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23 pages, 8508 KiB  
Article
An Evaluation of Optimization Algorithms for the Optimal Selection of GNSS Satellite Subsets
by Abdulaziz Alluhaybi, Panos Psimoulis and Rasa Remenyte-Prescott
Remote Sens. 2024, 16(10), 1794; https://doi.org/10.3390/rs16101794 - 18 May 2024
Viewed by 1117
Abstract
Continuous advancements in GNSS systems have led, apart from the broadly used GPS, to the development of other satellite systems (Galileo, BeiDou, GLONASS), which have significantly increased the number of available satellites for GNSS positioning applications. However, despite GNSS satellites’ redundancy, a potential [...] Read more.
Continuous advancements in GNSS systems have led, apart from the broadly used GPS, to the development of other satellite systems (Galileo, BeiDou, GLONASS), which have significantly increased the number of available satellites for GNSS positioning applications. However, despite GNSS satellites’ redundancy, a potential poor GNSS satellite signal (i.e., low signal-to-noise ratio) can negatively affect the GNSS’s performance and positioning accuracy. On the other hand, selecting high-quality GNSS satellite signals by retaining a sufficient number of GNSS satellites can enhance the GNSS’s positioning performance. Various methods, including optimization algorithms, which are also commonly adopted in artificial intelligence (AI) methods, have been applied for satellite selection. In this study, five optimization algorithms were investigated and assessed in terms of their ability to determine the optimal GNSS satellite constellation, such as Artificial Bee Colony optimization (ABC), Ant Colony Optimization (ACO), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). The assessment of the optimization algorithms was based on two criteria, such as the robustness of the solution for the optimal satellite constellation and the time required to find the solution. The selection of the GNSS satellites was based on the weighted geometric dilution of precision (WGDOP) parameter, where the geometric dilution of precision (GDOP) is modified by applying weights based on the quality of the satellites’ signal. The optimization algorithms were tested on the basis of 24 h of tracking data gathered from a permanent GNSS station, for GPS-only and multi-GNSS data (GPS, GLONASS, and Galileo). According to the comparison results, the ABC, ACO, and PSO algorithms were equivalent in terms of selection accuracy and speed. However, ABC was determined to be the most suitable algorithm due it requiring the fewest number of parameters to be set. To further investigate ABC’s performance, the method was applied for the selection of an optimal GNSS satellite subset according to the number of total available tracked GNSS satellites (up to 31 satellites), leading to more than 300 million possible combinations of 15 GNSS satellites. ABC was able to select the optimal satellite subsets with 100% accuracy. Full article
(This article belongs to the Topic Artificial Intelligence in Navigation)
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Figure 1

Figure 1
<p>Representation of the ABC searching process and the roles of employed scout and onlooker bees.</p>
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<p>Schematic representation of the solution building process by ants in ACO.</p>
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<p>Representation of the GA processing steps.</p>
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<p>Representation of PSO travelling technique for the solution optimization.</p>
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<p>Schematic representation of SA algorithm procedure.</p>
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<p>Time period of satellites’ mean movement by one degree, considering satellite azimuth and elevation angles.</p>
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<p>(<b>Left</b>) View of the roof of NGI building, with the location of control point NGB2 and (<b>right</b>) the GNSS antenna installed on the top of the pillar of NGB2.</p>
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<p>Number of available GNSS satellites at NGB2 GNSS station for a 24 h period on 20 September 2021.</p>
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<p>Sample of the file of the GPS data information, which includes (i) date–time, (ii) satellite PRN, (iii) azimuth, (iv) elevation angle, and (v) CNR (in dB-Hz).</p>
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<p>The possible combinations of satellite constellations for (<b>left</b>) GPS-only in the cases of 8 and 13 available GPS satellites and (<b>right</b>) multi-GNSS satellite constellation in the case of 18 and 31 available GNSS satellites.</p>
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<p>(<b>Left</b>) The quality of match (accuracy) of the selection of the optimal GPS satellite subset by the optimization algorithms with respect to the actual optimal GPS satellite subset derived by the TM. (<b>Right</b>) The time required for the TM and the optimization algorithms to perform optimal GPS satellite subset selection.</p>
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<p>The comparison of the performance of the optimization algorithms with respect to TM, expressed as the difference between the CNR-WGDOP of the optimal satellite constellation of each optimization algorithm and the corresponding CNR-WDGOP of TM. The results of the four cases of GPS satellite constellations (4, 5, 6, and 7 satellites) are presented. On the left axis, the CNR-WGDOP value of the optimal satellite constellation based on the TM is presented, and on the right axis is the difference between each of the optimization algorithms and the TM.</p>
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<p>The sky plots of epoch 55 (<b>left</b>) and epoch 184 (<b>right</b>) presenting the selection of the optimal GPS satellite subset by the ACO and the TM, and showing the satellites commonly selected (blue) by the two methods, but also those that were differently selected by ACO (yellow) and TM (orange).</p>
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<p>Same as <a href="#remotesensing-16-01794-f013" class="html-fig">Figure 13</a>, this figure presents the sky plots for epoch 81 (<b>left</b>) and epoch 215 (<b>right</b>), as well as differences between the selection of the optimal GPS satellite subset for PSO and TM.</p>
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<p>(<b>Left</b>) The accuracy of the selection of the optimal GNSS satellite subset of ABC with respect to TM for the various cases of satellite constellations and parameter settings and (<b>right</b>) the required time of the TM and ABC algorithm to compute the selection of optimal GNSS satellite subset.</p>
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<p>A comparison of the performance of the ABC algorithm for the three sets of parameter settings with respect to TM, expressed as the difference between the CNR-WGDOP of the optimal satellite constellation of each ABC parameter setting and the corresponding CNR-WDGOP of TM. On the left axis, the CNR-WGDOP value of the optimal satellite constellation based on the TM is presented, and on the right axis is the difference between each of the ABC parameter settings and the TM.</p>
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<p>Sky plots of epochs 20 (<b>left</b>) and 88 (<b>right</b>), presenting the difference in the selection of optimal GNSS satellite subset between ABC setting 1 and the actual TM, by showing the common satellites (blue) and the differences between ABC’s (yellow) and TM’s (orange) satellite selection.</p>
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17 pages, 4718 KiB  
Article
Precise Positioning of Primary System of Geodetic Points by GNSS Technology in Railway Operating Conditions
by Jiri Bures, Ondrej Vystavel, Dalibor Bartoněk, Ladislav Barta and Radomir Havlicek
Appl. Sci. 2024, 14(8), 3288; https://doi.org/10.3390/app14083288 - 13 Apr 2024
Viewed by 912
Abstract
This article deals with the analysis of the accuracy of the geodetic real-time GNSS measurement procedure used in railway operating conditions in the Czech Republic. The purpose was to determine to what extent the operating conditions affect the accuracy of the measurement result [...] Read more.
This article deals with the analysis of the accuracy of the geodetic real-time GNSS measurement procedure used in railway operating conditions in the Czech Republic. The purpose was to determine to what extent the operating conditions affect the accuracy of the measurement result and whether an accuracy of standard deviation σx,y = 5 mm in the horizontal plane could be achieved. The use of geodetic GNSS equipment with an IMU unit was also tested. The accuracy obtained in operational conditions is compared with the accuracy obtained on a calibration base using the same measurement procedure. The consistency between the accuracy of the primary system (satellite-based) and the secondary system (terrestrially measured by the traverse method) is also discussed. The analysis includes the issue of residual inhomogeneities of the uniform transformation key when converted to the Czech national coordinate system S-JTSK. It is shown that a homogeneous accuracy in coordinate standard deviation better than σx,y = 5 mm can be achieved. The results indicate that the accuracy under operational conditions is two–three times worse than the accuracy achieved by the same procedure under ideal conditions on a calibration base. This is due to the non-ideal observing conditions, i.e., horizon occlusion by overlays, surrounding vegetation and multipath effects. It has been shown that the effect of multipath can be reduced by repeating short observations 3–4 h apart. Older GNSS instruments using an IMU unit in combination with an electronic compass (eCompass) are at risk of a systematic bias of up to several tens of millimeters, which can be detected by rotating the antenna by 180°. The current uniform transformation key used in the Czech Republic for the conversion of GNSS coordinates into the national system has residual geometric inhomogeneities (p = 0.90 to 10 mm/km, sporadically up to 20 mm/km), which metrologically deteriorate the results of the calculation of the terrestrially measured secondary system inserted into the GNSS measured primary system. Achieving homogeneous accuracy in coordinate standard deviation in a horizontal plane better than σx,y = 5 mm has been demonstrated in non-ideal railway operating conditions with increased risk of multipath. The innovative aspect of the approach used is that it simplifies and thus increases the efficiency of the measurement with respect to the availability of GPS, GLONASS, Galileo and BeiDou satellites, as well as reducing the effect of multipath on the noise by repeating the measurement procedure. Full article
(This article belongs to the Special Issue Advances in Railway Infrastructure Engineering)
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Figure 1
<p>Localization of the discussed railway lines in the Czech Republic. Numbers correspond to order of appearance in text above.</p>
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<p>Railway lines details (indicated by red lines): (<b>a</b>) Velká Kraš—Vidnava; (<b>b</b>) Bojkovice—Hostětín; (<b>c</b>) Jeseník—Mikulovice; (<b>d</b>) Bzenec railway station.</p>
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<p>Process flow chart.</p>
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<p>Incorrect tilt compensation of Topcon HIPER HR receivers (IMU + eCompass technology) when the GNSS sensor is rotated by 180° in the horizontal plane.</p>
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<p>Model example of primary (yellow) and secondary system configuration.</p>
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<p>Overview of analyzed railway lines (sub-lines are distinguished by color) in the territory of the Czech Republic.</p>
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15 pages, 3209 KiB  
Technical Note
Effects of Equatorial Plasma Bubbles on Multi-GNSS Signals: A Case Study over South China
by Hao Han, Jiahao Zhong, Yongqiang Hao, Ningbo Wang, Xin Wan, Fuqing Huang, Qiaoling Li, Xingyan Song, Jiawen Chen, Kang Wang, Yanyan Tang, Zhuoliang Ou and Wenyu Du
Remote Sens. 2024, 16(8), 1358; https://doi.org/10.3390/rs16081358 - 12 Apr 2024
Cited by 1 | Viewed by 871
Abstract
Equatorial plasma bubbles (EPBs) occur frequently in low-latitude areas and have a non-negligible impact on navigation satellite signals. To systematically analyze the effects of a single EPB event on multi-frequency signals of GPS, Galileo, GLONASS, and BDS, all-sky airglow images over South China [...] Read more.
