[go: up one dir, main page]
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
8.3
4.2
Journals
Remote Sensing
Special Issues
High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II
remotesensing-logo
Submit to Remote Sensing Review for Remote Sensing Propose a Special Issue

Journal Menu

► Journal Menu

Journal Browser

► Journal Browser
share announcement

High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II

A special issue of Remote Sensing (ISSN 2072-4292). This special issue belongs to the section "Satellite Missions for Earth and Planetary Exploration".

Deadline for manuscript submissions: closed (1 March 2022) | Viewed by 50825

Special Issue Editors

Prof. Dr. Xingxing Li

E-Mail Website
Guest Editor
School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, China
Interests: GNSS precise positioning and orbit determination; real-time; high-precision GNSS
Prof. Dr. Jacek Paziewski

E-Mail Website
Guest Editor
The Faculty of Geoengineering, Department of Geodesy, University of Warmia and Mazury in Olsztyn (UWM), Oczapowskiego 1, 10-719 Olsztyn, Poland
Interests: GNSS; precise positioning; high-rate GNSS data processing; integration of multi-constellation signals; modelling of the ionospheric delay with GNSS; displacement and deformation monitoring; structural monitoring with GNSS; smartphone GNSS positioning
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Mattia Crespi

E-Mail Website
Guest Editor
Geodesy and Geomatics Division-DICEA, Sapienza University of Rome, Rome, Italy
Interests: remote sensing big data analysis; optical and SAR satellite remote sensing; photogrammetry and stereo-SAR; 3D terrain and object modeling; GNSS positioning and monitoring; GNSS seismology; GNSS meteorology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over the last few years, high-precision global navigation satellite systems (GNSS) have been applied to support numerous applications in geosciences. There are currently two fully operational constellations, and two more are in the implementation stage. The new Galileo and BDS systems already provide usable signals, and both GPS and GLONASS are currently undergoing significant modernization, adding more capacity, more signals, better accuracy, greater interoperability, etc. Meanwhile, significant technological developments are being provided by GNSS equipment (even at low cost in some cases), which is able to collect measurements at much higher rates (up to 100 Hz), thus presenting new possibilities. Therefore, on the one hand, the new developments in GNSS are facilitating a broad range of new applications for solid and fluid Earth investigations, both in post-processing and in real time; on the other, this is resulting in new problems and challenges in data processing warranting further GNSS research. Algorithmic advancements are needed to address the opportunities and challenges in enhancing the accuracy, availability, interoperability, and integrity of high-precision GNSS applications.

This collection is a continuation of the first edition Special Issue, “High-Precision GNSS: Methods, Open Problems and Geoscience Applications”, that was published in Remote Sensing. The goal of this Special Issue is to provide a platform for discussing new developments in high-precision GNSS algorithms and applications in geosciences; in this respect, contributions from other branches of geosciences (geodynamics, seismology, tsunamis, ionosphere, troposphere, etc.) are very welcome.

Prof. Dr. Xingxing Li
Dr. Jacek Paziewski
Prof. Dr. Mattia Crespi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Remote Sensing is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • GNSS
  • GPS
  • GLONASS
  • Galileo
  • BDS
  • Precise point positioning (PPP)
  • Real time kinematic (RTK)
  • Orbit determination
  • Ionosphere sounding
  • Troposphere sounding
  • Climate change monitoring with GNSS
  • Geoscience applications
  • High-rate positioning
  • GNSS for geodynamics
  • Low-cost GNSS receivers
  • Smartphone GNSS positioning and applications
  • GNSS contribution to geodynamics

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (15 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

