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Latest Results and Developments in GNSS Ionosphere Theory, Methods, Technologies, Applications and Future Challenges

A special issue of Remote Sensing (ISSN 2072-4292). This special issue belongs to the section "Atmospheric Remote Sensing".

Deadline for manuscript submissions: closed (30 June 2019) | Viewed by 37303

Special Issue Editors


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Guest Editor
Institute of Solar-Terrestrial Physics, German Aerospace Center (DLR), Kalkhorstweg 53, 17235 Neustrelitz, Germany
Interests: GNSS ionosphere sounding; space weather; space climate; satellite navigation; geodesy; remote sensing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The ionosphere is considered as one of the biggest error sources for space-based Global Navigation Satellite Systems (GNSS) positioning, navigation and timing applications. The use of multi-frequency and multi-GNSS observations from America’s GPS, Russia's GLONASS, China's BeiDou and EU's Galileo and regional systems such as Japan's QZSS and India's IRNSS enable precise remote sensing of the ionosphere and thus mitigation of ionospheric effects in numerous applications. This leads to unprecedented accuracy improvements in GNSS applications.

This Special Issue aims to provide a platform for addressing GNSS ionosphere theory, methods, technologies, applications and future challenges. The Special Issue is open to all scientists who may have the latest results and developments in GNSS ionosphere, including ionospheric delay estimating theory, algorithms, modelling and applications in engineering and Earth/space science, as well as combining multi-sensors observations. Manuscripts on new advances in GNSS ionosphere and space weather are also welcome.

Dr. M Mainul Hoque
Prof. Dr. Shuanggen Jin
Guest Editors

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Published Papers (7 papers)

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Research

18 pages, 6719 KiB  
Article
Satellite Formation Flight Simulation Using Multi-Constellation GNSS and Applications to Ionospheric Remote Sensing
by YuXiang Peng and Wayne A. Scales
Remote Sens. 2019, 11(23), 2851; https://doi.org/10.3390/rs11232851 - 30 Nov 2019
Cited by 8 | Viewed by 5153
Abstract
The Virginia Tech Formation Flying Testbed (VTFFTB) is a global navigation satellite system (GNSS)-based hardware-in-the-loop (HIL) simulation testbed for spacecraft formation flying with ionospheric remote sensing applications. Past applications considered only the Global Positioning System (GPS) constellation. The rapid GNSS modernization offers more [...] Read more.
The Virginia Tech Formation Flying Testbed (VTFFTB) is a global navigation satellite system (GNSS)-based hardware-in-the-loop (HIL) simulation testbed for spacecraft formation flying with ionospheric remote sensing applications. Past applications considered only the Global Positioning System (GPS) constellation. The rapid GNSS modernization offers more signals from other constellations, including the growing European system—Galileo. This study presents an upgrade of VTFFTB with the incorporation of Galileo and the associated enhanced capabilities. By simulating an ionospheric plasma bubble scenario with a pair of LEO satellites flying in formation, the GPS-based simulations are compared to multi-constellation GNSS simulations including the Galileo constellation. A comparison between multi-constellation (GPS and Galileo) and single-constellation (GPS) shows the absolute mean and standard deviation of vertical electron density measurement errors for a specific Equatorial Spread F (ESF) scenario are decreased by 32.83% and 46.12% with the additional Galileo constellation using the 13 July 2018 almanac. Another comparison based on a simulation using the 8 March 2019 almanac shows the mean and standard deviation of vertical electron density