Equatorial plasma bubbles (EPBs) occur frequently in low-latitude areas and have a non-negligible impact on navigation satellite signals. To systematically analyze the effects of a single EPB event on multi-frequency signals of GPS, Galileo, GLONASS, and BDS, all-sky airglow images over South China are jointly used to visually determine the EPB structure and depletion degree. The results reveal that scintillations, or GNSS signal fluctuations, are directly linked to EPBs and that the intensity of scintillation is positively correlated with the airglow depletion intensity. The center of the airglow depletion often corresponds to stronger GNSS scintillation, while the edge of the bubble, which is considered to have the largest density gradient, corresponds to relatively smaller scintillation instead. This work also systematically analyzes the responses of multi-constellation and multi-frequency signals to EPBs. The results show that the L2 and L5 frequencies are more susceptible than the L1 frequency is. For different constellations, Galileo’s signal has the best tracking stability during an EPB event compared with GPS, GLONASS, and BDS. The results provide a reference for dual-frequency signal selection in precise positioning or TEC calculation, that is, L1C and L2L for GPS, L1C and L5Q for Galileo, L1P and L2C for GLONASS, and L1P and L5P for BDS. Notably, BDS-2 is significantly weaker than BDS-3. And inclined geosynchronous orbit (IGSO) satellites have abnormal data error rates, which should be related to the special signal path trajectory of the IGSO satellite. Full article
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Graphical abstract

Graphical abstract
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<p>An example of a post-processed airglow image at 15:24 UT on 3 April 2022. (<b>a</b>) Geographical distribution of relative airglow values with pseudocolor. The black star represents the location of the ground station, and the black triangle represents the ionospheric pierce point (IPP) location of BDS GEO satellite C03 at 300 km. The dashed and dash-dot lines mark the longitude and latitude of the IPP, respectively. (<b>b</b>) Airglow values at a fixed latitude of 21.2° extracted from panel (<b>a</b>). The black dashed line indicates the airglow value extracted at the fixed IPP.</p>
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<p>Comparison of the S<sub>4</sub> index (Galileo: L1C, GPS: L1C), airglow depletion, and deviation VTEC (Galileo: L1C-L5Q, GPS: L1C-L2W) for (<b>a</b>,<b>c</b>) Galileo and (<b>b</b>,<b>d</b>) GPS during 12–20 UT on 3 April 2022. The signal path with the highest elevation is selected among all the satellites at a certain epoch. (<b>a</b>,<b>b</b>) Distributions of the selected ionospheric pierce points (IPPs, color dots) at an effective height of 300 km. The selected area is at 19°–23°N, which is covered by the airglow image. The black stars represent the location of the GNSS receiver and airglow imager at Zhuhai, China. (<b>c</b>,<b>d</b>) Variations of the S<sub>4</sub> index (orange bar), airglow depletion (blue bar), and deviation VTEC (colored line) as a function of UT (LT ≈ UT + 7.5). The airglow values are the post-processed airglow values divided by a constant value (it is 200 in this work). The specific PRNs are also marked in the panels, and the colors used for specific PRNs are the same in panels (<b>a</b>,<b>c</b>).</p>
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<p>Comparison of the S<sub>4</sub> index (BDS: L2I, SBAS: L1C), airglow depletion, and deviation VTEC (BDS: L2I-L6I, SBAS: L1C-L5I) for eight GEO satellites during 12–20 UT on 3 April 2022. (<b>a</b>) Geographical distribution of ground-based station (red triangle) and IPPs (black pentagrams) for eight GEO satellites. From top to bottom (<b>b</b>–<b>i</b>) are eight GEO satellites distributed from west to east.</p>
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<p>Variations of signal quality parameters for L6I (1268.52 MHz) observations from the BDS-C03 GEO satellite during 12–20 UT on 3 April 2022. From top to bottom are the variations of (<b>a</b>) the S<sub>4</sub> index (L6I) and airglow depletion, (<b>b</b>) the deviation VTEC (L2I-L6I), (<b>c</b>) the signal-to-noise ratio (C/N0, S6I), (<b>d</b>) the number of cycle slips, and (<b>e</b>) the number of losses of lock as a function of UT.</p>
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<p>Comparison of the number of error epochs (cycle slip or loss of phase observation, blue bar), number of scintillation events (S<sub>4</sub> &gt; 1.5* averaged S<sub>4</sub>, orange bar), and corresponding mean S<sub>4</sub> intensity (yellow bar) at L1 frequency (GPS L1C, Galileo L1C, GLONASS L1C: 1575.42 MHz, and BDS-2 and BDS-3 L2I: 1561.098 MHz) band for different constellations. For better comparison with the S<sub>4</sub> index, the error epochs are divided into 1 min time bins. The constellation is marked in the upper left corner of each subpanel, and the upper right corner indicates the average number of satellites observed at each epoch.</p>
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<p>Comparison of the number of error epochs, number of scintillation events, and corresponding mean S<sub>4</sub> intensity for three orbits (MEO, GEO, IGSO) of the BDS at L1 frequency (L2I, 1561.098 MHz). This figure is similar to <a href="#remotesensing-16-01358-f005" class="html-fig">Figure 5</a>.</p>
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<p>Occurrence rate of error epochs for (<b>a</b>) GPS, (<b>b</b>) Galileo, (<b>c</b>) GLONASS, and (<b>d</b>) BDS during 12–20 UT on 3 April 2022. The color of the bar indicates the frequency band and the signal types are marked in x-label. When the S<sub>4</sub> index exceeds the threshold, the signal is considered to have passed through the EPB at this time. The occurrence rate is defined as the total epoch of cycle slips and loss of phase observations divided by the total epoch in which the signal passes through the EPB in 1 min.</p>
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<p>Occurrence rate of error epochs for BDS-2 and BDS-3 and for different orbit types (MEO, GEO, IGSO). This figure is similar to <a href="#remotesensing-16-01358-f007" class="html-fig">Figure 7</a>.</p>
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9 pages, 4083 KiB  
Communication
A Study of Outliers in GNSS Clock Products
by Kamil Maciuk, Inese Varna and Karolina Krzykowska-Piotrowska
Sensors 2024, 24(3), 799; https://doi.org/10.3390/s24030799 - 25 Jan 2024
Cited by 1 | Viewed by 843
Abstract
Time is an extremely important element in the field of GNSS positioning. In precise positioning with a single-centimetre accuracy, satellite clock corrections are used. In this article, the longest available data set of satellite clock corrections of four GNSS systems from 2014 to [...] Read more.
