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Keywords = high fix-rate GPS

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24 pages, 74760 KiB  
Article
The Application of Mobile Devices for Measuring Accelerations in Rail Vehicles: Methodology and Field Research Outcomes in Tramway Transport
by Michał Urbaniak, Jakub Myrcik, Martyna Juda and Jan Mandrysz
Sensors 2025, 25(15), 4635; https://doi.org/10.3390/s25154635 - 26 Jul 2025
Viewed by 363
Abstract
Unbalanced accelerations occurring during tram travel have a significant impact on passenger comfort and safety, as well as on the rate of wear and tear on infrastructure and rolling stock. Ideally, these dynamic forces should be monitored continuously in real-time; however, traditional systems [...] Read more.
Unbalanced accelerations occurring during tram travel have a significant impact on passenger comfort and safety, as well as on the rate of wear and tear on infrastructure and rolling stock. Ideally, these dynamic forces should be monitored continuously in real-time; however, traditional systems require high-precision accelerometers and proprietary software—investments often beyond the reach of municipally funded tram operators. To this end, as part of the research project “Accelerometer Measurements in Rail Passenger Transport Vehicles”, pilot measurement campaigns were conducted in Poland on tram lines in Gdańsk, Toruń, Bydgoszcz, and Olsztyn. Off-the-shelf smartphones equipped with MEMS accelerometers and GPS modules, running the Physics Toolbox Sensor Suite Pro app, were used. Although the research employs widely known methods, this paper addresses part of the gap in affordable real-time monitoring by demonstrating that, in the future, equipment equipped solely with consumer-grade MEMS accelerometers can deliver sufficiently accurate data in applications where high precision is not critical. This paper presents an analysis of a subset of results from the Gdańsk tram network. Lateral (x) and vertical (z) accelerations were recorded at three fixed points inside two tram models (Pesa 128NG Jazz Duo and Düwag N8C), while longitudinal accelerations were deliberately omitted at this stage due to their strong dependence on driver behavior. Raw data were exported as CSV files, processed and analyzed in R version 4.2.2, and then mapped spatially using ArcGIS cartograms. Vehicle speed was calculated both via the haversine formula—accounting for Earth’s curvature—and via a Cartesian approximation. Over the ~7 km route, both methods yielded virtually identical results, validating the simpler approach for short distances. Acceleration histograms approximated Gaussian distributions, with most values between 0.05 and 0.15 m/s2, and extreme values approaching 1 m/s2. The results demonstrate that low-cost mobile devices, after future calibration against certified accelerometers, can provide sufficiently rich data for ride-comfort assessment and show promise for cost-effective condition monitoring of both track and rolling stock. Future work will focus on optimizing the app’s data collection pipeline, refining standard-based analysis algorithms, and validating smartphone measurements against benchmark sensors. Full article
(This article belongs to the Collection Sensors and Actuators for Intelligent Vehicles)
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34 pages, 9572 KiB  
Article
Data Siting and Capacity Optimization of Photovoltaic–Storage–Charging Stations Considering Spatiotemporal Charging Demand
by Dandan Hu, Doudou Yang and Zhi-Wei Liu
Energies 2025, 18(13), 3306; https://doi.org/10.3390/en18133306 - 24 Jun 2025
Viewed by 314
Abstract
To address the charging demand challenges brought about by the widespread adoption of electric vehicles, integrated photovoltaic–storage–charging stations (PSCSs) enhance energy utilization efficiency and economic viability by combining photovoltaic (PV) power generation with an energy storage system (ESS). This paper proposes a two-stage [...] Read more.