measurement errors were decreased further to 43.34% and 49.92% by combining both GPS and Galileo data. A sensitivity study shows that the Galileo electron density measurements are correlated with the vertical separation of the formation configuration. Lower C/N 0 level increases the measurement errors and scattering level of vertical electron density retrieval. Relative state estimation errors are decreased, as well by utilizing GPS L1 plus Galileo E1 carrier phase instead of GPS L1 only. Overall, superior performance on both remote sensing and relative navigation applications is observed by adding Galileo to the VTFFTB. Full article
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Overall configuration of the multi-constellation version of the Virginia Tech Formation Flying Testbed (VTFFTB).</p>
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<p>Total electron content (TEC) processing algorithm flowchart.</p>
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<p>Illustration of the Equatorial Spread F (ESF) scenario.</p>
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<p>Hardware-in-the-loop (HIL) simulation results of the ESF scenario: (<b>a</b>) radial distance history; (<b>b</b>) in-track distance history; (<b>c</b>) thrust history.</p>
Full article ">Figure 5
<p>Vertical <span class="html-italic">Ne</span> retrieved from Galileo PRN 30 TEC: (<b>a</b>) E1 and E5a TEC (<b>b</b>) E1 and E5b TEC.</p>
Full article ">Figure 6
<p>Vertical <span class="html-italic">Ne</span> retrieved from selected GPS (L1 and L2) plus Galileo (E1 and E5b) PRNs: (<b>a</b>) 13 July 2018 almanac (<b>b</b>) 8 March 2019 almanac.</p>
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<p>Wavenumber spectrum comparison between GPS-only and multi-constellation global navigation satellite system (GNSS).</p>
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<p>Vertical <span class="html-italic">Ne</span> retrieval from Galileo PRN 1 with different radial offsets: (<b>i</b>) 100-m; (<b>ii</b>) 1-km; (<b>iii</b>) 3-km.</p>
Full article ">Figure 9
<p>Wavenumber spectrum comparison between different vertical separations.</p>
Full article ">Figure 10
<p>Vertical <span class="html-italic">Ne</span> retrieval for PRN 1 using Galileo E1 and E5b TEC with different signal power offsets against <a href="#remotesensing-11-02851-f008" class="html-fig">Figure 8</a>ii (reference level): (<b>a</b>) −3 dB power offset (<b>b</b>) −8 dB power offset.</p>
Full article ">Figure 11
<p>Vertical distribution of 1-Hz S4 observed from different Galileo frequency bands on the chief’s receiver: (<b>a</b>) Galileo E1; (<b>b</b>) Galileo E5a; (<b>c</b>) Galileo E5b.</p>
Full article ">Figure 11 Cont.
<p>Vertical distribution of 1-Hz S4 observed from different Galileo frequency bands on the chief’s receiver: (<b>a</b>) Galileo E1; (<b>b</b>) Galileo E5a; (<b>c</b>) Galileo E5b.</p>
Full article ">Figure 12
<p>Horizontal view of 1-Hz S4 level observed from different Galileo frequency bands on the chief’s receiver: (<b>a</b>) Galileo E1; (<b>b</b>) Galileo E5a; (<b>c</b>) Galileo E5b.</p>
Full article ">Figure 12 Cont.
<p>Horizontal view of 1-Hz S4 level observed from different Galileo frequency bands on the chief’s receiver: (<b>a</b>) Galileo E1; (<b>b</b>) Galileo E5a; (<b>c</b>) Galileo E5b.</p>
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15 pages, 5956 KiB  
Article
An Enhanced Mapping Function with Ionospheric Varying Height
by Yan Xiang and Yang Gao
Remote Sens. 2019, 11(12), 1497; https://doi.org/10.3390/rs11121497 - 25 Jun 2019
Cited by 33 | Viewed by 5672
Abstract
Mapping function (MF) converts the line-of-sight slant total electron content (STEC) into the vertical total electron content (VTEC), and vice versa. In an MF, an essential parameter is the ionospheric effective height. However, the inhomogeneous ionosphere makes this height vary spatially and temporally, [...] Read more.