Time is an extremely important element in the field of GNSS positioning. In precise positioning with a single-centimetre accuracy, satellite clock corrections are used. In this article, the longest available data set of satellite clock corrections of four GNSS systems from 2014 to 2021 was analysed. This study covers the determination of the quality (outliers number and magnitude), availability, stability, and determination of the specificity and nature of the clock correction for each satellite system. One problem with the two newest satellite systems (Galileo and BeiDou) is the lack of availability of satellite signals in the early years of the analysis. These data were available only in the later years of the period covered by the analysis, as most of the satellites have only been in orbit since 2018–2019. Interestingly, the percentage of outlying observations was highest in Galileo and lowest in BeiDou. Phase and frequency plots showed a significant number of outlying observations. On the other hand, after eliminating outlying observations, each system showed a characteristic graph waveform. The most consistent and stable satellite clock corrections are provided by the GPS and GLONASS systems. The main problems discussed in this paper are the determination of the number and magnitude of outliers in clock products of four GNSS systems (GPS, GLONASS, Galileo, Beidou) and the study on the long-term stability of GNSS clocks analysis, which covers the years 2014–2021. Full article
(This article belongs to the Section Vehicular Sensing)
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<p>Data coverage of the analysed period for each system and satellite: (<b>a</b>) BeiDou; (<b>b</b>) Galileo; (<b>c</b>) GPS; (<b>d</b>) GLONASS. Black dots represent a change in SVN.</p>
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<p>Description of the data processing steps.</p>
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<p>Sample frequency jump of satellite clock.</p>
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<p>Number of outliers in each set of clock corrections in each satellite divided by GNSS system: (<b>a</b>) BeiDou; (<b>b</b>) Galileo; (<b>c</b>) GPS; (<b>d</b>) GLONASS.</p>
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<p>Sample phase graphs: (<b>a</b>) satellite C06 raw; (<b>b</b>) satellite C06 cleaned; (<b>c</b>) satellite E08 raw; (<b>d</b>) satellite E08 cleaned; (<b>e</b>) satellite G13 raw; (<b>f</b>) satellite G13 cleaned; (<b>g</b>) satellite R26 raw; (<b>h</b>) satellite R26 cleaned.</p>
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<p>Sample frequency graphs: (<b>a</b>) satellite C06 raw; (<b>b</b>) satellite C06 cleaned; (<b>c</b>) satellite E08 raw; (<b>d</b>) satellite E08 cleaned; (<b>e</b>) satellite G13 raw; (<b>f</b>) satellite G13 cleaned; (<b>g</b>) satellite R26 raw; (<b>h</b>) satellite R26 cleaned.</p>
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<p>A yearly HDEV of selected satellites: (<b>a</b>) satellite C07; (<b>b</b>) satellite C14; (<b>c</b>) satellite E08; (<b>d</b>) satellite G05; (<b>e</b>) satellite G16; (<b>f</b>) satellite R02.</p>
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24 pages, 8560 KiB  
Article
Velocity Estimation Using Time-Differenced Carrier Phase and Doppler Shift with Different Grades of Devices: From Smartphones to Professional Receivers
by Antonio Angrisano, Giovanni Cappello, Salvatore Gaglione and Ciro Gioia
Algorithms 2024, 17(1), 2; https://doi.org/10.3390/a17010002 - 19 Dec 2023
Viewed by 2094
Abstract
Velocity estimation has a key role in several applications; for instance, velocity estimation in navigation or in mobile mapping systems and GNSSs is currently a common way to achieve reliable and accurate velocity. Two approaches are mainly used to obtain velocity based on [...] Read more.
Velocity estimation has a key role in several applications; for instance, velocity estimation in navigation or in mobile mapping systems and GNSSs is currently a common way to achieve reliable and accurate velocity. Two approaches are mainly used to obtain velocity based on GNSS measurements, i.e., Doppler observations and carrier phases differenced in time (that is, TDCP). In a benign environment, Doppler-based velocity can be estimated accurately to within a few cm/s, while TDCP-based velocity can be estimated accurately to within a few mm/s. On the other hand, the TDCP technique is more prone to availability shortage and the presence of blunders. In this work, the two mentioned approaches are tested, using three devices of different grades: a high-grade geodetic receiver, a high-sensitivity receiver, and a GNSS chip mounted on a smartphone. The measurements of geodetic receivers are inherently cleaner, providing an accurate solution, while the remaining two receivers provide worse results. The case of smartphone GNSS chips can be particularly critical owing to the equipped antenna, which makes the measurements noisy and largely affected by blunders. The GNSSs are considered separately in order to assess the performance of the single systems. The analysis carried out in this research confirms the previous considerations about receiver grades and processing techniques. Additionally, the obtained results highlight the necessity of adopting a diagnostic approach to the measurements, such as RAIM-FDE, especially for low-grade receivers. Full article
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<p>Panel (<b>a</b>): location of the test; the equipment is placed on point P. Panel (<b>b</b>): equipment deployment. Panel (<b>c</b>): multipath probability distribution for the uBlox receiver.</p>
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<p>Availability of Doppler and CP observables (mask angle and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> <mo>/</mo> <mi>N</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> limit not applied). Each panel refers to a single device and to a single GNSS. Panels in the first row, (<b>a–c</b>), refer to GPS; panels in the second row, (<b>d</b>,<b>e</b>), to Glonass; panels in the third row, (<b>f</b>,<b>g</b>), to Galileo; and panels in the fourth row, (<b>h</b>,<b>i</b>), to BeiDou. The panel in the first column, (<b>a</b>), refers to the Novatel device; panels in the second column, (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>), to uBlox; and panels in the third column, (<b>c</b>,<b>e</b>,<b>g</b>,<b>i</b>), to Xiaomi.</p>
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<p>Availability percentage of Doppler and CP measurements for satellite G02, panel (<b>a</b>), and for satellite G06, panel (<b>b</b>). Mask angle and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> <mo>/</mo> <mi>N</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> limit not applied.</p>
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<p><math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> <mo>/</mo> <mi>N</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> behavior over time (mask angle and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> <mo>/</mo> <mi>N</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> limit not applied). Each panel refers to a single device and to a single GNSS. Panels in the first row, (<b>a</b>–<b>c</b>), refer to GPS; panels in the second row, (<b>d</b>,<b>e</b>), to Glonass; panels in the third row, (<b>f</b>,<b>g</b>), to Galileo; and panels in the fourth row, (<b>h</b>,<b>i</b>), to BeiDou. The panel in the first column, <b>(a)</b>, refers to the Novatel device; panels in the second column, (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>), to uBlox; and panels in the third column, (<b>c</b>,<b>e</b>,<b>g</b>,<b>i</b>), to Xiaomi.</p>
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<p><math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> <mo>/</mo> <mi>N</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> behavior over time (mask angle and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> <mo>/</mo> <mi>N</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> limit not applied) for satellite G02, panel (<b>a</b>), and for satellite G06, panel (<b>b</b>).</p>
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<p>Numbers of Doppler and TDCP measurements (mask angle and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> <mo>/</mo> <mi>N</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> limit applied). Each panel refers to a single device and to a single GNSS. Panels in the first row, (<b>a</b>–<b>c</b>), refer to GPS; panels in the second row, (<b>d</b>,<b>e</b>), to Glonass; panels in the third row, (<b>f</b>,<b>g</b>), to Galileo; and panels in the fourth row, (<b>h</b>,<b>i</b>), to BeiDou. The panel in the first column, (<b>a</b>), refers to the Novatel device; panels in the second column, (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>), to uBlox; and panels in the third column, (<b>c</b>,<b>e</b>,<b>g</b>,<b>i</b>), to Xiaomi.</p>
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<p>Horizontal Doppler-based and TDCP-based velocity error. Each panel refers to a single device and to a single GNSS. Panels in the first row, (<b>a</b>–<b>c</b>), refer to GPS; panels in the second row, (<b>d</b>,<b>e</b>), to Glonass; panels in the third row, (<b>f</b>,<b>g</b>), to Galileo; and panels in the fourth row, (<b>h</b>,<b>i</b>), to BeiDou. The panel in the first column, (<b>a</b>), refers to the Novatel device; panels in the second column, (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>), to uBlox; and panels in the third column, (<b>c</b>,<b>e</b>,<b>g</b>,<b>i</b>), to Xiaomi.</p>
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<p>Vertical Doppler-based and TDCP-based velocity error. Each panel refers to a single device and to a single GNSS. Panels in the first row, (<b>a</b>–<b>c</b>), refer to GPS; panels in the second row, (<b>d</b>,<b>e</b>), to Glonass; panels in the third row, (<b>f</b>,<b>g</b>), to Galileo; and panels in the fourth row, (<b>h</b>,<b>i</b>), to BeiDou. The panel in the first column, <b>(a)</b>, refers to the Novatel device; panels in the second column, (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>), to uBlox; and panels in the third column, (<b>c</b>,<b>e</b>,<b>g</b>,<b>i</b>), to Xiaomi.</p>
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<p>Horizontal Doppler-based and TDCP-based velocity error with RAIM applied. Each panel refers to a single device and to a single GNSS. Panels in the first row, (<b>a</b>–<b>c</b>), refer to GPS; panels in the second row, (<b>d</b>,<b>e</b>), to Glonass; panels in the third row, (<b>f</b>,<b>g</b>), to Galileo; and panels in the fourth row, (<b>h</b>,<b>i</b>), to BeiDou. The panel in the first column, (<b>a</b>), refers to the Novatel device; panels in the second column, (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>), to uBlox; and panels in the third column, (<b>c</b>,<b>e</b>,<b>g</b>,<b>i</b>), to Xiaomi.</p>
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<p>Vertical Doppler-based and TDCP-based velocity error with RAIM applied. Each panel refers to a single device and to a single GNSS. Panels in the first row, (<b>a</b>–<b>c</b>), refer to GPS satellites; panels in the second row, (<b>d</b>,<b>e</b>), to Glonass; panels in the third row, (<b>f</b>,<b>g</b>), to Galileo; and panels in the fourth row, (<b>h</b>,<b>i</b>), to BeiDou. The panel in the first column, (<b>a</b>), refers to the Novatel device; panels in the second column, (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>), to uBlox; and panels in the third column, (<b>c</b>,<b>e</b>,<b>g</b>,<b>i</b>), to Xiaomi.</p>
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30 pages, 15689 KiB  
Article
Enhanced GNSS Reliability on High-Dynamic Platforms: A Comparative Study of Multi-Frequency, Multi-Constellation Signals in Jamming Environments
by Abdelsatar Elmezayen, Malek Karaim, Haidy Elghamrawy and Aboelmagd Noureldin
Sensors 2023, 23(23), 9552; https://doi.org/10.3390/s23239552 - 1 Dec 2023
Cited by 2 | Viewed by 1207
Abstract
The global navigation satellite system (GNSS) signals are vulnerable to disruption sources, such as signal jamming. This, in turn, can cause severe degradation or discontinuities of the GNSS-based position, navigation, and timing services. The availability of multi-frequency signals from multi-constellation GNSS systems, such [...] Read more.