To address the charging demand challenges brought about by the widespread adoption of electric vehicles, integrated photovoltaic–storage–charging stations (PSCSs) enhance energy utilization efficiency and economic viability by combining photovoltaic (PV) power generation with an energy storage system (ESS). This paper proposes a two-stage data-driven holistic optimization model for the siting and capacity allocation of charging stations. In the first stage, the location and number of charging piles are determined by analyzing the spatiotemporal distribution characteristics of charging demand using ST-DBSCAN and K-means clustering methods. In the second stage, charging load results from the first stage, photovoltaic generation forecast, and electricity price are jointly considered to minimize the operator’s total cost determined by the capacity of PV and ESS, which is solved by the genetic algorithm. To validate the model, we leverage large-scale GPS trajectory data from electric taxis in Shenzhen as a data-driven source of spatiotemporal charging demand. The research results indicate that the spatiotemporal distribution characteristics of different charging demands determine whether a charging station can become a PSCS and the optimal capacity of PV and battery within the station, rather than a fixed configuration. Stations with high demand volatility can achieve a balance between economic benefits and user satisfaction by appropriately lowering the peak instantaneous satisfaction rate (set between 70 and 80%). Full article
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24 pages, 6947 KiB  
Article
Enhanced Real-Time Onboard Orbit Determination of LEO Satellites Using GPS Navigation Solutions with Signal Transit Time Correction
by Daero Lee and Soon Sik Hwang
Aerospace 2025, 12(6), 508; https://doi.org/10.3390/aerospace12060508 - 3 Jun 2025
Viewed by 551
Abstract
Enhanced real-time onboard orbit determination for low-Earth-orbit satellites is essential for autonomous spacecraft operations. However, the accuracy of such systems is often limited by signal propagation delays between GPS satellites and the user spacecraft. These delays, primarily due to Earth’s rotation and ionospheric [...] Read more.
Enhanced real-time onboard orbit determination for low-Earth-orbit satellites is essential for autonomous spacecraft operations. However, the accuracy of such systems is often limited by signal propagation delays between GPS satellites and the user spacecraft. These delays, primarily due to Earth’s rotation and ionospheric effects become particularly significant in high-dynamic LEO environments, leading to considerable errors in range and range rate measurements, and consequently, in position and velocity estimation. To mitigate these issues, this paper proposes a real-time orbit determination algorithm that applies Earth rotation correction and dual-frequency (L1 and L2) ionospheric compensation to raw GPS measurements. The enhanced orbit determination method is processed directly in the Earth-centered Earth-fixed frame, eliminating repeated coordinate transformations and improving integration with ground-based systems. The proposed method employs a reduced-dynamic orbit determination strategy to balance model fidelity and computational efficiency. A predictive correction model is also incorporated to compensate for GPS signal delays under dynamic motion, thereby enhancing positional accuracy. The overall algorithm is embedded within an extended Kalman filter framework, which assimilates the corrected GPS observations with a stochastic process noise model to account for dynamic modeling uncertainties. Simulation results using synthetic GPS measurements, including pseudoranges and pseudorange rates from a dual-frequency spaceborne receiver, demonstrate that the proposed method provides a significant improvement in orbit determination accuracy compared to conventional techniques that neglect signal propagation effects. These findings highlight the importance of performing orbit estimation directly in the Earth-centered, Earth-fixed reference frame, utilizing pseudoranges that are corrected for ionospheric errors, applying reduced-dynamic filtering methods, and compensating for signal delays. Together, these enhancements contribute to more reliable and precise satellite orbit determination for missions operating in low Earth orbit. Full article
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20 pages, 7507 KiB  
Article
Undifferenced Ambiguity Resolution for Precise Multi-GNSS Products to Support Global PPP-AR
by Junqiang Li, Jing Guo, Shengyi Xu and Qile Zhao
Remote Sens. 2025, 17(8), 1451; https://doi.org/10.3390/rs17081451 - 18 Apr 2025
Cited by 1 | Viewed by 608
Abstract
Precise point positioning ambiguity resolution (PPP-AR) is a key technique for high-precision global navigation satellite system (GNSS) observations, with phase bias products playing a critical role in its implementation. The multi-GNSS experiment analysis center at Wuhan University (WUM) has adopted the undifferenced ambiguity [...] Read more.