Jump to: Other

21 pages, 5860 KiB  
Article
Analysis of Different Weighting Functions of Observations for GPS and Galileo Precise Point Positioning Performance
by Damian Kiliszek, Krzysztof Kroszczyński and Andrzej Araszkiewicz
Remote Sens. 2022, 14(9), 2223; https://doi.org/10.3390/rs14092223 - 6 May 2022
Cited by 6 | Viewed by 3057
Abstract
This research presents the analysis of using different weighting functions for the GPS and Galileo observations in Precise Point Positioning (PPP) performance for globally located stations for one week in 2021. Eight different weighting functions of observations dependent on the elevation angle have [...] Read more.
This research presents the analysis of using different weighting functions for the GPS and Galileo observations in Precise Point Positioning (PPP) performance for globally located stations for one week in 2021. Eight different weighting functions of observations dependent on the elevation angle have been selected. It was shown that the use of different weighting functions has no impact on the horizontal component but has a visible impact on the vertical component, the tropospheric delay and the convergence time. Depending on the solutions, i.e., GPS-only, Galileo-only or GPS+Galileo, various weighting functions turned out to the best. The obtained results confirm that the Galileo solution has comparable accuracy to the GPS solution. Also, with the Galileo solution, the best results were obtained for functions with a smaller dependence on the elevation angle than for GPS, since Galileo observations at lower elevation angles have better performance than GPS observations. Finally, a new weighting approach was proposed, using two different weighting functions from the best GPS-only and Galileo-only for GPS+Galileo solution. This approach improves the results by 5% for convergence time and 30% for the troposphere delay when compared to using the same function. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Location of test stations.</p> Full article ">Figure 2
<p>Signal to noise ratio (SNR) for the E1 and E5a observations for the Galileo and L1 and L2 observations for the GPS for the MAS100ESP station for the 39 DoY with function of elevation angle.</p> Full article ">Figure 3
<p>Multipath code combination (MP) for the E1 and E5a observations for the Galileo and L1 and L2 observations for the GPS for the MAS100ESP station for the 39 DoY with function of elevation angle.</p> Full article ">Figure 4
<p>Time series of U component, 2D and 3D errors for the first four hours for the weighting functions. Functions 1–4 for the MAS100ESP station for the 39 DoY for all solutions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution.</p> Full article ">Figure 5
<p>Time series of U component, 2D and 3D errors for the first four hours for the weighting functions. Functions 5–8 for the MAS100ESP station for the 39 DoY for all solutions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution.</p> Full article ">Figure 6
<p>Time series of ZPD differences between the estimated value from PPP and calculated by the IGS for the MAS100ESP station for the 39 DoY for all solutions and weighting functions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution.</p> Full article ">Figure 7
<p>Time series of estimated ISB for GE (<b>left</b>) and GE1 (<b>right</b>) for the MAS100ESP station for the 39 DoY for all weighting functions.</p> Full article ">Figure 8
<p>Mean accuracy with standard deviation from all stations and all periods for all analyzed weighting functions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution.</p> Full article ">Figure 9
<p>Mean convergence time with standard deviation from all stations and all periods for all analyzed weighting functions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution.</p> Full article ">Figure 10
<p>Mean accuracy of the ZPD with standard deviation from all stations and all periods for all analyzed weighting functions. Blue—E solution, orange—G solution, red—GE solution, green—GE1 solution.</p> Full article ">Figure 11
<p>Mean accuracy 3D (<b>left</b>), convergence time (<b>center</b>) and ZPD (<b>right</b>) from all stations and all periods for the proposed weighting method—GE_new (purple), GE (red) and GE1 (green) for Function 2.</p> Full article ">Figure 12
<p>Standard deviations of carrier-phase of ionosphere-free linear combination with elevation angle for analyzed weighting functions. Bottom plot for Function_6 and Function_8. Top plot for the rest of the functions.</p> Full article ">Figure A1
<p>Analyzed the impact of different reference coordinates for obtained accuracy. Blue—weekly reference coordinates from E solution, orange—weekly reference coordinates from G solution, red—weekly reference coordinates from GE solution and green—daily reference coordinates from AC CNES/CLS.</p> Full article ">
19 pages, 5648 KiB  
Article
Improving the Orbits of the BDS-2 IGSO and MEO Satellites with Compensating Thermal Radiation Pressure Parameters
by Chen Wang, Jing Guo, Qile Zhao and Maorong Ge
Remote Sens. 2022, 14(3), 641; https://doi.org/10.3390/rs14030641 - 28 Jan 2022
Cited by 8 | Viewed by 3169
Abstract
The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou [...] Read more.
The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou Navigation Satellite System (BDS-2), for which apparent deficiencies of non-conservative models are identified and evidenced in the Satellite Laser Ranging (SLR) residuals. The orbit errors derived from the empirical 5-parameter Extended CODE Orbit Model (ECOM) as well as a semi-analytical adjustable box-wing model show prominent dependency on the Sun elongation angle, even in the yaw-steering attitude mode. Hence, a periodic acceleration in the normal direction of the +X surface, presumably generated by the mismodeled thermal radiation pressure, is introduced. The SLR validations reveal that the Sun elongation angle-dependent systematic errors were significantly reduced, and the orbit accuracy was improved by 10–30% to approximately 4.5 cm and 3.0 cm for the BDS-2 IGSO and MEO satellites, respectively. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Figure 1