The global navigation satellite system (GNSS) signals are vulnerable to disruption sources, such as signal jamming. This, in turn, can cause severe degradation or discontinuities of the GNSS-based position, navigation, and timing services. The availability of multi-frequency signals from multi-constellation GNSS systems, such as Galileo and GLONASS, along with the modernization of GPS with multi-frequency signals, has the potential to increase the immunity of GNSS-based navigation systems to signal jamming. Despite various studies completed on the utilization of multi-frequency and multi-constellation global navigation satellite system (GNSS) signals to resist receiver jamming, there is still an urge to further investigate this concern under different circumstances. This paper presents an experimental evaluation of the advantages of the employment of multi-frequency multi-constellation GNSS signals for better GNSS receivers’ performance during signal jamming situations for high-dynamic platforms such as aircraft/drones. Additionally, the study examines the effects of both simulated and real jamming signals on all possible combinations of the GPS, Galileo, and GLONASS signal frequencies and constellations. Two airplane trajectory routes were built, and their corresponding RF signals were generated using the Spirent and Orolia GNSS signal simulators. The results indicated that the GPS multi-frequency-based solution maintains reliable positioning performance to some extent under low jamming scenarios. However, the combination of GPS, Galileo, and GLONASS signals proved its ability to provide a continuous and accurate positioning solution during both low and high jamming scenarios. Full article
(This article belongs to the Section Navigation and Positioning)
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<p>Spirent GSS6700 GNSS simulator.</p>
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<p>Orolia GSG-8 GNSS simulator.</p>
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<p>Imported trajectory to Orolia.</p>
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<p>Simulated trajectories: (<b>left</b>) first trajectory, (<b>right</b>) second trajectory.</p>
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<p>Orolia experimental setup.</p>
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<p>NEAT (<b>left</b>), and mini-circuits attenuator (<b>right</b>).</p>
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<p>Anechoic chamber including both Tx and Rx antennas.</p>
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<p>(<b>a</b>) Horizontal positioning error for different GNSS signal combinations [first trajectory]. (<b>b</b>) Zoomed view of horizontal positioning error for different GNSS signal combinations [first trajectory].</p>
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<p>(<b>a</b>) Vertical positioning error for different GNSS signal combinations [first trajectory]. (<b>b</b>) Zoomed view of vertical positioning error for different GNSS signal combinations [first trajectory].</p>
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<p>Number of visible satellites for different GNSS signal combinations [first trajectory].</p>
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<p>(<b>a</b>) Horizontal positioning error for different GNSS signal combinations [second trajectory]. (<b>b</b>) Zoomed view of horizontal positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>(<b>a</b>) Vertical positioning error for different GNSS signal combinations [second trajectory]. (<b>b</b>) Zoomed view of vertical positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>Number of visible satellites for different GNSS signal combinations [second trajectory].</p>
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<p>(<b>a</b>) Horizontal positioning error for different GNSS signal combinations [first trajectory]. (<b>b</b>) Zoomed view of horizontal positioning error for different GNSS signal combinations [first trajectory].</p>
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<p>(<b>a</b>) Vertical positioning error for different GNSS signal combinations [first trajectory]. (<b>b</b>) Zoomed view of vertical positioning error for different GNSS signal combinations [first trajectory].</p>
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<p>Number of visible satellites for different GNSS signal combinations [first trajectory].</p>
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<p>(<b>a</b>) Horizontal positioning error for different GNSS signal combinations [second trajectory]. (<b>b</b>) Zoomed view of horizontal positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>(<b>a</b>) Horizontal positioning error for different GNSS signal combinations [second trajectory]. (<b>b</b>) Zoomed view of horizontal positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>(<b>a</b>) Vertical positioning error for different GNSS signal combinations [second trajectory]. (<b>b</b>) Zoomed view of vertical positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>Number of visible satellites for different GNSS signal combinations [second trajectory].</p>
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<p>(<b>a</b>) Horizontal positioning error for different GNSS signal combinations [first trajectory]. (<b>b</b>) Zoomed view of horizontal positioning error for different GNSS signal combinations [first trajectory].</p>
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<p>(<b>a</b>) Vertical positioning error for different GNSS signal combinations [first trajectory]. (<b>b</b>) Zoomed view of vertical positioning error for different GNSS signal combinations [first trajectory].</p>
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<p>Number of visible satellites for different GNSS signal combinations [first trajectory].</p>
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<p>(<b>a</b>) Horizontal positioning error for different GNSS signal combinations [second trajectory]. (<b>b</b>) Zoomed view of horizontal positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>(<b>a</b>) Horizontal positioning error for different GNSS signal combinations [second trajectory]. (<b>b</b>) Zoomed view of horizontal positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>(<b>a</b>) Vertical positioning error for different GNSS signal combinations [second trajectory]. (<b>b</b>) Zoomed view of vertical positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>Number of visible satellites for different GNSS signal combinations [second trajectory].</p>
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<p>Horizontal positioning error for different GNSS signal combinations [first trajectory].</p>
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<p>Vertical positioning error for different GNSS signal combinations [first trajectory].</p>
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<p>Number of visible satellites for different GNSS signal combinations [first trajectory].</p>
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<p>Horizontal positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>Vertical positioning error for different GNSS signal combinations [second trajectory].</p>
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<p>Number of visible satellites for different GNSS signal combinations [second trajectory].</p>
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<p>RMS of horizontal errors for the simulated and actual jamming scenarios (low jamming).</p>
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<p>RMS of vertical errors for the simulated and actual jamming scenarios (low jamming).</p>
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<p>RMS of horizontal errors for the simulated and actual jamming scenarios (high jamming).</p>
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<p>RMS of vertical errors for the simulated and actual jamming scenarios (high jamming).</p>
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19 pages, 3243 KiB  
Article
Estimation and Evaluation of Zenith Tropospheric Delay from Single and Multiple GNSS Observations
by Sai Xia, Shuanggen Jin and Xuzhan Jin
Remote Sens. 2023, 15(23), 5457; https://doi.org/10.3390/rs15235457 - 22 Nov 2023
Cited by 1 | Viewed by 1285
Abstract
Multi-Global Navigation Satellite Systems (multi-GNSS) (including GPS, BDS, Galileo, and GLONASS) provide a significant opportunity for high-quality zenith tropospheric delay estimation and its applications in meteorology. However, the performance of zenith total delay (ZTD) retrieval from single- or multi-GNSS observations is not clear, [...] Read more.
Multi-Global Navigation Satellite Systems (multi-GNSS) (including GPS, BDS, Galileo, and GLONASS) provide a significant opportunity for high-quality zenith tropospheric delay estimation and its applications in meteorology. However, the performance of zenith total delay (ZTD) retrieval from single- or multi-GNSS observations is not clear, particularly from the new, fully operating BDS-3. In this paper, zenith tropospheric delay is estimated using the single-, dual-, triple-, or four-GNSS Precise Point Positioning (PPP) technique from 55 Multi-GNSS Experiment (MGEX) stations over one year. The performance of GNSS ZTD estimation is evaluated using the International GNSS Service (IGS) standard tropospheric products, radiosonde, and the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5). The results show that the GPS-derived ZTD time series is more consistent and reliable than those derived from BDS-only, Galileo-only, and GLONASS-only solutions. The performance of the single-GNSS ZTD solution can be enhanced with better accuracy and stability by combining multi-GNSS observations. The accuracy of the ZTD from multi-GNSS observations is improved by 13.8%, 43.8%, 27.6%, and 22.9% with respect to IGS products for the single-system solution (GPS, BDS, Galileo, and GLONASS), respectively. The ZTD from multi-GNSS observations presents higher accuracy and a significant improvement with respect to radiosonde and ERA5 data when compared to the single-system solution. Full article
(This article belongs to the Special Issue BDS/GNSS for Earth Observation: Part II)
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<p>The distribution of GNSS stations from MGEX networks and radiosonde stations. The black triangle is the GNSS station, and the red circle is the radiosonde station.</p>
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<p>ZTD time series of GPS (G), BDS (C), Galileo (E), and GLONASS (R) for the year 2019 (<b>top panel</b>: DGAR; <b>bottom panel</b>: PTGG).</p>
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<p>Linear correlation of GPS-derived ZTD to the other system-derived (BDS, Galileo, and GLONASS) ZTD at station DGAR (<b>a</b>−<b>c</b>) and PTGG (<b>d</b>−<b>f</b>).</p>
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<p>Distribution of ZTD differences between the GPS-only and the other single-system (BDS, Galileo, and GLONASS) solutions at stations DGAR (<b>a</b>−<b>c</b>) and PTGG (<b>d</b>−<b>f</b>).</p>
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<p>Between the GPS-only and the other single-system (BDS, Galileo, and GLONASS) solutions, the top panel shows the RMSs of ZTD differences and the bottom panel shows biases of ZTD differences.</p>
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<p>ZTD differences between four-system combined and single-system (G, C, E, and R) or multi-system combined (GC, GE, GR, GCE, GCR, and GER) solutions (<b>top panel</b>: DGAR; <b>bottom panel</b>: PTGG).</p>
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<p>ZTD derived from single-system and multi-system solutions and IGS final troposphere products during DOY 140–150, 2019 (<b>top panel</b>: DGAR; <b>bottom panel</b>: PTGG).</p>
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<p>The ZTD differences of single- and multi-system solutions with respect to IGS products during DOY 140–150, 2019 (<b>top panel</b>: DGAR; <b>bottom panel</b>: PTGG).</p>
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<p>RMS and mean absolute bias for the ZTD differences of single- and multi-system solutions with respect to IGS final products (<b>top panel</b>: RMS; <b>bottom panel</b>: absolute bias).</p>
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<p>ZTD derived from the four-system solution and radiosonde solution during DOY 80−180, 2019 (<b>top panel</b>: POAL; <b>bottom panel</b>: HOB2).</p>
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<p>RMSs of ZTD differences for single- and multi-system solutions with respect to the radiosonde solutions.</p>
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<p>ZTD time series from the four-system solution and ERA5 data for a period of 40 days (<b>top panel</b>: RGDG; <b>bottom panel</b>: STJ3).</p>
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<p>Geographical distribution of RMS values of ZTD differences for the multi-system solutions with respect to the ERA5 data at GNSS stations. (<b>a</b>) G. (<b>b</b>) GR. (<b>c</b>) GER. (<b>d</b>) GCER.</p>
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17 pages, 14717 KiB  
Article
Designed Structures of Interdigital Electrodes for Thin Film SAW Devices
by Yicong Qian, Yao Shuai, Chuangui Wu, Wenbo Luo, Xinqiang Pan and Wanli Zhang
Micromachines 2023, 14(10), 1929; https://doi.org/10.3390/mi14101929 - 14 Oct 2023
Cited by 2 | Viewed by 1436
Abstract
This paper studied the impact of the microstructure of interdigital electrodes on the performance of surface acoustic wave (SAW) resonators and proposed an innovative piston, dummy finger and tilt (PDT) structure, which was then applied to the GLONASS L3 band filters. Through the [...] Read more.
