blockage in complex scenarios can significantly degrade system performance. Moreover, ultra-wideband (UWB) technology, known for its high precision, is increasingly used as a complementary system to the GNSS. To tackle these challenges, this paper proposes a novel tightly coupled INS/UWB/GNSS-RTK integrated positioning system framework, leveraging a variational Bayesian adaptive Kalman filter based on the maximum mixture correntropy criterion. This framework is introduced to provide a high-precision and robust navigation solution. By incorporating the maximum mixture correntropy criterion, the system effectively mitigates interference from anomalous measurements. Simultaneously, variational Bayesian estimation is employed to adaptively adjust noise statistical characteristics, thereby enhancing the robustness and accuracy of the integrated system’s state estimation. Furthermore, sensor measurements are tightly integrated with the inertial measurement unit (IMU), facilitating precise positioning even in the presence of interference from multiple signal sources. A series of real-world and simulation experiments were carried out on a UGV to assess the proposed approach’s performance. Experimental results demonstrate that the approach provides superior accuracy and stability in integrated system state estimation, significantly mitigating position drift error caused by uncertainty-induced disturbances. In the presence of non-Gaussian noise disturbances introduced by anomalous measurements, the proposed approach effectively implements error control, demonstrating substantial advantages in positioning accuracy and robustness. Full article
(This article belongs to the Topic Multi-Sensor Integrated Navigation Systems)
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<p>Message exchange process in the DS-TWR.</p>
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<p>Schematic diagram of multilateration positioning.</p>
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<p>Overview of the TC INS/UWB/GNSS-RTK integrated positioning system.</p>
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<p>Flowchart of the MMCC-based VBAKF algorithm.</p>
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<p>Overview of the UGV equipment and reference trajectory. (<b>a</b>) Experimental data collection platform. (<b>b</b>) Top view of reference trajectory.</p>
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<p>Positioning error sequences in the ENU directions for various solution strategies in Case 1.</p>
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<p>Overview of estimated position trajectory for various solution strategies in Case 1.</p>
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<p>CDF curves of horizontal positioning errors for various solution strategies in Case 1.</p>
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<p>Distribution of horizontal positioning errors for various solution strategies in Case 1.</p>
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<p>Improved percentage of the proposed MMCC-VBAKF in Case 1.</p>
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<p>Positioning error sequences in the ENU directions for various solution strategies in Case 2.</p>
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<p>Overview of estimated position trajectory for various solution strategies in Case 2.</p>
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<p>CDF curves of horizontal positioning errors for various solution strategies in Case 2.</p>
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<p>Distribution of horizontal positioning errors for various solution strategies in Case 2.</p>
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<p>Improved percentage of the proposed MMCC-VBAKF in Case 2.</p>
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14 pages, 6078 KiB  
Data Descriptor
The EDI Multi-Modal Simultaneous Localization and Mapping Dataset (EDI-SLAM)
by Peteris Racinskis, Gustavs Krasnikovs, Janis Arents and Modris Greitans
Data 2025, 10(1), 5; https://doi.org/10.3390/data10010005 - 7 Jan 2025
Viewed by 472
Abstract
This paper accompanies the initial public release of the EDI multi-modal SLAM dataset, a collection of long tracks recorded with a portable sensor package. These include two global shutter RGB camera feeds, LiDAR scans, as well as inertial and GNSS data from an [...] Read more.
This paper accompanies the initial public release of the EDI multi-modal SLAM dataset, a collection of long tracks recorded with a portable sensor package. These include two global shutter RGB camera feeds, LiDAR scans, as well as inertial and GNSS data from an RTK-enabled IMU-GNSS positioning module&#x2014;both as satellite fixes and internally fused interpolated pose estimates. The tracks are formatted as ROS1 and ROS2 bags, with separately available calibration and ground truth data. In addition to the filtered positioning module outputs, a second form of sparse ground truth pose annotation is provided using independently surveyed visual fiducial markers as a reference. This enables the meaningful evaluation of systems that directly utilize data from the positioning module into their localization estimates, and serves as an alternative when the GNSS reference is disrupted by intermittent signals or multipath scattering. In this paper, we describe the methods used to collect the dataset, its contents, and its intended use. Full article
18 pages, 7697 KiB  
Article
GNSS/IMU/ODO Integrated Navigation Method Based on Adaptive Sliding Window Factor Graph
by Xinchun Ji, Chenjun Long, Liuyin Ju, Hang Zhao and Dongyan Wei
Electronics 2025, 14(1), 124; https://doi.org/10.3390/electronics14010124 - 31 Dec 2024
Viewed by 406
Abstract
One of the predominant technologies for multi-source navigation in vehicles involves the fusion of GNSS/IMU/ODO through a factor graph. To address issues such as the asynchronous sampling frequencies between the IMU and ODO, as well as diminished accuracy during GNSS signal loss, we [...] Read more.
One of the predominant technologies for multi-source navigation in vehicles involves the fusion of GNSS/IMU/ODO through a factor graph. To address issues such as the asynchronous sampling frequencies between the IMU and ODO, as well as diminished accuracy during GNSS signal loss, we propose a GNSS/IMU/ODO integrated navigation method based on an adaptive sliding window factor graph. The measurements from the ODO are utilized as observation factors to mitigate prediction interpolation errors associated with traditional ODO pre-integration methods. Additionally, online estimation and compensation for both installation angle deviations and scale factors of the ODO further enhance its ability to constrain pose errors during GNSS signal loss. A multi-state marginalization algorithm is proposed and then utilized to adaptively adjust the sliding window size based on the quality of GNSS observations, enhancing pose optimization accuracy in multi-source fusion while prioritizing computational efficiency. Tests conducted in typical urban environments and mountainous regions demonstrate that our proposed method significantly enhances fusion navigation accuracy under complex GNSS conditions. In a complex city environment, our method achieves a 55.3% and 29.8% improvement in position and velocity accuracy and enhancements of 32.0% and 61.6% in pitch and heading angle accuracy, respectively. These results match the precision of long sliding windows, with a 75.8% gain in computational efficiency. In mountainous regions, our method enhances the position accuracy in the three dimensions by factors of 89.5%, 83.7%, and 43.4%, the velocity accuracy in the three dimensions by factors of 65.4%, 32.6%, and 53.1%, and reduces the attitude errors in roll, pitch, and yaw by 70.5%, 60.8%, and 26.0%, respectively, demonstrating strong engineering applicability through an optimal balance of precision and efficiency. Full article
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<p>General framework of the algorithm.</p>
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<p>GNSS/IMU/ODO fusion algorithm based on a factor graph.</p>
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<p>Factor graph fusion algorithm using ODO as a factor.</p>
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<p>The lever arm and installation angle.</p>
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<p>Fixed window and adaptive window.</p>
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<p>Test Vehicle and Equipment Installation.</p>
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<p>Test route and scene.</p>
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<p>GNSS positioning accuracy (B: latitude, L: longitude, H: height).</p>
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<p>Dataset of IMU and ODO.</p>
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<p>Error of without ODO, ODO as pre-integrals, ODO as factors: (<b>a</b>) Position; (<b>b</b>) Velocity; (<b>c</b>) Attitude. (E: East, N: North, U: Up).</p>
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<p>Error of with and without installation angle: (<b>a</b>) Position; (<b>b</b>) Velocity; (<b>c</b>) Attitude. (FAC: without installation angle, ESTABV: with installation angle).</p>
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<p>ODO scale factor and installation angle.</p>
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<p>Error of fixed and adaptive sliding window: (<b>a</b>) Position; (<b>b</b>) Velocity; (<b>c</b>) Attitude.</p>
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<p>Mountainous region test route.</p>
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<p>Error of fixed and adaptive sliding window (mountainous regions): (<b>a</b>) Position; (<b>b</b>) Velocity; (<b>c</b>) Attitude.</p>
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24 pages, 7901 KiB  
Article
Design of CubeSat-Based Multi-Regional Positioning Navigation and Timing System in Low Earth Orbit
by Georgios Tzanoulinos, Nori Ait-Mohammed and Vaios Lappas
Aerospace 2025, 12(1), 19; https://doi.org/10.3390/aerospace12010019 - 31 Dec 2024
Viewed by 615
Abstract
The Global Navigation Satellite System (GNSS) provides critical positioning, navigation, and timing (PNT) services worldwide, enabling a wide range of applications from everyday use to advanced scientific and military operations. The importance of Low Earth Orbit (LEO) PNT systems lies in their ability [...] Read more.