Mapping function (MF) converts the line-of-sight slant total electron content (STEC) into the vertical total electron content (VTEC), and vice versa. In an MF, an essential parameter is the ionospheric effective height. However, the inhomogeneous ionosphere makes this height vary spatially and temporally, meaning it is not a global constant. In the paper, we review several mapping functions and propose a mapping function that utilizes the ionospheric varying height (IVH). We investigate impacts of the IVH on mapping errors and on the ionospheric modeling, as well as on the satellite and receiver differential code biases (DCBs). Our analysis results indicate that the mapping errors using IVH are smaller than those from the fixed height of 450 km. The integral height achieves smaller mapping errors than using a fixed height of 450 km, an improvement of about 8% when compared with the fixed height of 450 km. And 35% smaller mapping errors were found using HmF2 at the lower latitude. Also, the effects of IVH on the satellite DCBs are about 0.1 ns, and larger impacts on the receiver DCBs at 1.0 ns. Full article
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Figure 1

Figure 1
<p>Scheme of the ionosphere single-layer model. The varying line around the fixed height denotes the varying height of the ionosphere. The <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">H</mi> <mrow> <mi>ion</mi> </mrow> </msub> </mrow> </semantics></math> is the assumed heights of the single-layer model (SLM). <math display="inline"><semantics> <mrow> <mi>El</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mi mathvariant="normal">z</mi> </semantics></math> are the elevation and zenithal distance or angle. The ionospheric pierce point (IPP) is the intersection of propagation path and the layer. <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="normal">z</mi> <mo>′</mo> </msup> </mrow> </semantics></math> is the angle distance at IPP.</p>
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<p>Mapping Functions (MFs) against elevation (<b>a</b>). The relative deviation with reference to SLM-450 (<b>b</b>).</p>
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<p>Ionospheric density profile on a station called PRDS (50.87° N, −114.29° W) at local time 14:00 from international reference ionosphere (IRI) 2016. The red square is the HmF2, and the blue is the integral height.</p>
Full article ">Figure 4
<p>Geographic distribution of the 14 processed stations in red circles were used to estimate satellite and receiver DCBs. Two regions of Western Canada and South America in blue circles were selected to evaluate mapping errors.</p>
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<p>K index on March 16 and 17, 2015 in Meanook (54.62°N, 246.65°E).</p>
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<p>On (<b>a</b>), station-specific and daily variation of the HmF2 (below) and the numerical integral height (upper) using the IRI 2016 model against the local time. The differences between the integral height and the HmF2 are on (<b>b</b>).</p>
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<p>The mapping errors against the lower elevation in the South America and Western Canada. <math display="inline"><semantics> <mi>N</mi> </semantics></math> is the total number of coinciding pierce points.</p>
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<p>Ionospheric observables using the uncombined precise point positioning (UPPP) model on March 16 (<b>a</b>) and 17 (<b>b</b>), 2015. The ionospheric observables from a satellite correspond to one color.</p>
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<p>The VTEC variation over station ALBH with fixed height 450 km, HmF2, and integral height (<b>left</b>), and the differences with reference to the fixed height 450 km (<b>right</b>).</p>
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<p>Satellite DCB estimated using the fixed height of 450 km compared with IGS products on 17 March 2015.</p>
Full article ">Figure 11
<p>Satellite and receiver DCB differences of HmF2, and numerical integral height compared with the fixed height 450 km on 16 (<b>a</b>,<b>c</b>) and 17 (<b>b</b>,<b>d</b>) March 2015. The blue is DCBs from HmF2 and the yellow is that from the integral height.</p>
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21 pages, 4383 KiB  
Article
A New Empirical Model of NmF2 Based on CHAMP, GRACE, and COSMIC Radio Occultation
by Zhendi Liu, Hanxian Fang, M. M. Hoque, Libin Weng, Shenggao Yang and Ze Gao
Remote Sens. 2019, 11(11), 1386; https://doi.org/10.3390/rs11111386 - 11 Jun 2019
Cited by 9 | Viewed by 4753
Abstract
To facilitate F2-layer peak density (NmF2) modeling, a nonlinear polynomial model approach based on global NmF2 observational data from ionospheric radio occultation (IRO) measurements onboard the CHAMP, GRACE, and COSMIC satellites, is presented in this paper. We divided the globe into 63 slices [...] Read more.