This paper studied the impact of the microstructure of interdigital electrodes on the performance of surface acoustic wave (SAW) resonators and proposed an innovative piston, dummy finger and tilt (PDT) structure, which was then applied to the GLONASS L3 band filters. Through the adoption of 3D finite element simulation (FEM), photolithography, and testing on an incredible high-performance surface acoustic wave (I.H.P. SAW) substrate, it is concluded that the total aperture length is 20T (T is period), resulting in a more optimal resonator performance; changing the width and length of the piston can suppress transverse modes spurious, but it does not enhance impedance ratio; to further improve the quality of the SAW resonator, the proposed PDT structure has been experimentally proven to not only effectively suppress transverse modes spurious but also possess a high impedance ratio. By utilizing a PDT structure within a “T + π” topology circuit, we successfully designed and manufactured a GLONASS L3 band filter with a bandwidth of 8 MHz and an insertion loss of 3.73 dB. The design of these resonators and filters can be applied to the construction of SAW filters in similar frequency bands such as BeiDou B2 band or GPS L2/L5 band. Full article
(This article belongs to the Section D1: Semiconductor Devices)
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Figure 1
<p>Schematic diagram of BAW/SAW resonators. (<b>a</b>) SMR type BAW resonator; (<b>b</b>) SAW bulk resonator; (<b>c</b>) I.H.P. SAW resonator.</p>
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<p>Interdigital electrode structure. (<b>a</b>) Uniform interdigital electrode; (<b>b</b>) piston mode interdigital electrode.</p>
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<p>Resonator cross-sectional view and 3D FEM model. (<b>a</b>) The cross-sectional view of resonator; (<b>b</b>) overall 3D FEM model; (<b>c</b>) top view of the 3D FEM model.</p>
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<p>Simulation and measurement impedance curves with different total aperture lengths at different periods. (<b>a</b>–<b>c</b>) The simulation curves; (<b>d</b>–<b>f</b>) the measurement curves.</p>
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<p>Comparison between simulation and measurement of I.H.P. SAW resonators with different periods and total aperture lengths. (<b>a</b>) Impedance ratio comparison diagram; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>K</mi> <mi mathvariant="normal">t</mi> <mn>2</mn> </msubsup> </mrow> </semantics></math> comparison diagram.</p>
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<p>Schematic diagram of the relationship between the piston width and the SAW phase velocity, impact ratio, and <math display="inline"><semantics> <mrow> <msubsup> <mi>K</mi> <mi mathvariant="normal">t</mi> <mn>2</mn> </msubsup> </mrow> </semantics></math>. (<b>a</b>) SAW phase velocity; (<b>b</b>) impedance ratio; (<b>c</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>K</mi> <mi mathvariant="normal">t</mi> <mn>2</mn> </msubsup> </mrow> </semantics></math>.</p>
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<p>Simulation and measurement impedance curves with different piston lengths at different periods. (<b>a</b>–<b>c</b>) The simulation curves; (<b>d</b>–<b>f</b>) the measurement curves. For the convenience of observation and comparison, based on the impedance curve when the piston length is 0.2<span class="html-italic">T</span>, the remaining impedance curves are sequentially added by 20 dB.</p>
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<p>Comparison between simulation and measurement of I.H.P. SAW resonators with different periods and piston lengths. (<b>a</b>) Impedance ratio comparison curves; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>K</mi> <mi mathvariant="normal">t</mi> <mn>2</mn> </msubsup> </mrow> </semantics></math> comparison curves.</p>
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<p>Schematic diagram of PDT structure.</p>
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<p>Measured impedance curves of I.H.P. SAW resonators with different periods under PDT structure. (<b>a</b>) Impedance curves at different periods; (<b>b</b>) impedance curves under periods are 2.92 μm and 3.28 μm.</p>
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<p>Measurement of I.H.P. SAW resonators with different periods under PDT structure. (<b>a</b>) Impedance ratio diagram; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>K</mi> <mi mathvariant="normal">t</mi> <mn>2</mn> </msubsup> </mrow> </semantics></math> diagram.</p>
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<p>Circuit diagram of a third-order “T + π” type SAW filter.</p>
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<p>SAW filter layout. (<b>a</b>) CP test structure layout; (<b>b</b>) packaging structure layout.</p>
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<p>Drawing and appearance diagram of SMD 3030C packaged SAW filter. (<b>a</b>) Top view of drawing; (<b>b</b>) side view of drawing; (<b>c</b>) bottom pin diagram of drawing; (<b>d</b>) appearance of filter top view; (<b>e</b>) appearance of filter bottom pin diagram; (<b>f</b>) internal circuit diagram of SAW filter.</p>
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<p>SEM image of the SAW filter and resonator. (<b>a</b>) The overall filter circuit; (<b>b</b>) the single overall resonator; (<b>c</b>) partial enlarged view of the aperture; (<b>d</b>) partial enlarged view of the PDT structure.</p>
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<p>SEM image of the SAW filter and resonator. (<b>a</b>) The overall filter circuit; (<b>b</b>) the single overall resonator; (<b>c</b>) partial enlarged view of the aperture; (<b>d</b>) partial enlarged view of the PDT structure.</p>
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<p>The frequency response curves of the SAW filter. (<b>a</b>) Broad band frequency response curves between 500 MHz and 2000 MHz; (<b>b</b>) narrow band frequency response curves between 1182 MHz and 1222 MHz.</p>
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28 pages, 9250 KiB  
Article
Using the Commercial GNSS RO Spire Data in the Neutral Atmosphere for Climate and Weather Prediction Studies
by Shu-peng Ho, Xinjia Zhou, Xi Shao, Yong Chen, Xin Jing and William Miller
Remote Sens. 2023, 15(19), 4836; https://doi.org/10.3390/rs15194836 - 5 Oct 2023
Cited by 3 | Viewed by 1598
Abstract
Recently, the NOAA has included GNSS (Global Navigation Satellite System) Radio Occultation (RO) data as one of the crucial long-term observables for weather and climate applications. To include more GNSS RO data in its numerical weather prediction systems, the NOAA Commercial Weather Data [...] Read more.