Precise point positioning ambiguity resolution (PPP-AR) is a key technique for high-precision global navigation satellite system (GNSS) observations, with phase bias products playing a critical role in its implementation. The multi-GNSS experiment analysis center at Wuhan University (WUM) has adopted the undifferenced ambiguity resolution (UDAR) approach to generate high-precision orbit, clock, and observable-specific bias (OSB) products to support PPP-AR since day 162 of 2023. This study presents the analysis strategy employed and assesses the impact of the transition to ambiguity resolution on the orbit precision, using metrics such as orbit boundary discontinuities (OBD) and satellite laser ranging (SLR) validation. Additionally, the stability of the OSB products and the overall performance of PPP-AR solutions are evaluated. The OBD demonstrates specific improvements of 7.1% and 9.5% for GPS and Galileo, respectively, when UDAR is applied. Notably, BDS-3 medium Earth orbit satellites show a remarkable 15.2% improvement compared to the double-differenced results. However, for the remaining constellations, the improvements are either minimal or result in degradation. Using GPS and GLONASS solutions from the International GNSS Service (IGS) and other solutions from the European Space Agency (ESA) as references, the orbit differences of WUM solutions based on UDAR exhibit a significant reduction. However, the improvements in SLR validation are limited, as the radial orbit precision is primarily influenced by the dynamic model. The narrow-lane ambiguity fixing rate for static PPP-AR, based on data from approximately 430 globally distributed stations, reaches 99.2%, 99.2%, 88.8%, and 98.6% for GPS, Galileo, BDS-2, and BDS-3, respectively. The daily repeatability of station coordinates is approximately 1.4 mm, 1.9 mm, and 3.9 mm in the east, north, and up directions, respectively. Overall, these results demonstrate the effectiveness and potential of WUM’s undifferenced ambiguity resolution approach in enhancing GNSS data processing and facilitating PPP-AR applications. Full article
(This article belongs to the Section Earth Observation Data)
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17 pages, 7035 KiB  
Article
High-Precision Satellite Clock Offset Estimated by SRIF Based on Epoch-Wise Updated Orbit
by Yu Cao, Le Wang, Zhiwei Qin, Wen Lai, Shi Du and Yuanyuan Wang
Remote Sens. 2025, 17(8), 1391; https://doi.org/10.3390/rs17081391 - 14 Apr 2025
Viewed by 377
Abstract
High-precision clock offset products directly affect the performance and reliability of precise point positioning (PPP) applications. Currently, real-time clock offset products offered by institutions such as the Centre national d’études spatiales (CNES) rely on ultra-rapid predicted orbits. However, these orbits have limited accuracy [...] Read more.
High-precision clock offset products directly affect the performance and reliability of precise point positioning (PPP) applications. Currently, real-time clock offset products offered by institutions such as the Centre national d’études spatiales (CNES) rely on ultra-rapid predicted orbits. However, these orbits have limited accuracy and exhibit jumps during updates, constraining the accuracy of real-time clock estimation. To address this issue, we propose an undifferenced ambiguity resolution (UD AR) technique for clock offset estimation based on epoch-wise updated orbits. Clock estimation experiments were performed using both predicted and epoch-wise updated orbits, with square root information filtering (SRIF) applied in three schemes: double-differenced (DD), UD, and float solutions. Compared with predicted orbits, epoch-wise updated orbits provided smoother sequences with higher accuracy, significantly improving clock offset estimation accuracy in all schemes. Moreover, the UD AR solution significantly enhanced clock offset estimation accuracy, and the high-precision epoch-wise updated orbit products increased the narrow-lane fixing rate of the UD solutions. The clock accuracies of BDS-3, Galileo, and GPS reached 0.032 ns, 0.023 ns, and 0.026 ns, respectively, representing improvements of 36%, 34%, and 41% compared with the float solutions and 41%, 30%, 26% compared with the UD solution based on 1 h predicted orbits. Finally, the positioning performance of the proposed method was validated via PPP using 25 stations, showing improvements of 50%, 48%, and 41% in the north, east, and up directions compared with CNES products. Therefore, by combining epoch-wise updated orbit products with the UD AR to improve clock accuracy, this method provides a new approach to generating high-precision clock products, significantly contributing to enhancing PPP services. Full article
(This article belongs to the Special Issue Advances in Multi-GNSS Technology and Applications)
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27 pages, 8424 KiB  
Article
Research on the Algorithm of Lake Surface Height Inversion in Qinghai Lake Based on Sentinel-3A Altimeter
by Chuntao Chen, Xiaoqing Li, Jianhua Zhu, Hailong Peng, Youhua Xue, Wanlin Zhai, Mingsen Lin, Yufei Zhang, Jiajia Liu and Yili Zhao
Remote Sens. 2025, 17(4), 647; https://doi.org/10.3390/rs17040647 - 14 Feb 2025
Cited by 1 | Viewed by 754
Abstract
Lakes are a crucial component of inland water bodies, and changes in their water levels serve as key indicators of global climate change. Traditional methods of lake water level monitoring rely heavily on hydrological stations, but there are problems such as regional representativeness, [...] Read more.