The Global Navigation Satellite System (GNSS) provides critical positioning, navigation, and timing (PNT) services worldwide, enabling a wide range of applications from everyday use to advanced scientific and military operations. The importance of Low Earth Orbit (LEO) PNT systems lies in their ability to enhance the GNSS by implementing signals in additional frequency bands, offering increased signal strength, reduced latency, and improved accuracy and coverage, particularly in challenging environments such as urban canyons or polar regions, thereby addressing the limitations of the traditional Medium Earth Orbit (MEO) GNSS. This paper details the system engineering of a novel CubeSat-based multi-regional PNT system tailored for deployment in LEO. The proposed system leverages on a miniaturized CubeSat-compatible PNT payload that includes a chip-scale atomic clock (CSAC) and relies on MEO GNSS technologies to deliver positioning and timing information across multiple regions. The findings indicate that the proposed CubeSat-based PNT system offers a viable solution for enhancing global navigation and timing services, with potential commercial and scientific applications. This work contributes to the growing body of knowledge on LEO-based PNT systems and lays the groundwork for future research and development in this rapidly evolving field. Full article
(This article belongs to the Special Issue Small Satellite Missions)
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<p>Architecture of a CubeSat-based PNT payload in line with New Space.</p>
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<p>Mission architecture.</p>
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<p>GCS locations.</p>
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<p>Constellation configuration tradeoff process.</p>
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<p>Walker Delta 61°: 100/10/1 constellation at 550 km that tracks Germany.</p>
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<p>CROC 3D model.</p>
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<p>Number of impacts (<b>a</b>) and catastrophic impacts (<b>b</b>) vs. time for objects between 1 mm and 1 cm and number of impacts (<b>c</b>) and catastrophic impacts (<b>d</b>) vs. time for objects above 1 cm.</p>
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<p>Orbital decay analysis—passive disposal after deorbit maneuver.</p>
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<p>SARA re-entry simulation—altitude vs. time.</p>
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<p>S/C internal (<b>a</b>) and external (<b>b</b>) view.</p>
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<p>Battery SoC—day in the life simulation—nominal scenario for a single day (<b>a</b>) and for 5 days (<b>b</b>).</p>
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<p>A CubeSat in nadir pointing mode remains oriented towards the center of Earth throughout the orbit [<a href="#B20-aerospace-12-00019" class="html-bibr">20</a>].</p>
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<p>Thermal simulation: 5 days in the life—50% electrical power-to-heat conversion ratio (<b>a</b>) and 100% electrical power-to-heat conversion ratio (<b>b</b>).</p>
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<p>Frequency response of the CSAC while exposed to −10 °C to +50 °C [<a href="#B24-aerospace-12-00019" class="html-bibr">24</a>].</p>
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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 627
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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Graphical abstract
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<p>PWV variation trend in different regions of China from GNSS observations (Reprinted from Ref. [<a href="#B26-remotesensing-16-04800" class="html-bibr">26</a>]).</p>
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<p>Geometric model of GNSS multipath reflectometry (GNSS-R).</p>
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<p>Convergence time using different system combinations and ‘GBM’ products with the average floating-point solution (<b>top</b>) and fixed solution (<b>bottom</b>) at each site (Reprinted from Ref. [<a href="#B32-remotesensing-16-04800" class="html-bibr">32</a>]).</p>
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<p>The positioning-error sequence of dynamic PPP by using the ambiguity floating point solution and the ambiguity-fixed solution of real-time products (Reprinted from Ref. [<a href="#B32-remotesensing-16-04800" class="html-bibr">32</a>]).</p>
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<p>The positioning accuracy of the GPS + Galileo combined solution is improved in kinematic PPP when compared to the GPS-only and Galileo-only solutions (Reprinted from Ref. [<a href="#B33-remotesensing-16-04800" class="html-bibr">33</a>]).</p>
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<p>Static positional biases of AR and float solutions for MGEX stations on DoY 183, 2022 (Reprinted from Ref. [<a href="#B34-remotesensing-16-04800" class="html-bibr">34</a>]).</p>
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<p>The spatial distribution of TEC at 13:00 UT during DOY 80, 170, 270, and 360 in 2023 for the double-layer SH model (<b>left</b>) and GIM-IGS (<b>right</b>) (Reprinted with permission from Ref. [<a href="#B44-remotesensing-16-04800" class="html-bibr">44</a>]. 2024 Jin, S.).</p>
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<p>Daily average TEC from GIM, GEDM, IRI-2020 in 2010 (<b>left</b>), and 2014 (<b>right</b>) (Reprinted with permission from Ref. [<a href="#B45-remotesensing-16-04800" class="html-bibr">45</a>]. 2024 Jin, S.).</p>
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<p>Ionospheric disturbance characteristics during Typhoon Chandu, from GPS PRN32 and GLONASS PRN1 (Reprinted with permission from Ref. [<a href="#B47-remotesensing-16-04800" class="html-bibr">47</a>]. 2024 Jin, S.).</p>
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<p>Estimation and evaluation of ZTD from single and multiple GNSS observations (Reprinted from Ref. [<a href="#B24-remotesensing-16-04800" class="html-bibr">24</a>]).</p>
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<p>The differences in ZTD RMSE between La Nina and non-La Nina IGS stations (Reprinted with permission from Ref. [<a href="#B48-remotesensing-16-04800" class="html-bibr">48</a>]. 2024 Ye, S.).</p>
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<p>Data processing flow chart for high-frequency GNSS-R water level monitoring (Reprinted with permission from Ref. [<a href="#B50-remotesensing-16-04800" class="html-bibr">50</a>]. 2022 Jin, S.).</p>
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<p>Biases (<b>a</b>,<b>b</b>) and RMSEs (<b>c</b>,<b>d</b>) of the retrieved wind speed for (<b>a</b>,<b>c</b>) cyclone-free and (<b>b</b>,<b>d</b>) cyclonic conditions (Reprinted with permission from Ref. [<a href="#B54-remotesensing-16-04800" class="html-bibr">54</a>]. 2023 Zhang, G.).</p>
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21 pages, 6254 KiB  
Article
Gaussian–Student’s t Mixture Distribution-Based Robust Kalman Filter for Global Navigation Satellite System/Inertial Navigation System/Odometer Data Fusion
by Jiaji Wu, Jinguang Jiang, Yanan Tang and Jianghua Liu
Remote Sens. 2024, 16(24), 4716; https://doi.org/10.3390/rs16244716 - 17 Dec 2024
Viewed by 589
Abstract
Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS/INS/odometer integrated navigation system is complex and [...] Read more.
Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS/INS/odometer integrated navigation system is complex and non-stationary; it approximates a Gaussian distribution in an open-sky environment, and it has heavy-tailed properties in the GNSS challenging environment. This work models the measurement noise and one-step prediction as the Gaussian and Student’s t mixture distribution to adjust to different scenarios. The mixture distribution is formulated as the hierarchical Gaussian form by introducing Bernoulli random variables, and the corresponding hierarchical Gaussian state-space model is constructed. Then, the mixing probability of Gaussian and Student’s t distributions could adjust adaptively according to the real-time kinematic solution state. Based on the novel distribution, a robust variational Bayesian Kalman filter is proposed. Finally, two vehicle test cases conducted in GNSS-friendly and challenging environments demonstrate that the proposed robust Kalman filter with the Gaussian–Student’s t mixture distribution can better model heavy-tailed non-Gaussian noise. In challenging environments, the proposed algorithm has position root mean square (RMS) errors of 0.80 m, 0.62 m, and 0.65 m in the north, east, and down directions, respectively. With the assistance of inertial sensors, the positioning gap caused by GNSS outages has been compensated. During seven periods of 60 s simulated GNSS data outages, the RMS position errors in the north, east, and down directions were 0.75 m, 0.30 m, and 0.20 m, respectively. Full article
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<p>Running trajectory of test vehicle. The trajectory of test case 1 is on the left, and the trajectory of test case 2 is on the right.</p>
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<p>Testing equipment and installation.</p>
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<p>Q-Q plot of GNSS measurement noise in open-sky and urban areas.</p>
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<p>Determined reference and GNSS trajectories for test case 1. Brown represents the trajectory during 7 simulated GNSS outages.</p>
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<p>The position error results of the three schemes in test case 1 under intentional GNSS outages.</p>
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<p>The velocity error results of the three schemes in test case 1 under intentional GNSS outages.</p>
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<p>The attitude error results of the three schemes in test case 1 under intentional GNSS outages.</p>
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<p>CDF results of the three schemes in test case 1 under intentional GNSS outages.</p>
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<p>The resulting position error of the three schemes in test case 2.</p>
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<p>The velocity error results of the three schemes in test case 2.</p>
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<p>The attitude error results of the three schemes in test case 2.</p>
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<p>CDF results of the three schemes in test case 2.</p>
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39 pages, 11124 KiB  
Article
XAI GNSS—A Comprehensive Study on Signal Quality Assessment of GNSS Disruptions Using Explainable AI Technique
by Arul Elango and Rene Jr. Landry
Sensors 2024, 24(24), 8039; https://doi.org/10.3390/s24248039 - 17 Dec 2024
Viewed by 736
Abstract
The hindering of Global Navigation Satellite Systems (GNSS) signal reception by jamming and spoofing attacks degrades the signal quality. Careful attention needs to be paid when post-processing the signal under these circumstances before feeding the signal into the GNSS receiver’s post-processing stage. The [...] Read more.
The hindering of Global Navigation Satellite Systems (GNSS) signal reception by jamming and spoofing attacks degrades the signal quality. Careful attention needs to be paid when post-processing the signal under these circumstances before feeding the signal into the GNSS receiver’s post-processing stage. The identification of the time domain statistical attributes and the spectral domain characteristics play a vital role in analyzing the behaviour of the signal characteristics under various kinds of jamming attacks, spoofing attacks, and multipath scenarios. In this paper, the signal records of five disruptions (pure, continuous wave interference (CWI), multi-tone continuous wave interference (MCWI), multipath (MP), spoofing, pulse, and chirp) are examined, and the most influential features in both the time and frequency domains are identified with the help of explainable AI (XAI) models. Different Machine learning (ML) techniques were employed to assess the importance of the features to the model’s prediction. From the statistical analysis, it has been observed that the usage of the SHapley Additive exPlanations (SHAP) and local interpretable model-agnostic explanations (LIME) models in GNSS signals to test the types of disruption in unknown GNSS signals, using only the best-correlated and most important features in the training phase, provided a better classification accuracy in signal prediction compared to traditional feature selection methods. This XAI model reveals the black-box ML model’s output prediction and provides a clear explanation of the specific signal occurrences based on the individual feature contributions. By using this black-box revealer, we can easily analyze the behaviour of the GNSS ground-station signals and employ fault detection and resilience diagnosis in GNSS post-processing. Full article
(This article belongs to the Special Issue Signal Processing for Satellite Navigation and Wireless Localization)
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<p>(<b>a</b>) Skydel CSG-8 GNSS simulator setup for recording jamming and spoofing signals, (<b>b</b>) Various GNSS disruption recording setups and post-processing using GNSS SDR.</p>
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<p>(<b>a</b>) Clean GNSS signal in the time domain and its spectrum in the frequency domain recorded using RTL SDR. (<b>b</b>) CWI GNSS signals in the time domain and its spectrum in the frequency domain recorded using RTL SDR. (<b>c</b>) Pulse interference GNSS signal in the time domain and its spectrum in the frequency domain recorded using RTL SDR. (<b>d</b>) Chirp interference GNSS signal in the time domain and its spectrum in the frequency domain recorded using RTL SDR.</p>
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<p>(<b>a</b>) Clean GNSS signal in the time domain and its spectrum in the frequency domain recorded using RTL SDR. (<b>b</b>) CWI GNSS signals in the time domain and its spectrum in the frequency domain recorded using RTL SDR. (<b>c</b>) Pulse interference GNSS signal in the time domain and its spectrum in the frequency domain recorded using RTL SDR. (<b>d</b>) Chirp interference GNSS signal in the time domain and its spectrum in the frequency domain recorded using RTL SDR.</p>
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<p>(<b>a</b>) Correlation maps for time domain features (<b>i</b>) Clean GNSS (<b>ii</b>) Chirp (<b>iii</b>) Pulse (<b>iv</b>) CWI (<b>v</b>) Spoofing (<b>vi</b>) Multipath (<b>vii</b>) MCWI. (<b>b</b>) Correlation maps for frequency domain features (<b>i</b>) Clean GNSS (<b>ii</b>) Chirp (<b>iii</b>) Pulse (<b>iv</b>) CWI (<b>v</b>) Spoofing (<b>vi</b>) Multipath (<b>vii</b>) MCWI.</p>