Recently, the NOAA has included GNSS (Global Navigation Satellite System) Radio Occultation (RO) data as one of the crucial long-term observables for weather and climate applications. To include more GNSS RO data in its numerical weather prediction systems, the NOAA Commercial Weather Data Pilot program (CWDP) started to explore the commercial RO data available on the market. After two rounds of pilot studies, the CWDP decided to award the first Indefinite Delivery Indefinite Quantity (IDIQ) contract to GeoOptics and Spire Incs. in 2020. This study examines the quality of Spire RO data products for weather and climate applications. Spire RO data collected from commercial CubeSats are carefully compared with data from Formosa Satellite Mission 7–Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2), the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis (ERA5), and high-quality radiosonde data. The results demonstrate that, despite their generally lower Signal-Noise-Ratio (SNR), Spire RO data show a pattern of lowest penetration height similar to that of COSMIC-2. The Spire and COSMIC-2 penetration heights are between 0.6 and 0.8 km altitude over tropical oceans. Although using different GNSS RO receivers, the precision of Spire STRATOS receivers is of the same quality as those of the COSMIC-2 TriG (Global Positioning System—GPS, GALILEO, and GLObal NAvigation Satellite System—GLONASS) RO Receiver System (TGRS) receivers. Furthermore, the Spire and COSMIC-2 retrieval accuracies are quite comparable. We validate the Spire temperature and water vapor profiles by comparing them with collocated radiosonde observation (RAOB) data. Generally, over the height region between 8 km and 16.5 km, the Spire temperature profiles match those from RS41 RAOB very well, with temperature biases of <0.02 K. Over the height range from 17.8 to 26.4 km, the temperature differences are ~−0.034 K, with RS41 RAOB being warmer. We also estimate the error covariance matrix for Spire, COSMIC-2, and KOMPSAT-5. The results show that the COSMIC-2 estimated error covariance values are slightly more significant than those from Spire over the oceans at the mid-latitudes (45°N–30°N and 30°S–45°S), which may be owing to COSMIC-2 SNR being relatively lower at those latitudinal zones. Full article
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Figure 1
<p>The distribution of the normalized SNR frequency sample numbers (defined as the sample numbers for each SNR bin normalized to the maximum number of the SNR bin) for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) signals on (<b>a</b>) Spire, (<b>b</b>) COSMIC-2, and (<b>c</b>) KOMPSAT-5 over the CWDP Delivery-Order 3 (DO3, from 8 September 2021 to 15 March 2022). The total number of observations from each GNSS satellite is listed in the figures.</p>
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<p>Spatial distribution of the RO sample numbers for each 5° × 5° grid for (<b>a</b>) Spire, (<b>b</b>) COSMIC-2, and (<b>c</b>) KOMPSAT-5 for the whole DO3 period.</p>
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<p>Same as <a href="#remotesensing-15-04836-f002" class="html-fig">Figure 2</a>, but for the hourly local time distribution binned at 5° latitude bin for (<b>a</b>) Spire, (<b>b</b>) COSMIC-2, and (<b>c</b>) KOMPSAT-5 for the DO3 period. The observation numbers at each box are indicated by the color bar.</p>
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<p>Latitudinal distribution for Spire L1 SNR from 15 February to 15 March 2022 for (<b>a</b>) GPS, (<b>b</b>) GLONASS, and (<b>c</b>) GALILEO.</p>
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<p>Latitudinal distribution for COSMIC-2 L1 SNR from 15 February to 15 March 2022, for (<b>a</b>) GPS and (<b>b</b>) GLONASS.</p>
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<p>Two-line element (TLE)-based SRO event prediction for two LEO receivers with the same GNSS satellite.</p>
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<p>The global mean of the lowest penetration height in June 2022 binned into a 5° × 5° grid for (<b>a</b>) Spire (from 90°N–90°S) and (<b>b</b>) COSMIC-2 (from 45°N–45°S).</p>
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<p>(<b>a</b>) The RO penetration percentage (defined as the observation number at each penetration depth relative to the observation number at 8 km) over oceans within [45°N, 45°S] during the DO3 period and (<b>b</b>) the corresponding numbers of observations from surface to 14 km altitude for COSMIC-2, Spire, KOMPSAT5, and PAZ.</p>
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<p>The mean difference (in red line) and standard deviation (in green line) for (<b>a</b>) fractional bending angle, (<b>b</b>) dry temperature, and (<b>c</b>) water vapor mixing ratio comparisons for the Spire S128 and S119 DO3 SRO pairs. The corresponding numbers of observations are in blue lines.</p>
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<p>The DO3 SRO fractional BA comparison for Spire S120 and S124 receivers for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) for (<b>a</b>) the fractional mean difference, (<b>b</b>) the standard deviation, and (<b>c</b>) the observation numbers from surface to 40 km altitude.</p>
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<p>The fractional BA difference, the corresponding standard deviation, and the sample number at each vertical level from surface to 40 km altitude for Spire (in red line), COSMIC-2 (in green line), and COSMIC-1 (in blue line) for (<b>a</b>) mid-latitude for the southern hemisphere (20°S–45°S), (<b>b</b>) tropical region (20°N–20°S), and (<b>c</b>) mid-latitude for the northern hemisphere (45°N–20°N). We also compute the standard error of the mean (SEM) in a vertical line superimposed on the mean.</p>
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<p>The fractional BA Spire–RO comparison for (<b>a</b>) mean differences, (<b>b</b>) the standard deviations, and (<b>c</b>) observation numbers for the Spire–PAZ, Spire–KOMPSAT-5, Spire–Metop-B, Spire–Metop-C, and Spire–TerraSAR-X SRO pairs during the DO4 period.</p>
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<p>Bending angle profile comparison between COSMIC-2 and Spire for (<b>a</b>) fractional BA profile differences, (<b>b</b>) the standard deviations, and (<b>c</b>) vertical observation numbers for five COSMIC-2 SNR groups (i.e., 0–500 <span class="html-italic">v</span>/<span class="html-italic">v</span>, 500–1000 <span class="html-italic">v</span>/<span class="html-italic">v</span>, 1000–1500 <span class="html-italic">v</span>/<span class="html-italic">v</span>, 1500–2000 <span class="html-italic">v</span>/<span class="html-italic">v</span>, and &gt;2000 <span class="html-italic">v</span>/<span class="html-italic">v</span>).</p>
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<p>Bending angle profile comparison between STAR and UCAR Spire for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) for (<b>a</b>) the fractional mean difference, (<b>b</b>) the standard deviation, and (<b>c</b>) the observation numbers from surface to 40 km altitude.</p>
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<p>Spire–ERA5 mean BA fractional difference and corresponding standard deviations for (<b>a</b>) 45°N to 45°S, (<b>b</b>) 45°N to 30°N, (<b>c</b>) 30°N to 30°S, and (<b>d</b>) 30°S to 45°S. Similar to (<b>a</b>–<b>d</b>), we also compare the COSMIC-2 and ERA5 BA fractional differences and corresponding standard deviations in (<b>e</b>) 45°N to 45°S, (<b>f</b>) 45°N to 30°N, (<b>g</b>) 30°N to 30°S, and (<b>h</b>) 30°S to 45°S.</p>
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<p>(<b>a</b>) Differences (dash lines) and uncertainties (dot lines) of Spire temperature profiles retrieved by UCAR wetPf2 compared to RS41 RAOB data. (<b>c</b>) Differences (dash lines) and uncertainties (dot lines) of Spire-specific humidity profiles retrieved by UCAR wetPf2 compared to RS41 RAOB data. (<b>b</b>) Shows the number of collocated Spire–RAOB temperature profiles, and (<b>d</b>) is the number of Spire–RAOB water vapor profiles.</p>
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<p>(<b>a</b>) Height-dependent mean temperature differences (K) of UCAR wetPf2 versus RS41 RAOB in the zones of daytime (SZA &lt; 80°), nighttime (SZA &gt; 100°), and dusk/dawn (80° &lt; SZA &lt; 100°) in the upper troposphere and lower stratosphere. (<b>b</b>) The height-dependent profile numbers for the analysis.</p>
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<p>(<b>a</b>) The height-dependent mean humidity differences (g/kg) of UCAR wetPf2 versus RS41 RAOB for daytime (SZA &lt; 80°), nighttime (SZA &gt; 100°), and dusk/dawn (80° &lt; SZA &lt; 100°). Corresponding profile numbers are shown in (<b>b</b>).</p>
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<p>Fractional BA observation errors (in %) estimated for the region within [45°N, 45°S] for (<b>a</b>) over oceans, (<b>b</b>) over land, and (<b>c</b>) over oceans and land, (<b>d</b>) over oceans [20°S, 45°S], (<b>e</b>) over oceans [20°N, 20°S], and (<b>f</b>) over oceans [45°N, 20°N]. One month (from 15 December 2020 to 15 January 2021) of COSMIC-2, KOMPSAT-5, GeoOptics, and Spire bending angle observations were used for generating these figures.</p>
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<p>The STAR Spire RO data-processing flow chart.</p>
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<p>STAR-processed Spire RO excess phase comparison with those processed by UCAR for three cases representing RO tracking to (left) GPS, (middle) GLONASS, and (right) GALILEO systems, respectively. (<b>a</b>–<b>c</b>) The excess phase comparison for GPS, GLONASS, and GALILEO, respectively. (<b>d</b>–<b>f</b>) The excess Doppler comparison for GPS, GLONASS, and GALILEO.</p>
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12 pages, 5666 KiB  
Technical Note
Ionosphere Total Electron Content Modeling and Multi-Type Differential Code Bias Estimation Using Multi-Mode and Multi-Frequency Global Navigation Satellite System Observations
by Qisheng Wang, Jiaru Zhu and Feng Hu
Remote Sens. 2023, 15(18), 4607; https://doi.org/10.3390/rs15184607 - 19 Sep 2023
Cited by 1 | Viewed by 1106
Abstract
With the rapid development of multi-mode and multi-frequency GNSSs (including GPS, GLONASS, BDS, Galileo, and QZSS), more observations for research on ionosphere can be provided. The Global Ionospheric Map (GIM) products are generated based on the observation of multi-mode and multi-frequency GNSSs, and [...] Read more.