Figure 1
<p>SLR residuals of C13 with distribution on the Sun elongation angle (<math display="inline"><semantics> <mo>ϵ</mo> </semantics></math>) for CODE (<b>top</b>), GFZ (<b>middle</b>), and WHU (<b>bottom</b>).</p> Full article ">Figure 2
<p>Distributions of the approximately 90 ground stations used in this study. Red circles indicate IGS MGEX stations. Blue triangles represent iGMAS stations.</p> Full article ">Figure 3
<p>Distribution of the SLR residual with respect to the Sun elongation angle (<math display="inline"><semantics> <mo>ϵ</mo> </semantics></math>) for C08 (<b>top</b>) and C13 (<b>bottom</b>) determined with the ABW model.</p> Full article ">Figure 4
<p>SLR residuals distributed with respect to β and μ for the C13 ABW orbit solution.</p> Full article ">Figure 5
<p>Estimated parameters of the ECOM SRP model for C13 orbit solutions (The areas shaded in grey indicate eclipse seasons).</p> Full article ">Figure 6
<p>Distribution of the SLR residual with respect to the Sun elongation angle (<math display="inline"><semantics> <mo>ϵ</mo> </semantics></math>) for C13 orbits determined with the ABW model plus a constant acceleration along the X direction.</p> Full article ">Figure 7
<p>Simulated TRR-induced accelerations (unit: nm/s<sup>2</sup>) along the D direction with distribution along the Sun elevation angle β and orbital angle μ for C13.</p> Full article ">Figure 8
<p>Correlations between the satellite state, ABW as well as the thermal scale factor <math display="inline"><semantics> <mi>k</mi> </semantics></math> parameters of C13 on DOY 200, 2018 (β angle of approximately 20 deg).</p> Full article ">Figure 9
<p>Daily estimates of the thermal scale factors for C13 with distribution on the β angle. (The grey represents the eclipse season).</p> Full article ">Figure 10
<p>The histograms of the SLR residuals of the four solutions for the four BDS-2 IGSO and MEO satellites tracked by ILRS. All values are in cm.</p> Full article ">Figure 11
<p>Distribution of the SLR residual for the ECOM + TRR orbit solution with respect to the Sun elongation angle for the BDS-2 C08, C10, C11, and C13 satellites.</p> Full article ">Figure 12
<p>The accuracy of 24-h predicted orbits averaged in the BDS-2 IGSO and MEO groups from the four solutions.</p> Full article ">
17 pages, 6730 KiB  
Article
Performance Assessment of BDS-2/BDS-3/GPS/Galileo Attitude Determination Based on the Single-Differenced Model with Common-Clock Receivers
by Mingkui Wu, Shuai Luo, Wang Wang and Wanke Liu
Remote Sens. 2021, 13(23), 4845; https://doi.org/10.3390/rs13234845 - 29 Nov 2021
Cited by 7 | Viewed by 2371
Abstract
Global navigation satellite system (GNSS)-based attitude determination has been widely applied in a variety of fields due to its high precision, no error accumulation, low power consumption, and low cost. Recently, the emergence of common-clock receivers and construction of GNSS systems have brought [...] Read more.
Global navigation satellite system (GNSS)-based attitude determination has been widely applied in a variety of fields due to its high precision, no error accumulation, low power consumption, and low cost. Recently, the emergence of common-clock receivers and construction of GNSS systems have brought new opportunities for high-precision GNSS-based attitude determination. In this contribution, we focus on evaluating the performance of the BeiDou regional navigation satellite system (BDS-2)/BeiDou global navigation satellite system (BDS-3)/Global Positioning System (GPS)/Galileo navigation satellite system (Galileo) attitude determination based on the single-differenced (SD) model with a common-clock receiver. We first investigate the time-varying characteristics of BDS-2/BDS-3/GPS/Galileo line bias (LB) with two different types of common-clock receivers. The results have confirmed that both the phase and code LBs are relatively stable in the time domain once the receivers have started. However, the phase LB is expected to change to an arbitrary value after each restart of the common-clock receivers. For the first time, it is also found that the phase LBs of overlapping frequencies shared by different GNSS systems are identical. Then, we primarily evaluated the performance of BDS-2/BDS-3/GPS/Galileo precise relative positioning and attitude determination based on the SD model with a common-clock receiver, using a static dataset collected at Wuhan. Experimental results demonstrated that, compared with the double-differenced (DD) model, the SD model can deliver a comparable root–mean–square (RMS) error of yaw but a significantly smaller RMS error of pitch, whether for BDS-2, BDS-3, GPS, or Galileo alone or a combination of them. The improvements of pitch accuracy are approximately 20.8–47.5% and 40.7–57.5% with single- and dual-frequency observations, respectively. Additionally, BDS-3 can deliver relatively superior positioning and attitude accuracy with respect to GPS and Galileo, due to its better geometry. The three-dimensional positioning and attitude (including yaw and pitch) accuracy for both the DD and SD models can be remarkably improved by the BDS-2, BDS-3, GPS, and Galileo combination with respect to a single system alone. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Figure 1