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<p>(<b>a</b>) Correlation maps for time domain features (<b>i</b>) Clean GNSS (<b>ii</b>) Chirp (<b>iii</b>) Pulse (<b>iv</b>) CWI (<b>v</b>) Spoofing (<b>vi</b>) Multipath (<b>vii</b>) MCWI. (<b>b</b>) Correlation maps for frequency domain features (<b>i</b>) Clean GNSS (<b>ii</b>) Chirp (<b>iii</b>) Pulse (<b>iv</b>) CWI (<b>v</b>) Spoofing (<b>vi</b>) Multipath (<b>vii</b>) MCWI.</p>
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<p>(<b>a</b>) Correlation maps for time domain features (<b>i</b>) Clean GNSS (<b>ii</b>) Chirp (<b>iii</b>) Pulse (<b>iv</b>) CWI (<b>v</b>) Spoofing (<b>vi</b>) Multipath (<b>vii</b>) MCWI. (<b>b</b>) Correlation maps for frequency domain features (<b>i</b>) Clean GNSS (<b>ii</b>) Chirp (<b>iii</b>) Pulse (<b>iv</b>) CWI (<b>v</b>) Spoofing (<b>vi</b>) Multipath (<b>vii</b>) MCWI.</p>
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<p>(<b>a</b>) Frequency domain features at different jamming power levels, (<b>b</b>) Time domain features under various jamming power levels.</p>
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<p>(<b>a</b>) Frequency domain features at different jamming power levels, (<b>b</b>) Time domain features under various jamming power levels.</p>
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<p>(<b>a</b>) Frequency domain features at different jamming power levels, (<b>b</b>) Time domain features under various jamming power levels.</p>
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<p>(<b>a</b>) Frequency domain features at different jamming power levels, (<b>b</b>) Time domain features under various jamming power levels.</p>
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<p>Boxplot comparison of different disruptions in GNSS signals based on <span class="html-italic">p</span>-values.</p>
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<p>The proposed XAI framework-based GNSS signal disruption classification model.</p>
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<p>(<b>a</b>) Frequency domain LIME model decision for correct/incorrect predictions of GNSS signal for different ML models (<b>i</b>) Decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) Random forest, and (<b>v</b>) SVM. (<b>b</b>) Time domain LIME model decision of correct/incorrect predictions of GNSS signal for different ML models: (<b>i</b>) Decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) Random forest, and (<b>v</b>) SVM.</p>
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<p>(<b>a</b>) Frequency domain LIME model decision for correct/incorrect predictions of GNSS signal for different ML models (<b>i</b>) Decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) Random forest, and (<b>v</b>) SVM. (<b>b</b>) Time domain LIME model decision of correct/incorrect predictions of GNSS signal for different ML models: (<b>i</b>) Decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) Random forest, and (<b>v</b>) SVM.</p>
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<p>(<b>a</b>) Feature contributions based on frequency domain attributes: (<b>i</b>) decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) random forest, and (<b>v</b>) SVM. (<b>b</b>) Plots of contributions of combinations of time domain features for different types of GNSS signal disruptions: (<b>i</b>) decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) random forest, and (<b>v</b>) SVM.</p>
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<p>(<b>a</b>) Feature contributions based on frequency domain attributes: (<b>i</b>) decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) random forest, and (<b>v</b>) SVM. (<b>b</b>) Plots of contributions of combinations of time domain features for different types of GNSS signal disruptions: (<b>i</b>) decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) random forest, and (<b>v</b>) SVM.</p>
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<p>(<b>a</b>) Feature contributions based on frequency domain attributes: (<b>i</b>) decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) random forest, and (<b>v</b>) SVM. (<b>b</b>) Plots of contributions of combinations of time domain features for different types of GNSS signal disruptions: (<b>i</b>) decision tree, (<b>ii</b>) AdaBoost, (<b>iii</b>) KNN, (<b>iv</b>) random forest, and (<b>v</b>) SVM.</p>
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<p>(<b>a</b>): Frequency domain feature importance comparison using different ML algorithms. (<b>b</b>): Time domain feature importance comparison using different ML algorithms.</p>
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<p>(<b>a</b>) Waterfall summary plots (time domain), (<b>i</b>) Pulsed; (<b>ii</b>) CWI; (<b>iii</b>) MCWI; (<b>iv</b>) MP; (<b>v</b>) Clean; (<b>vi</b>) Chirp; (<b>vii</b>) Spoofing. (<b>b</b>) Waterfall summary plots (frequency domain), (<b>i</b>) Pulsed (<b>ii</b>) CWI; (<b>iii</b>) Clean; (<b>iv</b>) chirp; (<b>v</b>) MCWI; (<b>vi</b>) MP; (<b>vii</b>) Spoofing.</p>
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<p>(<b>a</b>) Waterfall summary plots (time domain), (<b>i</b>) Pulsed; (<b>ii</b>) CWI; (<b>iii</b>) MCWI; (<b>iv</b>) MP; (<b>v</b>) Clean; (<b>vi</b>) Chirp; (<b>vii</b>) Spoofing. (<b>b</b>) Waterfall summary plots (frequency domain), (<b>i</b>) Pulsed (<b>ii</b>) CWI; (<b>iii</b>) Clean; (<b>iv</b>) chirp; (<b>v</b>) MCWI; (<b>vi</b>) MP; (<b>vii</b>) Spoofing.</p>
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<p>(<b>a</b>) Waterfall summary plots (time domain), (<b>i</b>) Pulsed; (<b>ii</b>) CWI; (<b>iii</b>) MCWI; (<b>iv</b>) MP; (<b>v</b>) Clean; (<b>vi</b>) Chirp; (<b>vii</b>) Spoofing. (<b>b</b>) Waterfall summary plots (frequency domain), (<b>i</b>) Pulsed (<b>ii</b>) CWI; (<b>iii</b>) Clean; (<b>iv</b>) chirp; (<b>v</b>) MCWI; (<b>vi</b>) MP; (<b>vii</b>) Spoofing.</p>
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<p>(<b>a</b>) SHAP force plots for GNSS time domain features, From top: (<b>i</b>) pulse, (<b>ii</b>) CWI, (<b>iii</b>) clean, (<b>iv</b>) chirp, (<b>v</b>) MCWI, (<b>vi</b>) multipath, and (<b>vii</b>) spoofing signals. (<b>b</b>) SHAP force plots for GNSS frequency domain features. From top: (<b>i</b>) pulse, (<b>ii</b>) CWI, (<b>iii</b>) clean, (<b>iv</b>) chirp, (<b>v</b>) MCWI, (<b>vi</b>) multipath, and (<b>vii</b>) spoofing signals.</p>
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<p>(<b>a</b>) SHAP force plots for GNSS time domain features, From top: (<b>i</b>) pulse, (<b>ii</b>) CWI, (<b>iii</b>) clean, (<b>iv</b>) chirp, (<b>v</b>) MCWI, (<b>vi</b>) multipath, and (<b>vii</b>) spoofing signals. (<b>b</b>) SHAP force plots for GNSS frequency domain features. From top: (<b>i</b>) pulse, (<b>ii</b>) CWI, (<b>iii</b>) clean, (<b>iv</b>) chirp, (<b>v</b>) MCWI, (<b>vi</b>) multipath, and (<b>vii</b>) spoofing signals.</p>
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<p>ROC one-vs-rest multiclass plot of machine learning models tested under different GNSS signal disruptions.</p>
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<p>Confusion matrices (frequency domain features).</p>
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21 pages, 36735 KiB  
Article
Adaptive Navigation Based on Multi-Agent Received Signal Quality Monitoring Algorithm
by Hina Magsi, Madad Ali Shah, Ghulam E. Mustafa Abro, Sufyan Ali Memon, Abdul Aziz Memon, Arif Hussain and Wan-Gu Kim
Electronics 2024, 13(24), 4957; https://doi.org/10.3390/electronics13244957 - 16 Dec 2024
Viewed by 440
Abstract
In the era of industrial evolution, satellites are being viewed as swarm intelligence that does not rely on a single system but multiple constellations that collaborate autonomously. This has enhanced the potential of the Global Navigation Satellite System (GNSS) to contribute to improving [...] Read more.