To facilitate F2-layer peak density (NmF2) modeling, a nonlinear polynomial model approach based on global NmF2 observational data from ionospheric radio occultation (IRO) measurements onboard the CHAMP, GRACE, and COSMIC satellites, is presented in this paper. We divided the globe into 63 slices from 80°S to 80°N according to geomagnetic latitude. A Nonlinear Polynomial Peak Density Model (NPPDM) was constructed by a multivariable least squares fitting to NmF2 measurements in each latitude slice and the dependencies of NmF2 on solar activity, geographical longitude, universal time, and day of year were described. The model was designed for quiet and moderate geomagnetic conditions (Ap ≤ 32). Using independent radio occultation data, quantitative analysis was made. The correlation coefficients between NPPDM predictions and IRO data were 0.91 in 2002 and 0.82 in 2005. The results show that NPPDM performs better than IRI2016 and Neustrelitz Peak Density Model (NPDM) under low solar activity, while it undergoes performance degradation under high solar activity. Using data from twelve ionosonde stations, the accuracy of NPPDM was found to be better than that of NPDM and comparable to that of IRI2016. Additionally, NPPDM can well simulate the variations and distributions of NmF2 and describe some ionospheric features, including the equatorial ionization anomaly, the mid-latitude trough, and the wavenumber-four longitudinal structure. Full article
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Figure 1

Figure 1
<p>Data distributions with F10.7, day of year, geographical latitude, geographical longitude, magnetic latitude, and universal time.</p>
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<p>Histogram of relative deviation.</p>
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<p>Distributions of RMSE with geographical longitude, magnetic latitude, universal time, local time, and day of year.</p>
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<p>Data density of NPPDM (left), IRI2016 (middle), and NPDM (right) versus IRO NmF2 in 2005.</p>
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<p>Same as <a href="#remotesensing-11-01386-f004" class="html-fig">Figure 4</a>, but for 2002.</p>
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<p>Global map of used ionosonde. stations.</p>
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<p>Variations of hourly mean of NPPDM (red solid lines), IRI2016 (black dotted lines) and NPDM (red dotted lines) as a function of UT in comparisons with ionosonde observation (dots) under low solar activity. C1, C2, and C3 are the analog deviations between NPPDM, IRI2016, and NPDM and ionosonde observations, respectively.</p>
Full article ">Figure 8
<p>Same as <a href="#remotesensing-11-01386-f007" class="html-fig">Figure 7</a>, but for high solar activity.</p>
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<p>Global distribution of NPDM NmF2 (cm<sup>−3</sup>) at the September equinox under low (F10.7 = 80 sfu) solar activity.</p>
Full article ">Figure 10
<p>Same as <a href="#remotesensing-11-01386-f009" class="html-fig">Figure 9</a>, but for high (F10.7 = 150 sfu) solar activity.</p>
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<p>Global distributions of NPPDM NmF2 (cm<sup>−3</sup>) at the September equinox under middle (F10.7 = 120 sfu) solar activity.</p>
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<p>Longitudinal mean variations of NPPDM as functions of latitude and local time under both low solar activity (upper panel) and high solar activity (lower panel) (cm<sup>−3</sup>).</p>
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<p>Same as <a href="#remotesensing-11-01386-f009" class="html-fig">Figure 9</a>, but for NPPDM under low solar activity.</p>
Full article ">Figure 14
<p>Same as <a href="#remotesensing-11-01386-f010" class="html-fig">Figure 10</a>, but for NPPDM under high solar activity.</p>
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<p>Variations of hourly mean of NPPDM (red solid lines), IRI2016 (black dotted lines) and NPDM (red dotted lines) as a function of UT in comparisons with ionosonde observation (dots) during 20-21 November 2003.</p>
Full article ">
15 pages, 5366 KiB  
Article
Ionospheric Rayleigh Wave Disturbances Following the 2018 Alaska Earthquake from GPS Observations
by Yuhan Liu and Shuanggen Jin
Remote Sens. 2019, 11(8), 901; https://doi.org/10.3390/rs11080901 - 13 Apr 2019
Cited by 32 | Viewed by 4090
Abstract
Big earthquakes often excite the acoustic resonance between the earth’s surface and the lower atmosphere. The perturbations can propagate upward into the ionosphere and trigger ionospheric anomalies detected by dual-frequency GPS observations, but coseismic ionospheric disturbance (CID) directivity and mechanism are not clear. [...] Read more.