Lakes are a crucial component of inland water bodies, and changes in their water levels serve as key indicators of global climate change. Traditional methods of lake water level monitoring rely heavily on hydrological stations, but there are problems such as regional representativeness, data stability, and high maintenance costs. The satellite altimeter is an essential tool in lake research, with the Synthetic Aperture Radar (SAR) altimeter offering a high spatial resolution. This enables precise and quantitative observations of lake water levels on a large scale. In this study, we used Sentinel-3A SAR Radar Altimeter (SRAL) data to establish a more reasonable lake height inversion algorithm for satellite-derived lake heights. Subsequently, using this technology, a systematic analysis study was conducted with Qinghai Lake as the case study area. By employing regional filtering, threshold filtering, and altimeter range filtering techniques, we obtained effective satellite altimeter height measurements of the lake surface height. To enhance the accuracy of the data, we combined these measurements with GPS buoy-based geoid data from Qinghai Lake, normalizing lake surface height data from different periods and locations to a fixed reference point. A dataset based on SAR altimeter data was then constructed to track lake surface height changes in Qinghai Lake. Using data from the Sentinel-3A altimeter’s 067 pass over Qinghai Lake, which has spanned 96 cycles since its launch in 2016, we analyzed over seven years of lake surface height variations. The results show that the lake surface height exhibits distinct seasonal patterns, peaking in September and October and reaching its lowest levels in April and May. From 2016 to 2023, Qinghai Lake showed a general upward trend, with an increase of 2.41 m in lake surface height, corresponding to a rate of 30.0 cm per year. Specifically, from 2016 to 2020, the lake surface height rose at a rate of 47.2 cm per year, while from 2020 to 2022, the height remained relatively stable. Full article
(This article belongs to the Special Issue Remote Sensing in Monitoring Coastal and Inland Waters)
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15 pages, 4029 KiB  
Article
GPS Phase Integer Ambiguity Resolution Based on Eliminating Coordinate Parameters and Ant Colony Algorithm
by Ning Liu, Shuangcheng Zhang, Xiaoli Wu and Yu Shen
Sensors 2025, 25(2), 321; https://doi.org/10.3390/s25020321 - 8 Jan 2025
Viewed by 1046
Abstract
Correctly fixing the integer ambiguity of GNSS is the key to realizing the application of GNSS high-precision positioning. When solving the float solution of ambiguity based on the double-difference model epoch by epoch, the common method for resolving the integer ambiguity needs to [...] Read more.
Correctly fixing the integer ambiguity of GNSS is the key to realizing the application of GNSS high-precision positioning. When solving the float solution of ambiguity based on the double-difference model epoch by epoch, the common method for resolving the integer ambiguity needs to solve the coordinate parameter information, due to the influence of limited GNSS phase data observations. This type of method will lead to an increase in the ill-posedness of the double-difference solution equation, so that the fixed success rate of the integer ambiguity is not high. Therefore, a new integer ambiguity resolution method based on eliminating coordinate parameters and ant colony algorithm is proposed in this paper. The method eliminates the coordinate parameters in the observation equation using QR decomposition transformation, and only estimates the ambiguity parameters using the Kalman filter. On the basis that the Kalman filter will obtain the float solution of ambiguity, the decorrelation processing is carried out based on continuous Cholesky decomposition, and the optimal solution of integer ambiguity is searched using the ant colony algorithm. Two sets of static and dynamic GPS experimental data are used to verify the method and compared with conventional least squares and LAMBDA methods. The results show that the new method has good decorrelation effect, which can correctly and effectively realize the integer ambiguity resolution. Full article
(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation)
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17 pages, 3104 KiB  
Article
Experimental Assessment of Corrosion Properties for Materials Intended for Heavy Crude Processing
by Raúl González-Durán, Alvaro Rodríguez-Prieto, Ana María Camacho, Darío Y. Peña-Ballesteros and Aníbal Serna
Materials 2024, 17(21), 5275; https://doi.org/10.3390/ma17215275 - 30 Oct 2024
Viewed by 1079
Abstract
Heavy crude oil processing presents significant challenges owing to its complex composition and requirement for processing conditions, which increase the process safety risk in crude processing units, such as fixed equipment, for instance pressure vessels and pipes. The aim of this work is [...] Read more.