In the era of industrial evolution, satellites are being viewed as swarm intelligence that does not rely on a single system but multiple constellations that collaborate autonomously. This has enhanced the potential of the Global Navigation Satellite System (GNSS) to contribute to improving position, navigation, and timing (PNT) services. However, multipath (MP) and non-line-of-sight (NLOS) receptions remain the prominent vulnerability for the GNSS in harsh environments. The aim of this research is to investigate the impact of MP and NLOS receptions on GNSS performance and then propose a Received Signal Quality Monitoring (RSQM) algorithm. The RSQM algorithm works in two ways. Initially, it performs a signal quality test based on a fuzzy inference system. The input parameters are carrier-to-noise ratio (CNR), Normalized Range Residuals (NRR), and Code–Carrier Divergence (CCD), and it computes the membership functions based on the Mamdani method and classifies the signal quality as LOS, NLOS, weak NLOS, and strong NLOS. Secondly, it performs an adaptive navigation strategy to exclude/mask the affected range measurements while considering the satellite geometry constraints (i.e., DOP2). For this purpose, comprehensive research to quantify the multi-constellation GNSS receiver with four constellation configurations (GPS, BeiDou, GLONASS, and Galileo) has been carried out in various operating environments. This RSQM-based GNSS receiver has the capability to identify signal quality and perform adaptive navigation accordingly to improve navigation performance. The results suggest that GNSS performance in terms of position error is improved from 5.4 m to 2.3 m on average in the complex urban environment. Combining the RSQM algorithm with the GNSS has great potential for the future industrial revolution (Industry 5.0), making things automatic and sustainable like autonomous vehicle operation. Full article
(This article belongs to the Special Issue Collaborative Intelligence in the Era of Industry 5.0)
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<p>Complete organization of the paper.</p>
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<p>Potential Vulnerabilities of satellite signal reception in urban environment. S1–S4 are satellites in the space from 1 to 4.</p>
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<p>Workflow of the paper.</p>
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<p>Candidate sites for Static experiments; (<b>a</b>) Best case environment, (<b>b</b>) Mediocre Multipath, (<b>c</b>) Worst Multipath (highlighted in box).</p>
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<p>Live images of moving candidate sites; (<b>a</b>) Complete route of moving experiment, (<b>b</b>) clear site, (<b>c</b>) sub-urban, (<b>d</b>) highly urban environment.</p>
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<p>Flow chart of the RSQM.</p>
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<p>Fuzzy inference system.</p>
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<p>Fuzzy logic memebrship functions.</p>
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<p>Positioning performance comparison of multi-constellation GNSS in dynamic (moving) mode. (<b>a</b>) Satellite Availability, (<b>b</b>) PDOP and (<b>c</b>) Position Error (m).</p>
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<p>Positioning performance comparison of multi-constellation GNSS.</p>
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<p>Satellite Signal Characteristics in Urban Canyon. (<b>a</b>) CNR (dB-Hz), (<b>b</b>) CCD (m) and (<b>c</b>) RR (m) for all three candidate sites clear open sky, moderately degraded and severe degraded.</p>
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<p>Histogram and normal distribution of CNR for all the environments (<b>a</b>) Clear open sky, (<b>b</b>) Degraded Environment and (<b>c</b>) Highly degraded environment.</p>
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<p>Histogram and normal distribution of CCD for all the environments (<b>a</b>) Clear open sky, (<b>b</b>) Degraded Environment and (<b>c</b>) Highly degraded environment.</p>
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<p>Histogram and normal distribution of CNR for all the environments (<b>a</b>) Clear open sky, (<b>b</b>) Degraded Environment and (<b>c</b>) Highly degraded environment.</p>
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<p>Performance of GNSS after mitigation strategy. (<b>a</b>) Satellite availability, (<b>b</b>) PDOP and (<b>c</b>) Position Error (m).</p>
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26 pages, 11470 KiB  
Article
An Elastic Filtering Algorithm with Visual Perception for Vehicle GNSS Navigation and Positioning
by Wenzhuo Ma, Zhe Yue, Zengzeng Lian, Kezhao Li, Chenchen Sun and Mengshuo Zhang
Sensors 2024, 24(24), 8019; https://doi.org/10.3390/s24248019 - 16 Dec 2024
Viewed by 418
Abstract
Amidst the backdrop of the profound synergy between navigation and visual perception, there is an urgent demand for accurate real-time vehicle positioning in urban environments. However, the existing global navigation satellite system (GNSS) algorithms based on Kalman filters fall short of precision. In [...] Read more.