With the rapid development of multi-mode and multi-frequency GNSSs (including GPS, GLONASS, BDS, Galileo, and QZSS), more observations for research on ionosphere can be provided. The Global Ionospheric Map (GIM) products are generated based on the observation of multi-mode and multi-frequency GNSSs, and comparisons with other GIMs provided by the ionosphere analysis centers are provided in this paper. Taking the CODE (Center of Orbit Determination in Europe) GIM as a reference during 30 days in January 2019, for the GIMs from JPL (Jet Puls Laboratory), UPC (Technical University of Catalonia), ESA (European Space Agency), WHU (Wuhan University), CAS (Chinese Academy of Sciences), and MMG (The multi-mode and multi-frequency GNSS observations used in this paper), the mean bias with respect to CODE products is 1.87, 1.30, −0.10, 0.01, −0.02, and −0.71 TECu, and the RMS is 2.12, 2.00, 1.33, 0.88, 0.88, and 1.30 TECu, respectively. The estimated multi-type DCB is also in good agreement with the DCB products provided by the MGEX. Full article
(This article belongs to the Special Issue BDS/GNSS for Earth Observation: Part II)
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<p>Distribution of the selected stations (red = GPS only, blue = GPS + GLONASS, yellow = GPS + GLONASS + BDS, and so on).</p>
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<p>Distribution of the IPPs for different constellations (DOY 002, 2019).</p>
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<p>Global VTEC maps of MMG for DOY 002, 2019.</p>
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<p>VTEC difference between MMG and CODE for DOY 002, 2019.</p>
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<p>The bias and RMS of GIM estimated by different IGS analysis centers and MMG, relative to the GIM provided by CODE.</p>
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<p>The RMS of MMG estimated satellite DCB of GPS and GLONASS relative to the DCB product provided by MGEX.</p>
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<p>The RMS of MMG estimated satellite DCB of BDS and Galileo relative to the DCB product provided by MGEX.</p>
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<p>The RMS of MMG estimated receiver DCB for some elected stations relative to the DCB product provided by MGEX.</p>
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<p>Single frequency PPP accuracy comparison, while using the TEC from CODE and this paper.</p>
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13 pages, 2892 KiB  
Article
Kinematic Precise Point Positioning Performance-Based Cost-Effective Robot Localization System
by Ashraf Farah and Mehdi Tlija
Appl. Sci. 2023, 13(18), 10408; https://doi.org/10.3390/app131810408 - 18 Sep 2023
Cited by 1 | Viewed by 1581
Abstract
The use of high-precision positioning systems in modern navigation applications is crucial since location data is one of the most important pieces of information in Industry 4.0, especially for robots operating outdoors. In the modernization process of global navigation satellite system (GNSS) positioning, [...] Read more.
The use of high-precision positioning systems in modern navigation applications is crucial since location data is one of the most important pieces of information in Industry 4.0, especially for robots operating outdoors. In the modernization process of global navigation satellite system (GNSS) positioning, precise point positioning (PPP) has demonstrated its effectiveness in comparison to traditional differential positioning methods over the past thirty years. However, various challenges hinder the integration of PPP techniques into Internet of Things (IoT) systems for robot localization, with accuracy being a primary concern. This accuracy is impacted by factors such as satellite availability and signal disruptions in outdoor environments, resulting in less precise determination of satellite observations. Effectively addressing various GNSS errors is crucial when collecting PPP observations. The paper investigates the trade-off between kinematic PPP accuracy and cost effectiveness, through the examination of various influencing factors, including the choice of GNSS system (single or mixed), observation type (single or dual frequency), and satellite geometry. This research investigates kinematic PPP accuracy variation on a 10.4 km observed track based on different factors, using the GNSS system (single or mixed), and observation type (single or dual frequency). It can be concluded that mixed (GPS/GLONASS) dual frequency offers a 3D position accuracy of 9 cm, while mixed single frequency offers a 3D position accuracy of 13 cm. In industry, the results enable manufacturers to select suitable robot localization solutions according to the outdoor working environment (number of available satellites), economical constraint (single or dual frequency), and 3D position accuracy. Full article
(This article belongs to the Special Issue Advanced Robotics and Mechatronics)
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<p>The architecture of CPS-based mobile robots for localization function.</p>
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<p>Study scope.</p>
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<p>The study’s observed kinematic track (KSU campus), Riyadh, KSA (8 October 2022).</p>
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<p>The rover setup for the study’s observed track (KSU campus), Riyadh, KSA (8 October 2022).</p>
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<p>Kinematic PPP coordinate differences using (<b>a</b>) GPS single-frequency observations, (<b>b</b>) GLONASS single-frequency observations, (<b>c</b>) mixed GPS/GLONASS single-frequency observations, (<b>d</b>) GPS dual-frequency observations, (<b>e</b>) GLONASS dual-frequency observations, and (<b>f</b>) mixed GPS/GLONASS dual-frequency observations.</p>
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<p>Kinematic PPP coordinate differences using (<b>a</b>) GPS single-frequency observations, (<b>b</b>) GLONASS single-frequency observations, (<b>c</b>) mixed GPS/GLONASS single-frequency observations, (<b>d</b>) GPS dual-frequency observations, (<b>e</b>) GLONASS dual-frequency observations, and (<b>f</b>) mixed GPS/GLONASS dual-frequency observations.</p>
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<p>Kinematic PPP RMSE from GPS, GLONASS, and mixed GPS/GLONASS using (<b>a</b>) single-frequency observations, and (<b>b</b>) dual-frequency observations.</p>
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26 pages, 55800 KiB  
Article
Software Design for Airborne GNSS Air Service Performance Evaluation under Ionospheric Scintillation
by Tieqiao Hu, Gaojian Zhang and Lunlong Zhong
Electronics 2023, 12(17), 3713; https://doi.org/10.3390/electronics12173713 - 2 Sep 2023
Viewed by 963
Abstract
The performance analysis and evaluation of satellite navigation systems under ionospheric scintillation have been a focal point in the field of modern aviation. With the development and upgrading of satellite navigation systems, the performance indicators and evaluation techniques of these systems also require [...] Read more.
The performance analysis and evaluation of satellite navigation systems under ionospheric scintillation have been a focal point in the field of modern aviation. With the development and upgrading of satellite navigation systems, the performance indicators and evaluation techniques of these systems also require continuous iteration and optimization. In this study, based on the ionospheric scintillation model and satellite navigation algorithm, we designed a software tool to evaluate the performance of GNSS aviation services under various ionospheric scintillation intensities. The software is implemented in the C/C++ programming language and provides assessment capabilities for different ionospheric scintillation environments and flight phases. By encapsulating the software task modules using technologies such as dynamic link libraries and thread pools, the software can flexibly adjust the ionospheric scintillation intensity and control the flight trajectory. This ensures the strong scalability and reusability of the software. The software supports the performance evaluation of aviation services during all flight phases of global flights and is compatible with GPS, BDS, GALILEO, and GLONASS systems. Through verification of the accuracy, integrity, continuity, and availability of the GNSS system under different flight phases and ionospheric scintillation effects, the effectiveness of the software design has been validated. Full article
(This article belongs to the Section Computer Science & Engineering)
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<p>Software system architecture.</p>
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<p>Obtaining ionospheric scintillation sequences using the Cornell model.</p>
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<p>Data generation module process.</p>
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<p>Anomaly detection module process.</p>
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<p>Performance evaluation module process.</p>
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<p>Positioning error indicators in three dimensions.</p>
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<p>Location service availability distribution.</p>
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<p>Software design process.</p>
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<p>Parameter setting interface in software.</p>
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<p>The principles of a thread pool.</p>
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<p>Flight monitoring system design process.</p>
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<p>GUI for flight monitoring system.</p>
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<p>Reference trajectory for performance evaluation (CDG1197) in Cruise Phase.</p>
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<p>Reference trajectory for performance evaluation (UAL235) in Cruise Phase.</p>
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<p>Display of GPS L1 accuracy evaluation results (CDG1197) within the software interface.</p>
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<p>Display of GPS L1 accuracy evaluation results (UAL235) within the software interface.</p>
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<p>Display of GPS L1 integrity evaluation results (CDG1197) within the software interface.</p>
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<p>Display of GPS L1 integrity evaluation results (UAL235) within the software interface.</p>
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<p>Reference trajectory for performance evaluation (CDG1197) in Approach Phase.</p>
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<p>Reference trajectory for performance evaluation (UAL235) in Approach Phase.</p>
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<p>Display of BDS B1 accuracy evaluation results (CDG1197) within the software interface.</p>
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<p>Display of GPS L1 accuracy evaluation results (UAL235) within the software interface.</p>
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<p>Display of BDS B1 integrity evaluation results (CDG1197) within the software interface.</p>
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<p>Display of GPS L1 integrity evaluation results (UAL235) within the software interface.</p>
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17 pages, 5452 KiB  
Review
Global Navigation Satellite Systems as State-of-the-Art Solutions in Precision Agriculture: A Review of Studies Indexed in the Web of Science
by Dorijan Radočaj, Ivan Plaščak and Mladen Jurišić
Agriculture 2023, 13(7), 1417; https://doi.org/10.3390/agriculture13071417 - 17 Jul 2023
Cited by 16 | Viewed by 5033
Abstract
Global Navigation Satellite Systems (GNSS) in precision agriculture (PA) represent a cornerstone for field mapping, machinery guidance, and variable rate technology. However, recent improvements in GNSS components (GPS, GLONASS, Galileo, and BeiDou) and novel remote sensing and computer processing-based solutions in PA have [...] Read more.