Heavy crude oil processing presents significant challenges owing to its complex composition and requirement for processing conditions, which increase the process safety risk in crude processing units, such as fixed equipment, for instance pressure vessels and pipes. The aim of this work is to evaluate the influence of heavy crude oils named A and B and the effect of sulfur-rich compounds and organic acids on the performance at high temperatures of three metallic alloys (5Cr-1/2Mo/ASTM A335GP5, X6CrNiMoTi17122/AISI-SAE 316Ti and Ni66.5Cu31.5/Monel 400) and propose an alternative to be used in pressure vessels and piping in refineries. This work was based on the need to understand the corrosivity of two heavy crude oils (A and B) from eastern Colombia in three materials, evaluated at three temperatures (200 °C, 250 °C and 300 °C) under the same conditions of pressure (200 psi) and rotation velocity (600 rpm) in a dynamic autoclave to simulate atmospheric conditions and conditions in vacuum refinery towers. An understanding of how these factors interact with the fundamental principles of corrosion kinetics is essential for developing an effective corrosion mitigation strategy. The results were interesting for applications requiring high corrosion resistance. X6CrNiMoTi17122/AISI-SAE 316Ti is a solid candidate for this application, with corrosion rates of 0.2 to 0.87 mpy. Ni66.5Cu31.5/Monel 400 exhibited significant corrosion rates up to 74.89 mpy, especially at higher temperatures (300 °C). 5Cr-1/2Mo/ASTM A335GP5 showed a generally moderate corrosion rate (2.04–5.57 mpy) in the evaluated temperature range. 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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18 pages, 11903 KiB  
Article
Improved Medium Baseline RTK Positioning Performance Based on BDS/Galileo/GPS Triple-Frequency-Only Observations
by Xifeng Dang, Xiao Yin, Yize Zhang, Chengfa Gao, Jincheng Wu and Yongqiang Liu
Remote Sens. 2023, 15(21), 5198; https://doi.org/10.3390/rs15215198 - 1 Nov 2023
Cited by 2 | Viewed by 2045
Abstract
With the global service of the BeiDou Navigation Satellite System (BDS), the Galileo Navigation Satellite System (Galileo), and the modernization of the Global Positioning System (GPS), achieving high-precision positioning through triple-frequency-only observations in medium baseline real-time kinematics (RTK) is anticipated. This study investigates [...] Read more.
With the global service of the BeiDou Navigation Satellite System (BDS), the Galileo Navigation Satellite System (Galileo), and the modernization of the Global Positioning System (GPS), achieving high-precision positioning through triple-frequency-only observations in medium baseline real-time kinematics (RTK) is anticipated. This study investigates the impacts of double-difference (DD) troposphere delay and ionosphere delay on ambiguity resolution (AR) based on six medium baselines at a latitude of 30°. Additionally, it evaluates positioning accuracy, fixing rate, convergence time, and computational time using triple-frequency-only (B1I/B2a/B3I, E1/E5a/E5b, L1/L2/L5) data, comparing these results to those obtained from dual-frequency (B1I/B2a, E1/E5a, L1/L2) and combined dual-frequency and triple-frequency data. The experimental findings suggest that, for geometry-based wide-lane (WL) AR, the DD troposphere delay and ionosphere delay can be disregarded. However, they cannot be overlooked when aiming to resolve the raw ambiguity. Triple-frequency-only RTK exhibits comparable positioning accuracy to dual-frequency RTK, with its primary advantage lying in faster convergence. The probability of achieving convergence within 180 s is approximately 8.0% higher for triple-frequency-only RTK compared to dual-frequency RTK. In terms of computational time, the use of triple-frequency-only data reduces the required time by 8.26 s compared to the approach that simultaneously employs both dual-frequency and triple-frequency data, resulting in a computational time reduction of approximately 20%. Therefore, when conducting medium baseline RTK positioning, it is recommended to adopt the ambiguity resolution method proposed in this paper based on triple-frequency-only observations. Full article
(This article belongs to the Special Issue New Progress in GNSS Data Processing Technology and Modeling)
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21 pages, 7707 KiB  
Article
Investigation of the Physical Mechanical Properties and Durability of Sustainable Ultra-High Performance Concrete with Recycled Waste Glass
by Mohamed Amin, Ibrahim Saad Agwa, Nuha Mashaan, Shaker Mahmood and Mahmoud H. Abd-Elrahman
Sustainability 2023, 15(4), 3085; https://doi.org/10.3390/su15043085 - 8 Feb 2023
Cited by 118 | Viewed by 6814
Abstract
Construction material sustainability and waste reuse have emerged as significant environmental issues. Concrete is widely used in the building and engineering fields. Ultra-high performance concrete (UHPC), which has remarkably high mechanical properties, has become one of the most common concrete varieties in recent [...] Read more.