Amidst the backdrop of the profound synergy between navigation and visual perception, there is an urgent demand for accurate real-time vehicle positioning in urban environments. However, the existing global navigation satellite system (GNSS) algorithms based on Kalman filters fall short of precision. In response, we introduce an elastic filtering algorithm with visual perception for vehicle GNSS navigation and positioning. Firstly, the visual perception system captures real-time environmental data around the vehicle. It utilizes the interframe differential optical flow method and vehicle state switching characteristics to assess the current driving status. Secondly, we design an elastic filtering model specifically for various vehicle states. This model enhances the precision of Kalman filter-based GNSS navigation. In urban driving, vehicles often experience frequent stationary parking. To address this, we incorporate a zero-speed constraint to further refine vehicle location data when the vehicle is stationary. This constraint matches the data with the appropriate elastic filtering model. Ultimately, we conduct simulation and real-world vehicle navigation experiments to confirm the validity and rationality of our proposed algorithm. Compared with the conventional algorithm and the existing interactive multi-model algorithm, the proposed algorithm significantly improves the navigation and positioning accuracy of vehicle GNSS in urban environments. Compared to the commonly used constant acceleration (CA) and Constant Velocity (CV) models, there has been a significant improvement in positioning accuracy. Furthermore, when benchmarked against the more advanced interactive multi-model (IMM) model, the method proposed in this paper has enhanced the positioning accuracy enhancements in three dimensions: 21.8%, 20.9%, and 31.3%, respectively. Full article
(This article belongs to the Special Issue Navigation and Autonomous Driving in Electric Vehicles)
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<p>Flowchart of the Proposed Algorithm.</p>
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<p>Experimental Platform.</p>
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<p>Captured Upward-Facing Environmental Information.</p>
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<p>Inter-Frame Differential Optical Flow Visualization.</p>
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<p>Vehicle Stationary Interval Result.</p>
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<p>Vehicle Turning Interval Result.</p>
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<p>Vehicle Acceleration and Deceleration Interval.</p>
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<p>Simulation Experiment Path.</p>
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<p>Simulation Experiment X-Direction Positioning Error.</p>
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<p>Simulation Experiment Y-Direction Positioning Error.</p>
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<p>Simulation Experiment Z-Direction Positioning Error.</p>
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<p>RMSE Statistics in Simulation Experiments.</p>
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<p>Environmental Information Collection Process.</p>
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<p>Data Storage Set Construction.</p>
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<p>Data File Check Interface.</p>
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<p>Top view of the experimental path.</p>
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<p>Actual Experimental Path Result.</p>
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<p>Actual experimental X-direction error and an enlarged view of certain periods.</p>
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<p>Actual experimental Y-direction error and an enlarged view of certain periods.</p>
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<p>Actual experimental Z-direction error and an enlarged view of certain periods.</p>
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<p>RMSE Statistics in Actual Experiments.</p>
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19 pages, 21587 KiB  
Article
Multipath Mitigation in Single-Frequency Multi-GNSS Tightly Combined Positioning via a Modified Multipath Hemispherical Map Method
by Yuan Tao, Chao Liu, Runfa Tong, Xingwang Zhao, Yong Feng and Jian Wang
Remote Sens. 2024, 16(24), 4679; https://doi.org/10.3390/rs16244679 - 15 Dec 2024
Viewed by 588
Abstract
Multipath is a source of error that limits the Global Navigation Satellite System (GNSS) positioning precision in short baselines. The tightly combined model between systems increases the number of observations and enhances the strength of the mathematical model owing to the continuous improvement [...] Read more.
Multipath is a source of error that limits the Global Navigation Satellite System (GNSS) positioning precision in short baselines. The tightly combined model between systems increases the number of observations and enhances the strength of the mathematical model owing to the continuous improvement in GNSS. Multipath mitigation of the multi-GNSS tightly combined model can improve the positioning precision in complex environments. Interoperability of the multipath hemispherical map (MHM) models of different systems can enhance the performance of the MHM model due to the small multipath differences in single overlapping frequencies. The adoption of advanced sidereal filtering (ASF) to model the multipath for each satellite brings computational challenges owing to the characteristics of the multi-constellation heterogeneity of different systems; the balance efficiency and precision become the key issues affecting the performance of the MHM model owing to the sparse characteristics of the satellite distribution. Therefore, we propose a modified MHM method to mitigate the multipath for single-frequency multi-GNSS tightly combined positioning. The method divides the hemispherical map into 36 × 9 grids at 10° × 10° resolution and then searches with the elevation angle and azimuth angle as independent variables to obtain the multipath value of the nearest point. We used the k-d tree to improve the search efficiency without affecting precision. Experiments show that the proposed method improves the mean precision over ASF by 10.20%, 10.77%, and 9.29% for GPS, BDS, and Galileo satellite single-difference residuals, respectively. The precision improvements of the modified MHM in the E, N, and U directions were 32.82%, 40.65%, and 31.97%, respectively. The modified MHM exhibits greater performance and behaves more consistently. Full article
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<p>Time delays of orbital repeat period of GPS, BDS, and Galileo satellites in 2022.</p>
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<p>Hemispherical map with two typical grids.</p>
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<p>Construction process of the k-d tree.</p>
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<p>The processing flow of the modified MHM model.</p>
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<p>Observation environment around the station.</p>
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<p>PDOP, HDOP, VDOP, and the number of observable satellites for multi-GNSS.</p>
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<p>RMS of single-difference residuals for different elevation.</p>
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<p>Single-difference residuals and elevation of GPS MEO G12 (<b>a</b>), Galileo MEO E19 (<b>b</b>), BDS-3 MEO C38 (<b>c</b>) and IGSO C20 (<b>d</b>).</p>
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<p>Original single-difference residuals for the G12 satellite and the multipath obtained by modified MHM and the residuals mitigated by modified MHM.</p>
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<p>Hemispherical maps of the original single difference residual (<b>a</b>–<b>d</b>) and mitigated by using the modified MHM method (<b>e</b>–<b>h</b>) for GPS, Galileo, BDS, and GPS/Galileo/BDS combined observations, respectively. (The black rectangles in (<b>d</b>,<b>h</b>) are used to mark the areas in the sky map where multipath errors and improvements are evident).</p>
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<p>RMS of the original residuals and residuals mitigated by the modified MHM of DOY92 in the E/N/U directions.</p>
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<p>Original single-difference residuals of G12, E19, C20, and C38 and the residuals mitigated by ASF and modified MHM methods.</p>
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<p>Precision improvement of GPS, BDS, and Galileo single-difference residuals, respectively.</p>
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<p>Original baseline series and the series after multipath mitigation by using ASF and modified MHM methods in DOY92.</p>
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<p>PSD of the original series and the series mitigated by both methods.</p>
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<p>Precision improvement of original components and the components after multipath mitigation by three methods from DOY92-DOY106.</p>
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19 pages, 4869 KiB  
Article
A Noise Reduction Method for Signal Reconstruction and Error Compensation of a Maglev Gyroscope Under Persistent External Interference
by Di Liu, Zhen Shi, Ziyi Yang and Chenxi Zou
Sensors 2024, 24(24), 8005; https://doi.org/10.3390/s24248005 - 15 Dec 2024
Viewed by 545
Abstract
To eliminate the noise interference caused by continuous external environmental disturbances on the rotor signals of a maglev gyroscope, this study proposes a noise reduction method that integrates an adaptive particle swarm optimization variational modal decomposition algorithm with a strategy for error compensation [...] Read more.