Figure 1
<p>The observational conditions for the two static experiments. (<b>a</b>) Dataset 1; (<b>b</b>) Dataset 2.</p> Full article ">Figure 2
<p>Phase (<b>left</b>) and code (<b>right</b>) LBs for BDS/GPS/Galileo with Trimble BD992. (<b>a</b>,<b>b</b>) BDS; (<b>c</b>,<b>d</b>) GPS; (<b>e</b>,<b>f</b>) Galileo.</p> Full article ">Figure 2 Cont.
<p>Phase (<b>left</b>) and code (<b>right</b>) LBs for BDS/GPS/Galileo with Trimble BD992. (<b>a</b>,<b>b</b>) BDS; (<b>c</b>,<b>d</b>) GPS; (<b>e</b>,<b>f</b>) Galileo.</p> Full article ">Figure 3
<p>Phase (<b>left</b>) and code (<b>right</b>) LBs for BDS/GPS/Galileo with Unicore UB482. (<b>a</b>,<b>b</b>) BDS; (<b>c</b>,<b>d</b>) GPS; (<b>e</b>,<b>f</b>) Galileo.</p> Full article ">Figure 4
<p>Numbers of observed satellites (<b>a</b>) and their corresponding PDOP (<b>b</b>) series.</p> Full article ">Figure 5
<p>Positioning errors with dual-frequency observations under 10° elevation cutoff angle for BDS-2, BDS-3, GPS, Galileo, BDS-2/BDS-3, and BDS-2/BDS-3/GPS/Galileo. (<b>a</b>) BDS-2; (<b>b</b>) BDS-3; (<b>c</b>) GPS; (<b>d</b>) Galileo; (<b>e</b>) BDS-2/BDS-3; (<b>f</b>) BDS-2/BDS-3/GPS/Galileo.</p> Full article ">Figure 5 Cont.
<p>Positioning errors with dual-frequency observations under 10° elevation cutoff angle for BDS-2, BDS-3, GPS, Galileo, BDS-2/BDS-3, and BDS-2/BDS-3/GPS/Galileo. (<b>a</b>) BDS-2; (<b>b</b>) BDS-3; (<b>c</b>) GPS; (<b>d</b>) Galileo; (<b>e</b>) BDS-2/BDS-3; (<b>f</b>) BDS-2/BDS-3/GPS/Galileo.</p> Full article ">Figure 6
<p>Attitude errors with dual-frequency observations under 10° elevation cutoff angle for BDS-2, BDS-3, GPS, Galileo, BDS-2/BDS-3, and BDS-2/BDS-3/GPS/Galileo. (<b>a</b>) BDS-2; (<b>b</b>) BDS-3; (<b>c</b>) GPS; (<b>d</b>) Galileo; (<b>e</b>) BDS-2/BDS-3; (<b>f</b>) BDS-2/BDS-3/GPS/Galileo.</p> Full article ">
44 pages, 7500 KiB  
Article
Broadcast Ephemeris with Centimetric Accuracy: Test Results for GPS, Galileo, Beidou and Glonass
by Alessandro Caporali and Joaquin Zurutuza
Remote Sens. 2021, 13(20), 4185; https://doi.org/10.3390/rs13204185 - 19 Oct 2021
Cited by 5 | Viewed by 3909
Abstract
Here we test the capability of the Broadcast Ephemeris Message, in both its GPS-like (Keplerian ellipse with secular and periodic perturbations) and Glonass-like (numerical integration of a 9D state vector) formats, to reproduce a corresponding precise ephemeris. We start from a daily Rinex [...] Read more.
Here we test the capability of the Broadcast Ephemeris Message, in both its GPS-like (Keplerian ellipse with secular and periodic perturbations) and Glonass-like (numerical integration of a 9D state vector) formats, to reproduce a corresponding precise ephemeris. We start from a daily Rinex 3.04 navigation file for multiple GNSS and the corresponding SP3 precise orbits computed by CNES (Centre National d’Etudes Spatiales) for GPS, Glonass, Galileo and CODE (Center for Orbit Determination in Europe) for Beidou, and compute broadcast ECEF coordinates and clocks. The pre-fit discrepancies are converted by least squares to corrections to the broadcast ephemeris parameters in two-hour consecutive arcs (for GPS, Galileo and Beidou) and to a set of seven Helmert parameters for the entire day, to align in origin, orientation and scale to the common GNSS IGS14 Reference Frame. The test cases suggest that the Broadcast Ephemeris Message, complemented with Reference Frame information, can reproduce the precise ephemeris and clocks with centimetric accuracy for intervals at least equal to the respective validity times, typically 2 h. The broadcast ephemeris of Glonass consists of three initial positions and velocities at epoch, three constant Lunisolar accelerations for the satellite position, and of three polynomial coefficients for the satellite clock. The 9D vector of state is numerically integrated to generate position and velocity data within the validity time (0.5 h) of the message. To test the capability of this model to reproduce the corresponding values of a precise ephemeris, the 9D vector of state and clock polynomials are adjusted until the rms (root mean squared spread) of the post-fit residuals relative to a precise orbit (CNES’s in our case) is minimum. We show in one example (one satellite for one day) that the Glonass type of message can reproduce a precise ephemeris and clock with a rms spread of 0.025 m over one-hour arcs. Volume computations on one month of data with all available satellites confirm the test results. For GPS, Glonass, Galileo and Beidou, the best fitting clock values predicted by our second order polynomials, based on a 15 min sampling, are shown to fit the corresponding high rate clocks (30 s sampling) of MGEX with zero bias and a rms spread of 0.062 ns (GPS G01), 0.023 ns (Galileo E01), 0.43 ns (Glonass R01), 0.086 ns (Beidou C07) and 0.086 ns (Beidou C12). Modifications to the GPS-like message structure and Glonass algorithm are proposed to increase the validity time by including the effect of the 3rd zonal harmonic of the Earth’s gravity field. The potential of the RTCM messages for broadcasting the improved navigation message is reviewed. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Figure 1