Construction material sustainability and waste reuse have emerged as significant environmental issues. Concrete is widely used in the building and engineering fields. Ultra-high performance concrete (UHPC), which has remarkably high mechanical properties, has become one of the most common concrete varieties in recent years. As a result, substantial amounts of Portland cement (PC) are frequently used, raising the initial cost of UHPC and restricting its broad use in structural applications. A significant amount of CO2 is produced and a large amount of natural resources are consumed in its production. To make UHPC production more eco-friendly and economically viable, it is advised that the PC in concrete preparations be replaced with different additives and that the recycled aggregates from various sources be substituted for natural aggregates. This research aims to develop an environmentally friendly and cost-effective UHPC by using glass waste (GW) of various sizes as an alternative to PC with replacement ratios of 0%, 10%, 20%, 30%, 40%, and 50% utilizing glass powder (GP). Fine aggregate “sand (S)” is also replaced by glass particles (G) with replacement ratios of 0%, 50%, and 100%. To accomplish this, 18 mixes, separated into three groups, are made and examined experimentally. Slump flow, mechanical properties, water permeability, and microstructural characteristics are all studied. According to the results, increasing the S replacement ratio with G improved workability. Furthermore, the ideal replacement ratios for replacing PC with GP and S with G to achieve high mechanical properties were 20% and 0%, respectively. Increasing the replacement rate of GP in place of PC at a fixed ratio of G to S resulted in a significant decrease in water permeability values. Finally, a microstructural analysis confirms the experimental findings. In addition, PC100-S100 was the best mix compared to PC100-S50 G50 and PC100-G100. Full article
(This article belongs to the Special Issue Sustainable Concrete Design)
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14 pages, 3095 KiB  
Article
A New Optimal Subset Selection Method of Partial Ambiguity Resolution for Precise Point Positioning
by Caiya Yue, Yamin Dang, Shuqiang Xue, Hu Wang, Shouzhou Gu and Changhui Xu
Remote Sens. 2022, 14(19), 4819; https://doi.org/10.3390/rs14194819 - 27 Sep 2022
Cited by 8 | Viewed by 2066
Abstract
Rapid and accurate ambiguity resolution is the core of high-precision precise point positioning (PPP) data processing. However, the ambiguity parameters in PPP observation models are easily affected by atmospheric residual and gross errors, which lead to the probability of successfully fixing decreases and [...] Read more.
Rapid and accurate ambiguity resolution is the core of high-precision precise point positioning (PPP) data processing. However, the ambiguity parameters in PPP observation models are easily affected by atmospheric residual and gross errors, which lead to the probability of successfully fixing decreases and computational burden increases in full ambiguity resolution. Therefore, an increasing number of partial ambiguity resolution (PAR) strategies have been proposed. The selection of the optimal subset of PAR is crucial in this method. The traditional optimal subset selection method of PAR commonly leads to a single judgment criterion and weakened geometric configuration strength because the satellites with low elevation angles are often easily eliminated during the optimal subset selection. In this paper, a multi-factor constrained optimal subset selection method for PAR was proposed, which incorporates the ambiguity variance, the ambiguity dilution of precision (ADOP), satellite position dilution of precision (PDOP) and ratio test values. In order to verify the feasibility of the proposed optimal subset selection method, PAR tests under two schemes were performed for GPS/Galileo based on the static observation data of 15 Multi-GNSS Experiment (MGEX) tracking stations. The results show that, compared with the ambiguity variance sorting method, the proposed subset selection method can further improve the accuracy of the coordinate solution and the strength of geometric figure positioning. The average root mean square of the coordinate residuals is found to decrease by about 12.90%, 6.83% and 9.39% in the eastern, northern and vertical directions, respectively. The increase in the fixed epoch rate ranged from 0.87% to 33.33%, with an average of about 8.71%. Full article
(This article belongs to the Special Issue Beidou/GNSS Precise Positioning and Atmospheric Modeling)
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16 pages, 2262 KiB  
Technical Note
Inter-Satellite Single-Difference Ionospheric Delay Interpolation Model for PPP-RTK and Its Positioning Performance Verification
by Ju Hong, Rui Tu, Shixuan Zhang, Fangxin Li, Mingyue Liu and Xiaochun Lu
Remote Sens. 2022, 14(17), 4153; https://doi.org/10.3390/rs14174153 - 24 Aug 2022
Cited by 3 | Viewed by 1930
Abstract
In PPP-RTK, obtaining accurate atmospheric delay information for the user through interpolation is one of the keys to achieving high-precision real-time positioning. The ionospheric delay that is extracted by a reference network based on uncalibrated phase delay (UPD) products is often difficult to [...] Read more.