To eliminate the noise interference caused by continuous external environmental disturbances on the rotor signals of a maglev gyroscope, this study proposes a noise reduction method that integrates an adaptive particle swarm optimization variational modal decomposition algorithm with a strategy for error compensation of the trend term in reconstructed signals, significantly improving the azimuth measurement accuracy of the gyroscope torque sensor. The optimal parameters for the variational modal decomposition algorithm were determined using the adaptive particle swarm optimization algorithm, allowing for the accurate decomposition of noisy rotor signals. Additionally, using multi-scale permutation entropy as a criterion for discriminant, the signal components were filtered and summed to obtain the denoised reconstructed signal. Furthermore, an empirical mode decomposition algorithm was employed to extract the trend term of the reconstructed signal, which was then used to compensate for the errors in the reconstructed signal, achieving significant noise reduction. On-site experiments were conducted on the high-precision GNSS baseline of the Xianyang Yuan Tunnel in the second phase of the project to divert water from the Han River to the Wei River, where this method was applied to process and analyze multiple sets of rotor signals. The experimental results show that this method effectively suppresses continuous external environmental interference, reducing the average standard deviation of the compensated signals by 46.10% and the average measurement error of the north azimuth by 45.63%. Its noise reduction performance surpasses that of the other four algorithms. Full article
(This article belongs to the Section Navigation and Positioning)
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<p>Time series of rotor sampling signals in different observation environments: (<b>a</b>) stable observation environment; (<b>b</b>) observation environment with persistent external interference.</p>
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<p>Mean distribution of rotor signal and its decomposed components under different observation environments: (<b>a</b>) stable observation environment; (<b>b</b>) observation environment with persistent external interference.</p>
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<p>The framework of rotor signal denoising algorithm integrating APVMD signal decomposition and reconstructed signal error compensation.</p>
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<p>Schematic diagram of the field experiment.</p>
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<p>Typical classification and data characteristics of rotor signals under persistent external environmental interference: (<b>a</b>,<b>b</b>) irregular periodic-type; (<b>c</b>,<b>d</b>) jitter-type; (<b>e</b>,<b>f</b>) mixed-type.</p>
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<p>Typical classification and data characteristics of rotor signals under persistent external environmental interference: (<b>a</b>,<b>b</b>) irregular periodic-type; (<b>c</b>,<b>d</b>) jitter-type; (<b>e</b>,<b>f</b>) mixed-type.</p>
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<p>Iteration process of fitness function values corresponding to different optimization algorithms: (<b>a</b>) Signal 1; (<b>b</b>) Signal 2; (<b>c</b>) Signal 3.</p>
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<p>Reconstructed results of rotor signals: (<b>a</b>) reconstructed signal corresponding to Signal 1; (<b>b</b>) reconstructed signal corresponding to Signal 2; (<b>c</b>) reconstructed signal corresponding to Signal 3.</p>
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<p>Trend term extraction results of the three sets of reconstructed signals: (<b>a</b>) trend term of Signal 1; (<b>b</b>) trend term of Signal 2; (<b>c</b>) trend term of Signal 3.</p>
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<p>Results of error compensation for the reconstructed signal and the mean value change of the compensated signal: (<b>a</b>,<b>b</b>) Signal 1; (<b>c</b>,<b>d</b>) Signal 2; (<b>e</b>,<b>f</b>) Signal 3.</p>
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<p>Evaluation of the noise reduction effect of the compensated signal: (<b>a</b>) changes in the <span class="html-italic">D</span> value metric; (<b>b</b>) changes in the <span class="html-italic">Std</span> metric.</p>
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22 pages, 7255 KiB  
Article
Evaluating Ionospheric Total Electron Content (TEC) Variations as Precursors to Seismic Activity: Insights from the 2024 Noto Peninsula and Nichinan Earthquakes of Japan
by Karan Nayak, Rosendo Romero-Andrade, Gopal Sharma, Charbeth López-Urías, Manuel Edwiges Trejo-Soto and Ana Isela Vidal-Vega
Atmosphere 2024, 15(12), 1492; https://doi.org/10.3390/atmos15121492 - 14 Dec 2024
Viewed by 974
Abstract
This study provides a comprehensive investigation into ionospheric perturbations associated with the Mw 7.5 earthquake on the Noto Peninsula in January 2024, utilizing data from the International GNSS Service (IGS) network. Focusing on Total Electron Content (TEC), the analysis incorporates spatial mapping and [...] Read more.
This study provides a comprehensive investigation into ionospheric perturbations associated with the Mw 7.5 earthquake on the Noto Peninsula in January 2024, utilizing data from the International GNSS Service (IGS) network. Focusing on Total Electron Content (TEC), the analysis incorporates spatial mapping and temporal pattern assessments over a 30-day period before the earthquake. The time series for TEC at the closest station to the epicenter, USUD, reveals a localized decline, with a significant negative anomaly exceeding 5 TECU observed 22 and 23 days before the earthquake, highlighting the potential of TEC variations as seismic precursors. Similar patterns were observed at a nearby station, MIZU, strengthening the case for a seismogenic origin. Positive anomalies were linked to intense space weather episodes, while the most notable negative anomalies occurred under geomagnetically calm conditions, further supporting their seismic association. Using Kriging interpolation, the anomaly zone was shown to closely align with the earthquake’s epicenter. To assess the consistency of TEC anomalies in different seismic events, the study also examines the Mw 7.1 Nichinan earthquake in August 2024. The results reveal a prominent negative anomaly, reinforcing the reliability of TEC depletions in seismic precursor detection. Additionally, spatial correlation analysis of Pearson correlation across both events demonstrates that TEC coherence diminishes with increasing distance, with pronounced correlation decay beyond 1000–1600 km. This spatial decay, consistent with Dobrovolsky’s earthquake preparation area, strengthens the association between TEC anomalies and seismic activity. This research highlights the complex relationship between ionospheric anomalies and seismic events, underscoring the value of TEC analysis as tool for earthquake precursor detection. The findings significantly enhance our understanding of ionospheric dynamics related to seismic events, advocating for a comprehensive, multi-station approach in future earthquake prediction efforts. Full article
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Figure 1
<p>Seismotectonic map of the Noto Peninsula in Japan depicting the earthquake on 1 January 2024 (highlighted by the black star). Aftershocks are marked with red stars, green triangles denote CORS points used for TEC analysis within the earthquake preparation zone, and active faults are represented by brown lines (modified after Styron et al., 2020 [<a href="#B30-atmosphere-15-01492" class="html-bibr">30</a>]).</p>
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<p>TEC readings taken at the closest USUD station in the month leading up to the earthquake. The upper and lower boundaries, determined by Equation (2), are represented by the black and green solid lines, respectively. The daily TEC values, measured in TEC units (TECU), are depicted by the red lines. Any deviations beyond these limits are identified as anomalies, with positive anomalies shown as black columns and negative anomalies as green columns.</p>
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<p>TEC readings taken at MIZU station in the month leading up to the earthquake. The upper and lower boundaries, determined by Equation (2), are represented by the black and green solid lines, respectively. The daily TEC values, measured in TEC units (TECU), are depicted by the red lines. Any deviations beyond these limits are identified as anomalies, with positive anomalies shown as black columns and negative anomalies as green columns.</p>