Global Navigation Satellite Systems (GNSS) in precision agriculture (PA) represent a cornerstone for field mapping, machinery guidance, and variable rate technology. However, recent improvements in GNSS components (GPS, GLONASS, Galileo, and BeiDou) and novel remote sensing and computer processing-based solutions in PA have not been comprehensively analyzed in scientific reviews. Therefore, this study aims to explore novelties in GNSS components with an interest in PA based on the analysis of scientific papers indexed in the Web of Science Core Collection (WoSCC). The novel solutions in PA using GNSS were determined and ranked based on the citation topic micro criteria in the WoSCC. The most represented citation topics micro based on remote sensing were “NDVI”, “LiDAR”, “Harvesting robot”, and “Unmanned aerial vehicles” while the computer processing-based novelties included “Geostatistics”, “Precise point positioning”, “Simultaneous localization and mapping”, “Internet of things”, and “Deep learning”. Precise point positioning, simultaneous localization and mapping, and geostatistics were the topics that most directly relied on GNSS in 93.6%, 60.0%, and 44.7% of the studies indexed in the WoSCC, respectively. Meanwhile, harvesting robot research has grown rapidly in the past few years and includes several state-of-the-art sensors, which can be expected to improve further in the near future. Full article
(This article belongs to the Section Digital Agriculture)
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<p>The annual number of scientific papers indexed in WoSCC per GNSS component.</p>
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<p>A display of the total number of scientific papers with the topic of GNSS in agriculture and PA indexed in WoSCC per country.</p>
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<p>The most frequent citation topics micro for scientific papers with the topic of GNSS and PA indexed in WoSCC.</p>
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<p>The annual number of scientific papers indexed in WoSCC for the remote sensing-based citation topics micro for the topics of GNSS and PA.</p>
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<p>The annual number of scientific papers indexed in WoSCC for the computer processing-based citation topics micro for the topics of GNSS and PA.</p>
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18 pages, 15145 KiB  
Article
BDS/GPS/Galileo Precise Point Positioning Performance Analysis of Android Smartphones Based on Real-Time Stream Data
by Mengyuan Li, Guanwen Huang, Le Wang and Wei Xie
Remote Sens. 2023, 15(12), 2983; https://doi.org/10.3390/rs15122983 - 8 Jun 2023
Cited by 4 | Viewed by 1836
Abstract
Smartphones with the Android operating system can acquire Global Navigation Satellite System (GNSS) raw pseudorange and carrier phase observations, which can provide a new way for the general public to obtain precise position information. However, only postprocessing precise orbit and clock offset products [...] Read more.
Smartphones with the Android operating system can acquire Global Navigation Satellite System (GNSS) raw pseudorange and carrier phase observations, which can provide a new way for the general public to obtain precise position information. However, only postprocessing precise orbit and clock offset products in some older smart devices are applied in current studies. The performances of precise point positioning (PPP) with the smartphone using real-time products and newly smartphones are still unrevealed, which is more valuable for real-time applications. This study investigates the observation data quality and multi-GNSS real-time PPP performance using recent smartphones. Firstly, the observed carrier-to-noise density ratio (C/N0), number of satellites and position dilution of precision (PDOP) of GNSS observations are evaluated. The results demonstrate that the C/N0 received by Huawei Mate40 is better than that of the Huawei P40 for GPS, BDS, QZSS and Galileo systems, while the GLONASS is poorer, and the PDOP of the Huawei P40 is slightly better than that of Mate40. Additionally, a comprehensive analysis of real-time precise orbit and clock offset products performance is conducted. The experiment result expresses that the orbit and clock offset performance of GPS and Galileo is better than that of BDS-3 and GLONASS, and BDS-2 is the worst. Finally, single- and dual-frequency multi-GNSS combined PPP experiments using observations received from smartphones and real-time products are conducted; the results indicate that the real-time static PPP using a smartphone can achieve decimeter-level positioning accuracy, and kinematic PPP can achieve meter-level positioning accuracy after convergence. Full article
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<p>Flow chart of real-time PPP solution with smartphones.</p>
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<p>Experimental environment.</p>
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<p>Average C/N0 with elevation for the Huawei Mate40.</p>
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<p>Average C/N0 with elevation for the Huawei P40.</p>
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<p>Number of satellites for Huawei Mate40 and P40.</p>
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<p>PDOP for Huawei Mate40 and P40.</p>
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<p>Real-time orbit accuracy for GNSS.</p>
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<p>Real-time orbit accuracy for GNSS.</p>
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<p>Real-time clock offset off accuracy for GNSS.</p>
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<p>Real-time static PPP accuracy for Huawei Mate40, P40 and Novatel.</p>
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<p>Real-time kinematic PPP accuracy for Huawei Mate40, P40 and Novatel.</p>
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15 pages, 3724 KiB  
Article
Analysis of the Influence of Flood on the L4 Combination Observation of GPS and GLONASS Satellites
by Juntao Wu, Mingkun Su, Jun Gong, Lingsa Pan, Jiale Long and Fu Zheng
Atmosphere 2023, 14(6), 934; https://doi.org/10.3390/atmos14060934 - 26 May 2023
Cited by 1 | Viewed by 1095
Abstract
With global warming, extreme weather such as floods and waterlogging occurs more frequently and seriously in recent years. During the flood, the surrounding environment of the GNSS (Global Navigation Satellite System) station will change as the volume of water increases. Considering the multipath [...] Read more.
With global warming, extreme weather such as floods and waterlogging occurs more frequently and seriously in recent years. During the flood, the surrounding environment of the GNSS (Global Navigation Satellite System) station will change as the volume of water increases. Considering the multipath error is directly relevant to the observation environment, thus, the influence of flood on the L4 combination observation (a geometry-free ionosphere-free linear combination of carrier phase) which is related to the multipath error of GPS (Global Positioning System) and GLONASS satellites is investigated in depth. In addition, the ground track repetition periods of GPS and GLONASS satellites are analyzed in the sky plot to illustrate the rationality of chosen reference day. Based on the results of the satellite sky plot, one and eight days are adopted to demonstrate the influence of flood on L4 combination observation for GPS and GLONASS satellites, respectively. Real data sets collected at the ZHNZ GNSS observation station during the flood from DOY (Day of Year) 193 to DOY 204, 2021 are used. Experimental results show that the flood has a significant impact on the L4 combination observation of GPS and GLONASS satellites, and the fluctuation of L4 under flood performs much larger than that of without flood. For GPS satellites, the maximum RMS (root mean square) increase rate of L4 under flood is approximately 186.67% on the G31 satellite. Even for the minimum RMS increase rate, it can reach approximately 23.52%, which is the G02 satellite. Moreover, the average RMS increase rate of GPS and GLONASS satellites can reach approximately 109.53% and 43.65%, respectively. In addition, the influence of rainfall and hardware device are also investigated, which can further demonstrate that the fluctuation of L4 is mainly caused by the flood but not by the rainfall and hardware device elements. Thus, based on the above results, the influence of flood on L4 observation should be taken into account during the applications of L4 used, such as the retrieval of soil moisture and vegetation water content based on GNSS L4 combination observations Full article
(This article belongs to the Special Issue GNSS Remote Sensing in Atmosphere and Environment)
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<p>Simple multipath error model on the GNSS receiver.</p>
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<p>The geographical location of ZHNZ station, located in Zhengzhou City, Henan Province, China.</p>
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<p>Accumulative rainfall from DOY 193 to DOY 204, 2021 in Zhengzhou, China.</p>
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<p>(<b>a</b>) The blue and green dots are the GNSS station and the reservoir; (<b>b</b>) The arrow in the subplot indicates the reservoir management station; (<b>c</b>) The view of the reservoir at 8:00 a.m. on DOY 202, 2021; (<b>d</b>) The hourly rainfall on DOY 202, 2021.</p>
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<p>Ground track of G10 satellite on DOY 199 (red), DOY 201 (green), and DOY 202 (black), 2021 in the view of sky plot.</p>
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<p>Residuals of L4 on G10, G18, G23, and G32 satellites. The blue line denotes the L4 residuals collected on DOY 199 (without flood), and the red line denotes the L4 residuals collected on DOY 202 (with flood).</p>
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<p>Histogram of L4 combination observation residuals and relative frequency. The blue and red bars denote the L4 collected on DOY 199 and DOY 202, 2021. |−,25) denotes that the amplitude of L4 residuals is lower than 0.25 cm. |0.75,+) means that the amplitude of L4 residuals is larger than 0.75 cm. Symbol|and) denote the inclusion and non-inclusion, respectively.</p>
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<p>RMS increase rate of L4 residuals on DOY 202 (with the flood) of GPS satellites compared with DOY 199 (without flood), 2021.</p>
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<p>Residuals of L4 on DOY 198 and DOY 200, 2021 for G10 satellite. The blue and red lines denote the residuals of L4 on DOY 198 (no rainfall) and DOY 200 (with rainfall), respectively. The green line means the elevation angle.</p>
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<p>Residuals of L4 on DOY 199 and DOY 204, 2021 for G10 satellite. The blue and red lines denote the residuals of L4 on DOY 199 and DOY 204, respectively.</p>
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<p>Sky plot of the GLONASS R24 satellites on DOY 193, DOY 194, and DOY 201, DOY 202, 2021.</p>
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<p>Residuals of L4 on R03, R05, R18, and R24 satellites. The blue line denotes the residuals of L4 collected on DOY 194 (without flood).</p>
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<p>RMS increase rate of L4 residuals on DOY 202 compared with DOY 194 for GLONASS satellites.</p>
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