Big earthquakes often excite the acoustic resonance between the earth’s surface and the lower atmosphere. The perturbations can propagate upward into the ionosphere and trigger ionospheric anomalies detected by dual-frequency GPS observations, but coseismic ionospheric disturbance (CID) directivity and mechanism are not clear. In this paper, the ionospheric response to the Mw = 7.9 Alaska earthquake on 23 January 2018 is investigated from about 100 continuous GPS stations near the epicenter. The fourth-order zero-phase Butterworth band-pass filter with cutoffs of 2.2 mHz and 8 mHz is applied to obtain the ionospheric disturbances. Results show that the CIDs with an amplitude of up to 0.06 total electron content units (TECU) are detected about 10 min after the Alaska earthquake. The CIDs are as a result of the upward propagation acoustic waves triggered by the Rayleigh wave. The propagation velocities of TEC disturbances are around 2.6 km/s, which agree well with the wave propagation speed of 2.7 km/s detected by the bottom pressure records. Furthermore, the ionospheric disturbances following the 2018 Mw = 7.9 Alaska earthquake are inhomogeneous and directional which is rarely discussed. The magnitude of ionospheric disturbances in the western part of the epicenter is more obvious than in the eastern part. This phenomenon also corresponds to the data obtained from the seismographs and bottom pressure records (BPRs) at the eastern and western side of the epicenter. Full article
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>The distribution of GPS stations, seismographs and NDBC (National Data Buoy Center) stations around the epicenter. The red pentagram represents the epicenter. The square points represent GPS stations, the red triangles represent seismographs stations and green triangles represent NDBC stations. The sub-picture shows the finite fault of the earthquake (<a href="https://earthquake.usgs.gov/earthquakes" target="_blank">https://earthquake.usgs.gov/earthquakes</a>). Strike-slip-faulting events of the size of the earthquake are typically about 230 × 30 km.</p>
Full article ">Figure 2
<p>The filtered TEC (total electron content) observed by station AV26 and PRN 05 during the Alaska earthquake on 23 January 2018. In (<b>a</b>), the blue line is the SIPs (sub-ionospheric points) track. The star and the point show the location of the epicenter and AV26 station. (<b>b</b>) shows the elevation angle of the satellite (the blue line) and the distance between the SIPs and the epicenter (the red line). (<b>c</b>) is the TEC obtained through different cutoff frequencies.</p>
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<p>The geomagnetic index Dst, Kp and solar activity index F10.7 for the week around the Alaska earthquake on 23 January 2018. The dotted lines indicate the time of the earthquake.</p>
Full article ">Figure 4
<p>The filtered TEC variations from the 9:31 to 9:55 UTC following the Alaska earthquake. The red star indicates the location of the epicenter of the Alaska earthquake and the dots represent the position of the sub-ionospheric points (SIPs). The color of the dots indicates the amplitude of the filtered TEC disturbances.</p>
Full article ">Figure 5
<p>The ionospheric responses to the Alaska earthquake. The left is the SIP tracks between the PRN05 and the stations, and the right is the travel time diagram of filtered TEC series. The dashed line indicates the time of the earthquake eruption, and the diagonal line is used to fit the speed of the TEC disturbances. Different colors show the magnitude of TEC interference.</p>
Full article ">Figure 6
<p>The diagram of disturbances propagation.</p>
Full article ">Figure 7
<p>The sea level change in the vicinity of the epicenter recorded by Bottom Pressure Records (BPRs). The location of the site is shown in (<b>a</b>,<b>c</b>). The sub-graphs in the (<b>d</b>) are the enlarged views of station 46419 and 46407.</p>
Full article ">Figure 8
<p>The correlation between filtered TEC and DART (Deep-ocean Assessment and Reporting of Tsunamis) buoy data. (<b>a</b>) shows the location of DART station 46403 and the satellite puncture. (<b>b</b>) shows the observational geometry between the station AV02 and the GPS satellite. The hollow circles in (<b>a</b>,<b>b</b>) show the moment when the earthquake struck. (<b>c</b>) shows the filtered TEC series of station AV02 in black and the copy of the filtered TEC series shifted 6.7 min advance in orange. (<b>d</b>) shows the vertical displacement series of station 46403. (<b>e</b>) shows the correlation between the filtered TEC series shifted 6.7 min forward and vertical displacement series.</p>
Full article ">Figure 9
<p>The ionospheric electron density from COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate) radio occultation data. (<b>a</b>) shows the ground projections of COSMIC radio occultation observations. (<b>b</b>) shows the electron density profiles observed with COSMIC satellites. (<b>c</b>) is the detrended COSMIC electron density perturbations. The blue trajectory represents the observations of the Alaska earthquake, and the red and yellow curves represent the result from observations of COSMIC the day before the earthquake and the day after the earthquake.</p>
Full article ">Figure 10