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<p>Elaborate depiction of the day-to-day changes in the Dst, Kp, and F10.7 index observed between 17 November and 31 December, covering the 45 days preceding the earthquake. In each subplot, red horizontal lines signify the predetermined threshold levels for these indices. Anomalies in the TEC patterns are taken into account only when the indices fall below their respective thresholds.</p>
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<p>Anomalous variations in TEC depletions exceeding a threshold of at least 3 TEC units (3 × 10<sup>16</sup> electrons/m<sup>2</sup>).</p>
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<p>Observation of TEC on the anomaly day with the PNA time at 3.367 UTC, considering data from the nearby 22 stations. The X-axis illustrates the CORS distance from the epicenter, while the Y-axis represents the vTEC in relation to TEC units.</p>
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<p>Relationship between TEC Pearson correlation and distance, showing spatial decay in correlation with statistical significance across stations for the anomaly day of 7 December 2023.</p>
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<p>Spatial distribution of vTEC based on data from 22 neighboring stations, depicted by green triangles, during the Peak Negative Anomaly time at 3.367 UTC on the anomaly day of 7 December.</p>
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<p>Observation of TEC on the anomaly day with, the PNA time at 3.117 UTC, considering data from the nearby 22 stations. The X-axis illustrates the CORS distance from the epicenter, while the Y-axis represents the vTEC in relation to TEC units.</p>
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<p>Relationship between TEC Pearson correlation and distance, showing spatial decay in correlation with statistical significance across stations for the anomaly day of 8 December 2023.</p>
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<p>Spatial distribution of vTEC based on data from 22 neighboring stations, depicted by green triangles, during the Peak Negative Anomaly time at 3.117 UTC on the anomaly day of 8 December.</p>
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<p>Anomalous variations in TEC depletions exceeding a threshold of at least 3 TEC units, as observed from the AIRA station for the Nichinan earthquake of Japan.</p>
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<p>Observation of TEC on the anomaly day with the PNA time at 3.85 UTC, considering data from the 17 stations. The X-axis illustrates the CORS distance from the epicenter, while the Y-axis represents the vTEC in relation to TEC units.</p>
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<p>Relationship between TEC Pearson correlation and distance, showing spatial decay in correlation with statistical significance for the Nichinan Earthquake across stations for the anomaly day of 28 July 2024.</p>
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<p>Spatial distribution of vTEC based on data from 17 neighboring stations, depicted by green triangles, during the Peak Negative Anomaly time at 3.85 UTC on the anomaly day of 28 July 2024.</p>
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<p>Space weather conditions preceding the Nichinan earthquake of 8 August 2024.</p>
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19 pages, 7501 KiB  
Article
Multi-Antenna GNSS–Accelerometer Fusion Attitude Correction Algorithm for Offshore Floating Platform Displacement Monitoring
by Xingguo Gao, Junyi Jiang, Guoyu Xu, Zengliang Chang and Jichao Yang
Sensors 2024, 24(23), 7804; https://doi.org/10.3390/s24237804 - 6 Dec 2024
Viewed by 497
Abstract
In order to solve the problem of fixed ambiguity and decreased accuracy in GNSS displacement monitoring of the offshore floating platforms, an attitude correction algorithm based on the fusion of a multi-antenna GNSS and an accelerometer was proposed using the Kalman filtering method. [...] Read more.
In order to solve the problem of fixed ambiguity and decreased accuracy in GNSS displacement monitoring of the offshore floating platforms, an attitude correction algorithm based on the fusion of a multi-antenna GNSS and an accelerometer was proposed using the Kalman filtering method. The algorithm was validated on a physical simulation platform and a real offshore floating platform. The results indicate that this fusion method effectively compensates for the loss of high-frequency displacement information caused by low GNSS sampling rates, improves situations in which the fusion effect deteriorates due to attitude changes, and enhances the accuracy of GNSS and accelerometer fusion monitoring through offshore buoy testing. Full article
(This article belongs to the Special Issue INS/GNSS Integrated Navigation Systems)
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<p>Accelerometer tilt diagram. (<b>a</b>): schematic diagram of coordinate axis pointing; (<b>b</b>): schematic diagram of coordinate axis pointing changes under posture changes.</p>
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<p>Base station and simulation platform.</p>
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<p>Installation diagram of GNSS antenna and accelerometer. a: the distance between the two antennas is 52.68 cm; b: the distance between the two antennas is 43.50 cm; c: the distance between the accelerometer and antenna is 2.79 cm.</p>
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<p>Multi-antenna GNSS buoy and GNSS reference station [<a href="#B30-sensors-24-07804" class="html-bibr">30</a>].</p>
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<p>GNSS displacement sequence and triaxial acceleration sequence after removing trend term. (<b>a</b>) GNSS displacement sequences; (<b>b</b>) acceleration sequence.</p>
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<p>GNSS displacement sequences at different frequencies.</p>
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<p>GNSS displacement and accelerometer data fusion at different frequency.</p>
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<p>The difference between the fusion result and the GNSS result.</p>
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<p>The displacement and attitude changes of the simulated platform.</p>
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<p>Accelerometer values before and after attitude correction.</p>
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<p>Comparison of fusion results before and after attitude correction. (<b>a</b>) Eastward acceleration before correction; (<b>b</b>) comparison of fusion effects after correction; (<b>c</b>) northward acceleration before correction; (<b>d</b>) comparison of fusion effects after correction; (<b>e</b>) skyward acceleration before correction; (<b>f</b>) comparison of fusion effect after correction. ACC: acceleration; KF: Kalman filtering results; GNSS: GNSS raw displacement sequence.</p>
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<p>Comparison of fusion results before and after attitude correction. (<b>a</b>) Eastward acceleration before correction; (<b>b</b>) comparison of fusion effects after correction; (<b>c</b>) northward acceleration before correction; (<b>d</b>) comparison of fusion effects after correction; (<b>e</b>) skyward acceleration before correction; (<b>f</b>) comparison of fusion effect after correction. ACC: acceleration; KF: Kalman filtering results; GNSS: GNSS raw displacement sequence.</p>
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<p>The main antenna elevation sequence of the multi-antenna GNSS, radar, and tide gauge.</p>
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<p>Error statistics of GNSS with radar and tide gauge data. (<b>a</b>) GNSS and radar data; (<b>b</b>) GNSS and tide gauge data.</p>
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<p>Multi-antenna GNSS buoy attitude sequence.</p>
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<p>Buoy elevation and attitude sequence on day 41. (<b>a</b>): the elevation of the main antenna, the elevation after the four-antenna network leveling and attitude correction, and the elevation correction value obtained through the attitude, respectively; (<b>b</b>) the information of the buoy’s roll angle, pitch angle, and heading angle.</p>
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