Figure 1
<p>Schematic structure of the partial derivative matrix for the GPS-like model. The first vertical block represents the partials of <span class="html-italic">XYZT</span> pre-fit residuals relative to the Helmert parameters, appropriately scaled. The block diagonal part contains 12 blocks each of 4 rows of 18 partial derivatives, using as a priori the broadcast values of the parameters which are indexed with Toe for the coordinates and Toc for the clock.</p> Full article ">Figure 2
<p>Pre-fit (dots: different colours for different ephemeris blocks) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for G01. Vertical line spacing is every two hours. The rectangle indicates a 4 h rather than 2 h arc. The residuals will be discussed in <a href="#sec4-remotesensing-13-04185" class="html-sec">Section 4</a>.</p> Full article ">Figure 2 Cont.
<p>Pre-fit (dots: different colours for different ephemeris blocks) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for G01. Vertical line spacing is every two hours. The rectangle indicates a 4 h rather than 2 h arc. The residuals will be discussed in <a href="#sec4-remotesensing-13-04185" class="html-sec">Section 4</a>.</p> Full article ">Figure 3
<p>Best fitting corrections to (<b>a</b>) the clock polynomial parameters; (<b>b</b>) the Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track (Cuc, Cus) due to the second zonal harmonic; the amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 26 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite G01 for day 2 January 2020.</p> Full article ">Figure 3 Cont.
<p>Best fitting corrections to (<b>a</b>) the clock polynomial parameters; (<b>b</b>) the Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track (Cuc, Cus) due to the second zonal harmonic; the amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 26 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite G01 for day 2 January 2020.</p> Full article ">Figure 3 Cont.
<p>Best fitting corrections to (<b>a</b>) the clock polynomial parameters; (<b>b</b>) the Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track (Cuc, Cus) due to the second zonal harmonic; the amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 26 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite G01 for day 2 January 2020.</p> Full article ">Figure 4
<p>Pre-fit (dots, different colors for different ephemeris blocks) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for E01.</p> Full article ">Figure 4 Cont.
<p>Pre-fit (dots, different colors for different ephemeris blocks) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for E01.</p> Full article ">Figure 4 Cont.
<p>Pre-fit (dots, different colors for different ephemeris blocks) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for E01.</p> Full article ">Figure 5
<p>Best fitting corrections to (<b>a</b>)the clock polynomial parameters, (<b>b</b>) Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track due to the second zonal harmonic (Cuc, Cus), and amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 26 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite E01 for day 2 January 2020.</p> Full article ">Figure 5 Cont.
<p>Best fitting corrections to (<b>a</b>)the clock polynomial parameters, (<b>b</b>) Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track due to the second zonal harmonic (Cuc, Cus), and amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 26 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite E01 for day 2 January 2020.</p> Full article ">Figure 6
<p>Pre-fit (dots, different colours refer to different ephemeris blocks) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z for C07. For T (plot (<b>d</b>)) pre-fit (dots) refer to the left y-axis and post-fit (diamonds) to the right y-axis.</p> Full article ">Figure 6 Cont.
<p>Pre-fit (dots, different colours refer to different ephemeris blocks) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z for C07. For T (plot (<b>d</b>)) pre-fit (dots) refer to the left y-axis and post-fit (diamonds) to the right y-axis.</p> Full article ">Figure 7
<p>(<b>a</b>) the clock polynomial parameters, (<b>b</b>) Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track due to the second zonal harmonic (Cuc, Cus), and amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 42 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite C07 for day 2 January 2020.</p> Full article ">Figure 7 Cont.
<p>(<b>a</b>) the clock polynomial parameters, (<b>b</b>) Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track due to the second zonal harmonic (Cuc, Cus), and amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 42 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite C07 for day 2 January 2020.</p> Full article ">Figure 8