In PPP-RTK, obtaining accurate atmospheric delay information for the user through interpolation is one of the keys to achieving high-precision real-time positioning. The ionospheric delay that is extracted by a reference network based on uncalibrated phase delay (UPD) products is often difficult to separate from errors such as receiver code hardware delay and UPD reference error. Inter-satellite single-difference (SD) ionospheric delay information is typically provided to the user. This paper proposes an interpolation model that uses the atmospheric delay coefficient to represent the SD ionospheric delay, based on the mean position of the ionospheric pierce point (IPP) of each satellite pair and the center position of the network, which is called the differenced surface model (DSM). We chose four scenarios to compare the interpolation accuracy of the proposed model with the inverse distance-based linear interpolation method (DIM) and USM based on the difference between the longitude and latitude of the reference and ionospheric pierce point (IPP) of every satellite (here, we call it USM for short). The four scenarios involve a medium-scale reference network with an average distance to the reference station of 41 km, a large-scale reference network with an average distance to the reference station of 98 km, and out-of-network users, and a network with a common minimum of three reference stations. The results show that the root mean square (RMS) of the SD residuals of ionospheric delay for DSM were 1.4, 3.2, 2.2, and 1.4 cm, respectively, for the four scenarios that were considered, which are slightly better delay values than those that were achieved using DIM and USM. For the scenario with three reference stations, the interpolation accuracies of DIM and DSM were no different from those for four reference stations, indicating that the server can still try to provide ionospheric correction service under the condition of fewer reference stations. In contrast, USM could not provide service because it lacked the sufficient number of reference stations. DSM was used as the ionospheric delay interpolation model to analyze GPS and Galileo dual-system PPP-RTK positioning performance. In addition, the atmospheric parameter constraint method of users was used in PPP-RTK in reference networks of different scales. For the 41-km and 98-km reference networks, the time to first fix (TTFF) were 14.5 s and 33.1 s, respectively, and the mean RMS values for the east (E), north (N), and up (U) directions were 0.80, 0.93, and 2.72 cm, respectively, and 1.0, 1.1, and 4.0 cm, respectively, for a period of 5 min after convergence. The fixing rate and positioning accuracy of DSM during the 5-min period were better than those of DIM when the same empirical model was used to determine the mean square error of atmospheric delay. Full article
(This article belongs to the Special Issue GNSS Precise Positioning and Geoscience Application)
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24 pages, 9965 KiB  
Article
The Performance of Three-Frequency GPS PPP-RTK with Partial Ambiguity Resolution
by Zhongbao Yan and Xiaohong Zhang
Atmosphere 2022, 13(7), 1014; https://doi.org/10.3390/atmos13071014 - 23 Jun 2022
Cited by 6 | Viewed by 2174
Abstract
The correct ambiguity resolution of real-time kinematic precise point positioning (PPP-RTK) plays an essential role in achieving fast, reliable, and high-precision positioning. However, the ambiguity of incorrect fixing will cause poor PPP-RTK positioning performance. Hence, it is essential to optimize the selected strategy [...] Read more.