<p>The results of the combination of COSMIC radio occultation and observations of ground-based GPS stations. (<b>a</b>) shows the puncture point trajectory of several GPS stations and the ground projection of radio occultation observations. (<b>b</b>) combines the normalized filtered TEC series with the detrended COSMIC electron density perturbation and the diagonal line is used to fit the speed of the TEC disturbances.</p>
Full article ">Figure 11
<p>The vertical ground motions from the observations of 91 broadband seismographers. The location of the stations in the east and west directions of epicenter are shown in (<b>a</b>,<b>c</b>). The vertical components in the east and west directions are shown in (<b>b</b>,<b>d</b>). The sub-graphs in the (<b>b</b>,<b>d</b>) show the enlarged views of two stations at 650 km and 670 km from epicenter respectively and the location of two stations are shown in the (<b>a</b>,<b>c</b>) with red triangles.</p>
Full article ">Figure 12
<p>The disturbance series extracted from the observations and the spectrum distribution obtained by Fourier transform. (<b>a</b>,<b>c</b>,<b>e</b>) show the data from the GPS, DART and seismograph respectively. (<b>b</b>,<b>d</b>,<b>f</b>) show the spectrum distribution of corresponding observations.</p>
Full article ">
19 pages, 24306 KiB  
Article
A New Global Total Electron Content Empirical Model
by Jiandi Feng, Baomin Han, Zhenzhen Zhao and Zhengtao Wang
Remote Sens. 2019, 11(6), 706; https://doi.org/10.3390/rs11060706 - 24 Mar 2019
Cited by 27 | Viewed by 4849
Abstract
Research on total electron content (TEC) empirical models is one of the important topics in the field of space weather services. Global TEC empirical models based on Global Ionospheric Maps (GIMs) TEC data released by the International GNSS Service (IGS) have developed rapidly [...] Read more.
Research on total electron content (TEC) empirical models is one of the important topics in the field of space weather services. Global TEC empirical models based on Global Ionospheric Maps (GIMs) TEC data released by the International GNSS Service (IGS) have developed rapidly in recent years. However, the accuracy of such global empirical models has a crucial restriction arising from the non-uniform accuracy of IGS TEC data in the global scope. Specifically, IGS TEC data accuracy is higher on land and lower over the ocean due to the lack of stations in the latter. Using uneven precision GIMs TEC data as a whole for model fitting is unreasonable. Aiming at the limitation of global ionospheric TEC modelling, this paper proposes a new global ionospheric TEC empirical model named the TECM-GRID model. The model consists of 5183 sections, corresponding to 5183 grid points (longitude 5°, latitude 2.5°) of GIM. Two kinds of single point empirical TEC models, SSM-T1 and SSM-T2, are used for TECM-GRID. According to the locations of grid points, the SSM-T2 model is selected as the sub-model in the Mid-Latitude Summer Night Anomaly (MSNA) region, and SSM-T1 is selected as the sub-model in other regions. The fitting ability of the TECM-GRID model for modelling data was tested in accordance with root mean square (RMS) and relative RMS values. Then, the TECM-GRID model was validated and compared with the NTCM-GL model and Center for Orbit Determination in Europe (CODE) GIMs at time points other than modelling time. Results show that TECM-GRID can effectively describe the Equatorial Ionization Anomaly (EIA) and the MSNA phenomena of the ionosphere, which puts it in good agreement with CODE GIMs and means that it has better prediction ability than the NTCM-GL model. Full article
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Graphical abstract

Graphical abstract
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<p>Geographic latitude and longitude range of the SSM-T1 and SSM-T2 for the TECM-GRID.</p>
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<p>Model Residual Distribution Histogram of TECM-GRID and sub-models (SSM-T1 and SSM-T2).</p>
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<p>RMS value of model residual for TECM-GRID. (<span class="html-italic">Notes.</span> The modified dip latitude is marked by a white line, henceforth.)</p>
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<p>Relative RMS values of model residuals for TECM-GRID.</p>
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<p>Comparison of CODE GIMs and TECM-GRID models (2004).</p>
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<p>Comparison of CODE GIMs and TECM-GRID models (2004).</p>
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<p>Comparison of CODE GIMs and TECM-GRID models (2008).</p>
Full article ">Figure 6 Cont.
<p>Comparison of CODE GIMs and TECM-GRID models (2008).</p>
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<p>Comparison of CODE GIMs and TECM-GRID models (2012).</p>
Full article ">Figure 7 Cont.
<p>Comparison of CODE GIMs and TECM-GRID models (2012).</p>
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<p>Comparison of TECM-GRID and NTCM-GL with the CODE GIM (1 February 2016).</p>
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<p>Comparison of TECM-GRID and NTCM-GL with the CODE GIM (1 April 2016).</p>
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<p>Comparison of TECM-GRID and NTCM-GL with the CODE GIM (1 June 2016).</p>
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<p>Comparison of TECM-GRID and NTCM-GL with the CODE GIM (1 August 2016).</p>
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<p>Comparison of TECM-GRID and NTCM-GL with the CODE GIM (1 October 2016).</p>
Full article ">Figure 12 Cont.