<p>Pre-fit (dots, different colours for different ephemeris blocks) and post fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for C12. Post-fits of the time offset T (diamonds) are plotted on the right y-axis.</p> Full article ">Figure 8 Cont.
<p>Pre-fit (dots, different colours for different ephemeris blocks) and post fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for C12. Post-fits of the time offset T (diamonds) are plotted on the right y-axis.</p> Full article ">Figure 8 Cont.
<p>Pre-fit (dots, different colours for different ephemeris blocks) and post fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for C12. Post-fits of the time offset T (diamonds) are plotted on the right y-axis.</p> Full article ">Figure 9
<p>Best fitting corrections to (<b>a</b>) the clock polynomial parameters, (<b>b</b>) Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track due to the second zonal harmonic (Cuc, Cus), and amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 26 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite C12 for day 2 January 2020.</p> Full article ">Figure 9 Cont.
<p>Best fitting corrections to (<b>a</b>) the clock polynomial parameters, (<b>b</b>) Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track due to the second zonal harmonic (Cuc, Cus), and amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 26 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite C12 for day 2 January 2020.</p> Full article ">Figure 9 Cont.
<p>Best fitting corrections to (<b>a</b>) the clock polynomial parameters, (<b>b</b>) Mean anomaly at Toe and amplitude of the cosine and sine perturbations along track due to the second zonal harmonic (Cuc, Cus), and amplitude of the cosine and sine perturbations in the (<b>c</b>) radial (Crc, Crs) and (<b>d</b>) cross track (Cic, Cis) directions. To convert to radians the scale factor 26 × 10<sup>6</sup> m should be used. Error bars are 1 sigma formal uncertainties. Satellite C12 for day 2 January 2020.</p> Full article ">Figure 10
<p>Structure of the partial derivative matrix H of the pre-fit discrepancies relative to the arc parameters. The arc parameters are indexed with the time Toc (Toe is equivalent) and the nominal values are dependent on the individual arcs being 2 h or 1 h long.</p> Full article ">Figure 11
<p>Pre-fit (dots) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for R01. Length of arc for fit is 1 h. Different colours denote different ephemeris blocks.</p> Full article ">Figure 11 Cont.
<p>Pre-fit (dots) and post-fit (diamonds) residuals of (<b>a</b>) X, (<b>b</b>) Y, (<b>c</b>) Z, and (<b>d</b>) T for R01. Length of arc for fit is 1 h. Different colours denote different ephemeris blocks.</p> Full article ">Figure 12
<p>Corrections to the broadcast (<b>a</b>) clock, (<b>b</b>) positions, (<b>c</b>) velocities, and (<b>d</b>) lunisolar accelerations for R01 using CNES precise orbits as reference. The vector of state (3 clock parameters + 9 orbit parameters) is estimated at intervals of 1 h. Rate of clock drift (a<sub>2</sub>) was computed but is not shown.</p> Full article ">Figure 12 Cont.
<p>Corrections to the broadcast (<b>a</b>) clock, (<b>b</b>) positions, (<b>c</b>) velocities, and (<b>d</b>) lunisolar accelerations for R01 using CNES precise orbits as reference. The vector of state (3 clock parameters + 9 orbit parameters) is estimated at intervals of 1 h. Rate of clock drift (a<sub>2</sub>) was computed but is not shown.</p> Full article ">Figure 12 Cont.
<p>Corrections to the broadcast (<b>a</b>) clock, (<b>b</b>) positions, (<b>c</b>) velocities, and (<b>d</b>) lunisolar accelerations for R01 using CNES precise orbits as reference. The vector of state (3 clock parameters + 9 orbit parameters) is estimated at intervals of 1 h. Rate of clock drift (a<sub>2</sub>) was computed but is not shown.</p> Full article ">Figure 13
<p>Plots of the differences between IGS high rate clocks and the prediction of our clock polynomials based on 15 min sampling. Update rate of the clock polynomials are 2 h for (<b>a</b>) G01, (<b>b</b>) E01, (<b>c</b>) 1 h for R01, (<b>d</b>) C07, and (<b>e</b>) C12. The mean and rms of the residuals are provided for each satellite.</p> Full article ">Figure 13 Cont.
<p>Plots of the differences between IGS high rate clocks and the prediction of our clock polynomials based on 15 min sampling. Update rate of the clock polynomials are 2 h for (<b>a</b>) G01, (<b>b</b>) E01, (<b>c</b>) 1 h for R01, (<b>d</b>) C07, and (<b>e</b>) C12. The mean and rms of the residuals are provided for each satellite.</p> Full article ">Figure 14
<p>Zoom of the first 4 h of the post-fit residuals of G01 shown in <a href="#remotesensing-13-04185-f002" class="html-fig">Figure 2</a> (red diamonds) showing an oscillatory pattern ((<b>a</b>) X, (<b>b</b>) Y, and (<b>c</b>) Z). The blue dots represent an attempt to model the oscillation with a signal driven by the third zonal harmonics of the Earth’s gravity field <span class="html-italic">J<sub>3</sub></span>.</p> Full article ">Figure 14 Cont.