The correct ambiguity resolution of real-time kinematic precise point positioning (PPP-RTK) plays an essential role in achieving fast, reliable, and high-precision positioning. However, the ambiguity of incorrect fixing will cause poor PPP-RTK positioning performance. Hence, it is essential to optimize the selected strategy of the ambiguity subset to obtain a more reliable ambiguity resolution performance for PPP-RTK. For this reason, a partial ambiguity resolution (PAR) method combining quality control and Schmidt orthogonalization (Gram–Schmidt) is proposed in this study. To investigate the performance of global positioning system (GPS) dual- and three-frequency PPP-RTK comprehensively, the PAR method based on the Gram–Schmidt method was analyzed and compared with the highest elevation angle method, which considered the satellite with the highest elevation angle as the reference satellite. The performance of ambiguity fixing, atmospheric corrections, and positioning were evaluated using five stations in Belgium and its surrounding area. The results showed average epoch fixing rates of 81.01%, 95.92%, 82.05%, and 97.93% in the dual-frequency highest elevation angle (F2-MAX), dual-frequency Gram–Schmidt (F2-ALT), three-frequency highest elevation angle (F3-MAX), and three–frequency Gram–Schmidt (F3-ALT), respectively. In terms of the time to first fix (TTFF), 89.02%, 94.25%, 90.24%, and 95.69% of the single-differenced (SD) narrow lane (NL) ambiguity fell within 3 min in F2-MAX, F2-ALT, F3-MAX, and F3-ALT, respectively. As far as the ionospheric corrections are concerned, the proportion of SD ionospheric residuals within ±0.25 total electron content units (TECU) were 95.08%, 95.93%, 95.68%, and 96.98% for the F2-MAX, F2-ALT, F3-MAX, and F3-ALT, respectively. The centimeter-level accuracy of both the horizontal and vertical positioning errors can be achieved almost instantaneously in F3-ALT. This is attributed to the accurate and reliable SD NL ambiguity fixing based on the Gram–Schmidt approach. Full article
(This article belongs to the Special Issue Techniques and Applications in High Precision GNSS)
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20 pages, 10186 KiB  
Article
An Efficient UD Factorization Implementation of Kalman Filter for RTK Based on Equivalent Principle
by Jian Liu, Bing Zhang, Tong Liu, Guochang Xu, Yuanfa Ji, Mengfei Sun, Wenfeng Nie and Yufang He
Remote Sens. 2022, 14(4), 967; https://doi.org/10.3390/rs14040967 - 16 Feb 2022
Cited by 5 | Viewed by 2886
Abstract
Real-time kinematic (RTK) is a technique frequently utilized to provide real-time highly precise positioning services for mobile Internet-of-Things (IoT)-embedded terminals from intelligence appliances and smartphones to autonomous drones and self-driving vehicles. To fully utilize hardware resources, the internal GNSS chips or modules equipped [...] Read more.
Real-time kinematic (RTK) is a technique frequently utilized to provide real-time highly precise positioning services for mobile Internet-of-Things (IoT)-embedded terminals from intelligence appliances and smartphones to autonomous drones and self-driving vehicles. To fully utilize hardware resources, the internal GNSS chips or modules equipped in IoT terminals should satisfy the traits of energy efficiency and low computational complexity. As the number of global navigation satellite system (GNSS) increases, the continuous accumulation of high-dimensional rounding errors, the rough system model, and seriously distorted observations will result in divergence and considerable processing burden in the conventional Kalman filter (KF) process. Computational efficiency is significant in the reduction in the power consumption and intensifies the positioning performance of GNSS receivers. Here, a new filter strategy based on UD factorization, where U stands for the unit upper-triangular factor and D indicates the diagonal factor, is proposed for RTK positioning to enhance the numerical stability and reduce the computational effort. The equivalent principle was applied to turn double-difference (DD) observations into zero-difference (ZD) observations. Then, the UD-factorization-based Kalman filter (UD-KF) is proposed as a way to sequentially provide accurate real-time estimations of the filter states and variance–covariance (VC) matrix. Both static and dynamic tests were carried out with single-frequency data from a GPS to evaluate the performance of UD-KF. The results of the zero-baseline test show that UD-KF can obtain smaller RMS of the estimated parameters as the noise of DD observations was twice that of the ZD observations. A short baseline test showed that, compared to the regular filter approach with DD observations, UD-KF achieved a shorter computation time with a higher data utilization rate for both filtering and fixing stages, with an average improvement of 32% and 18%. Finally, a dynamic test showed that the UD-KF can avoid the undesirable effect of satellite changes. Therefore, compared to KF with DD observations, the UD-KF with equivalent ZD observations can enhance the robustness as well as improve the positioning accuracy of RTK positioning. Full article
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