<p>Comparison of TECM-GRID and NTCM-GL with the CODE GIM (1 October 2016).</p>
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<p>Comparison of TECM-GRID and NTCM-GL with the CODE GIM (1 December 2016).</p>
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20 pages, 2058 KiB  
Article
Cycle Slip Detection during High Ionospheric Activities Based on Combined Triple-Frequency GNSS Signals
by Dongsheng Zhao, Craig M. Hancock, Gethin Wyn Roberts and Shuanggen Jin
Remote Sens. 2019, 11(3), 250; https://doi.org/10.3390/rs11030250 - 26 Jan 2019
Cited by 15 | Viewed by 4840
Abstract
The current cycle slip detection methods of Global Navigation Satellite System (GNSS) were mostly proposed on the basis of assuming the ionospheric delay varying smoothly over time. However, these methods can be invalid during active ionospheric periods, e.g., high Kp index value and [...] Read more.
The current cycle slip detection methods of Global Navigation Satellite System (GNSS) were mostly proposed on the basis of assuming the ionospheric delay varying smoothly over time. However, these methods can be invalid during active ionospheric periods, e.g., high Kp index value and scintillations, due to the significant increase of the ionospheric delay. In order to detect cycle slips during high ionospheric activities successfully, this paper proposes a method based on two modified Hatch–Melbourne–Wübbena combinations. The measurement noise in the Hatch–Melbourne–Wübbena combination is minimized by employing the optimally selected combined signals, while the ionospheric delay is detrended using a smoothing technique. The difference between the time-differenced ambiguity of the combined signal and this estimated ionospheric trend is adopted as the detection value, which can be free from ionospheric effect and hold the high precision of the combined signal. Five threshold determination methods are proposed and compared to decide the cycle slip from the magnitude aspect. This proposed method is tested with triple-frequency Global Navigation Satellite System observations collected under high ionospheric activities. Results show that the proposed method can correctly detect and fix cycle slips under disturbed ionosphere. Full article
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<p>Process of eliminating the outliers in the first-order time-differenced ambiguities.</p>
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<p>The changes of the detection value given by the two combined signals proposed in Zhao et al. [<a href="#B13-remotesensing-11-00250" class="html-bibr">13</a>] with the increase in the strength of ionospheric activities. The <b>top</b> panel shows the elevation angle and the S4 value of satellite PRN 25 from GPS, while the <b>middle</b> and <b>bottom</b> panels show the detection value given by the combined signal (1, −6, 5) and (4, 0, −5), respectively.</p>
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<p>Performance of the proposed method for eliminating outliers. The epochs where the outliers are eliminated are highlighted with gray background.</p>
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<p>Performance of the proposed smoothing technique. The <b>top</b> panel shows ionospheric trend given by LOWESS and RLOWESS, while the <b>bottom</b> panel shows the residuals given by RLOWESS.</p>
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<p>Detection value of the combined signal (−3, 1, 3) and the thresholds determined by the sample variation method (<b>A</b>), GARCH (<b>B</b>), GARCH with the partly fixed method (<b>C</b>), local backward method (<b>D</b>) and local backward with the partly fixed method (<b>E</b>).</p>
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<p>Kp index of 8–11 September 2017.</p>
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<p>PPP coordinate errors using the dataset with artificial cycle slips (green dots) and the dataset where the cycle slips are corrected with the proposed method (red dots).</p>
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19 pages, 3157 KiB  
Article
Evaluation of Ionospheric Delay Effects on Multi-GNSS Positioning Performance
by Ke Su, Shuanggen Jin and M. M. Hoque
Remote Sens. 2019, 11(2), 171; https://doi.org/10.3390/rs11020171 - 17 Jan 2019
Cited by 69 | Viewed by 6876
Abstract
Ionospheric delay is a significant error source in multi-GNSS positioning. We present different processing strategies to fully exploit the ionospheric delay effects on multi-frequency and multi-GNSS positioning performance, including standard point positioning (SPP) and precise point positioning (PPP) scenarios. Datasets collected from 10 [...] Read more.