<p>Zoom of the first 4 h of the post-fit residuals of G01 shown in <a href="#remotesensing-13-04185-f002" class="html-fig">Figure 2</a> (red diamonds) showing an oscillatory pattern ((<b>a</b>) X, (<b>b</b>) Y, and (<b>c</b>) Z). The blue dots represent an attempt to model the oscillation with a signal driven by the third zonal harmonics of the Earth’s gravity field <span class="html-italic">J<sub>3</sub></span>.</p> Full article ">Figure 15
<p>Spectrum of the pre-fit (top) and post-fit (bottom) residuals of the coordinates of the GPS satellites relative to the CNES precise ephemeris, projected on the radial, tangential and across track basis. Average values for January 2020.</p> Full article ">Figure 16
<p>Spectrum of the pre-fit (top) and post-fit (bottom) residuals of the coordinates of the Glonass satellites relative to the CNES precise ephemeris, projected on the radial, tangential and across track basis. Average values for January 2020.</p> Full article ">Figure 17
<p>Spectrum of the pre-fit (top) and post-fit (bottom) residuals of the coordinates of the Galileo satellites relative to the CNES precise ephemeris, projected on the radial, tangential and across track basis. Average values for January 2020.</p> Full article ">Figure 18
<p>Spectrum of the pre-fit (top) and post-fit (bottom) residuals of the coordinates of the Beidou satellites (IGSO and MEO) relative to the CODE precise ephemeris, projected on the radial, tangential and across track basis. Average values for January 2020.</p> Full article ">
18 pages, 3789 KiB  
Article
Impact of Tropospheric Mismodelling in GNSS Precise Point Positioning: A Simulation Study Utilizing Ray-Traced Tropospheric Delays from a High-Resolution NWM
by Florian Zus, Kyriakos Balidakis, Galina Dick, Karina Wilgan and Jens Wickert
Remote Sens. 2021, 13(19), 3944; https://doi.org/10.3390/rs13193944 - 2 Oct 2021
Cited by 8 | Viewed by 3672
Abstract
In GNSS analysis, the tropospheric delay is parameterized by applying mapping functions (MFs), zenith delays, and tropospheric gradients. Thereby, the wet and hydrostatic MF are derived under the assumption of a spherically layered atmosphere. The coefficients of the closed-form expression are computed utilizing [...] Read more.
In GNSS analysis, the tropospheric delay is parameterized by applying mapping functions (MFs), zenith delays, and tropospheric gradients. Thereby, the wet and hydrostatic MF are derived under the assumption of a spherically layered atmosphere. The coefficients of the closed-form expression are computed utilizing a climatology or numerical weather model (NWM) data. In this study, we analyze the impact of tropospheric mismodelling on estimated parameters in precise point positioning (PPP). To do so, we mimic PPP in an artificial environment, i.e., we make use of a linearized observation equation, where the observed minus modelled term equals ray-traced tropospheric delays from a high-resolution NWM. The estimated parameters (station coordinates, clocks, zenith delays, and tropospheric gradients) are then compared with the known values. The simulation study utilized a cut-off elevation angle of 3° and the standard downweighting of low elevation angle observations. The results are representative of a station located in central Europe and the warm season. In essence, when climatology is utilized in GNSS analysis, the root mean square error (RMSE) of the estimated zenith delay and station up-component equal about 2.9 mm and 5.7 mm, respectively. The error of the GNSS estimates can be reduced significantly if the correct zenith hydrostatic delay and the correct hydrostatic MF are utilized in the GNSS analysis. In this case, the RMSE of the estimated zenith delay and station up-component is reduced to about 2.0 mm and 2.9 mm, respectively. The simulation study revealed that the choice of wet MF, when calculated under the assumption of a spherically layered troposphere, does not matter too much. In essence, when the ‘correct’ wet MF is utilized in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component remain at about 1.8 mm and 2.4 mm, respectively. Finally, as a by-product of the simulation study, we developed a modified wet MF, which is no longer based on the assumption of a spherically layered atmosphere. We show that with this modified wet MF in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component can be reduced to about 0.5 mm and 1.0 mm, respectively. In practice, its success depends on the ability of current (future) NWM to predict the fourth coefficient of the developed closed-form expression. We provide some evidence that current NWMs are able to do so. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Figure 1