Ionospheric delay is a significant error source in multi-GNSS positioning. We present different processing strategies to fully exploit the ionospheric delay effects on multi-frequency and multi-GNSS positioning performance, including standard point positioning (SPP) and precise point positioning (PPP) scenarios. Datasets collected from 10 stations over thirty consecutive days provided by multi-GNSS experiment (MGEX) stations were used for single-frequency SPP/PPP and dual-frequency PPP tests with quad-constellation signals. The experimental results show that for single-frequency SPP, the Global Ionosphere Maps (GIMs) correction achieves the best accuracy, and the accuracy of the Neustrelitz TEC model (NTCM) solution is better than that of the broadcast ionospheric model (BIM) in the E and U components. Eliminating ionospheric parameters by observation combination is equivalent to estimating the parameters in PPP. Compared with the single-frequency uncombined (UC) approach, the average convergence time of PPP with the external ionospheric models is reduced. The improvement in BIM-, NTCM- and GIM-constrained quad-constellation L2 single-frequency PPP was 15.2%, 24.8% and 28.6%, respectively. The improvement in convergence time of dual-frequency PPP with ionospheric models was different for different constellations and the GLONASS-only solution showed the least improvement. The improvement in the convergence time of BIM-, NTCM- and GIM-constrained quad-constellation L1/L2 dual-frequency PPP was 5.2%, 6.2% and 8.5%, respectively, compared with the UC solution. The positioning accuracy of PPP is slightly better with the ionosphere constraint and the performance of the GIM-constrained PPP is the best. The combination of multi-GNSS can effectively improve the positioning performance. Full article
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Graphical abstract

Graphical abstract
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<p>Geographical distribution of the selective MGEX stations.</p>
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<p>F10.7 values and geomagnetic Kp index on 1–30 September 2018.</p>
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<p>Positioning error scatters of b1 or b2 SPP with different schemes in nine different constellation combinations at station CUT0 (DOY 244/2018, Kp ≈ 0.92) (<b>a</b>) Horizontal error of b1 SPP (<b>b</b>) Vertical error of b1 SPP (<b>c</b>) Horizontal error of b2 SPP (<b>d</b>) Vertical error of b2 SPP. Horizontal error: the horizontal and vertical axes represent the error of the N and E component, respectively (unit: m). Vertical error: the horizontal and vertical axes represent the universal time (unit: hour) and the error of the U component (unit: m), respectively.</p>
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<p>Positioning error scatters of b1 or b2 SPP with different schemes in nine different constellation combinations at station CUT0 (DOY 244/2018, Kp ≈ 0.92) (<b>a</b>) Horizontal error of b1 SPP (<b>b</b>) Vertical error of b1 SPP (<b>c</b>) Horizontal error of b2 SPP (<b>d</b>) Vertical error of b2 SPP. Horizontal error: the horizontal and vertical axes represent the error of the N and E component, respectively (unit: m). Vertical error: the horizontal and vertical axes represent the universal time (unit: hour) and the error of the U component (unit: m), respectively.</p>
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<p>Comparison of positioning error of b2 single-frequency PPP with different schemes for GPS, GLONASS and GPS/Beidou/GLONASS/Galileo solutions at station MRO1 (DOY 245/2018, Kp ≈ 1.17). The corresponding satellite numbers and PDOP values are also shown.</p>
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<p>Average convergence time for GPS-only, Beidou-only, GLONASS-only, Galileo-only, GPS/Beidou, GPS/GLONASS, GPS/Galileo, GPS/Beidou/GLONASS and GPS/Beidou/GLONASS/Galileo single-frequency PPP collected at ten stations over thirty days.</p>
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<p>Comparison of positioning error of b1/b2 dual-frequency PPP with different schemes for GPS, GLONASS and GPS/Beidou/GLONASS/Galileo solutions at station SEYG (DOY 246/2018, Kp ≈ 1.92). The corresponding satellite numbers and PDOP values are also shown.</p>
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<p>Time series of the estimated receiver DCB at station SEYG (DOY 246/2018).</p>
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<p>Average convergence time for GPS-only, Beidou-only, GLONASS-only, Galileo-only, GPS/Beidou, GPS/GLONASS, GPS/Galileo, GPS/Beidou/GLONASS and GPS/Beidou/GLONASS/Galileo dual-frequency PPP collected at ten stations over thirty days.</p>
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