Figure 1
<p>Map showing the locations of the stations in the simulation study. In total 431 stations cover the area of interest. The red dot indicates the location of the station POTS (Potsdam, Germany).</p> Full article ">Figure 2
<p>Results for the first simulation experiment. Left panel: the error in the ZTD and the error in the station up-component for the POTS station as a function of time. Right panel: the station-specific RMSE for the ZTD (top), the gradient components (middle), and the station up-component (bottom). The number with yellow background corresponds to the averaged RMSE of the respective parameter.</p> Full article ">Figure 3
<p>Results for the second simulation experiment. Left panel: the error in the ZTD and the error in the station up-component for the POTS station as a function of time. Right panel: the station-specific RMSE for the ZTD (top), the gradient components (middle), and the station up-component (bottom). The number with yellow background corresponds to the averaged RMSE of the respective parameter.</p> Full article ">Figure 4
<p>Results for the third simulation experiment. Left panel: the error in the ZTD and the error in the station up-component for the POTS station as a function of time. Right panel: the station-specific RMSE for the ZTD (top), the gradient components (middle), and the station up-component (bottom). The number with yellow background corresponds to the averaged RMSE of the respective parameter.</p> Full article ">Figure 5
<p>Results for the fourth simulation experiment. Left panel: the error in the ZTD and the error in the station up-component for the station POTS as a function of time. Right panel: the station-specific RMSE for the ZTD (top), the gradient components (middle), and the station up-component (bottom). The number with yellow background corresponds to the averaged RMSE of the respective parameter.</p> Full article ">Figure 6
<p>Results for the fifth simulation experiment. Left panel: the error in the ZTD and the error in the station up-component for the POTS station as a function of time. Right panel: the station-specific RMSE for the ZTD (top), the gradient components (middle), and the station up-component (bottom). The number with yellow background corresponds to the averaged RMSE of the respective parameter.</p> Full article ">Figure 7
<p>Left panel: the tropospheric parameter <span class="html-italic">Z</span><sub>0</sub> for the POTS station as a function of time. Right panel: the error in the ZTD as obtained from the fourth simulation experiment versus the tropospheric parameter <span class="html-italic">Z</span><sub>0</sub> for all stations and epochs analyzed. The red line indicates the linear fit.</p> Full article ">Figure 8
<p>A one-to-one comparison of GNSS and NWM ZWDs in meters on the 15 May 2021 at 11 UTC. Left panel: the ZWDs are estimated with the GNSS. Right panel: the ZWDs are derived from the NWM. For the considered epoch about 300 stations provide ZTDs. The numbers in the left panel correspond to the mean and standard deviation between the GNSS and NWM ZTDs. The numbers with the yellow background correspond to the case when we corrected the GNSS ZTDs a posteriori. For details, refer to the text.</p> Full article ">Figure 9
<p>Upper panel: the reduction in the standard deviation in percentage, as a function of time, when GNSS ZWD estimates are corrected a posterior for the month of May in 2021. The number with the yellow background corresponds to the average reduction in the standard deviation. Lower panel: the number of samples (corresponding to the number of stations that provide ZTDs), as a function of the time.</p> Full article ">
23 pages, 74104 KiB  
Article
Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series
by Sorin Nistor, Norbert-Szabolcs Suba, Ahmed El-Mowafy, Michal Apollo, Zinovy Malkin, Eduard Ilie Nastase, Jacek Kudrys and Kamil Maciuk
Remote Sens. 2021, 13(17), 3478; https://doi.org/10.3390/rs13173478 - 2 Sep 2021
Cited by 4 | Viewed by 3475
Abstract
The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study [...] Read more.
The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study is to explore the implication of different types of geophysical events on the seasonal signal in three stages—in the time span that contains the geophysical events, before and after the geophysical event, but also the stationarity phenomena, which is analysed on approximately 200 reference stations from the EPN network since 1995. The novelty of the article is demonstrated by correlating three different types of geophysical events, such as earthquakes with a magnitude greater than 6° on the Richter scale, landslides, and volcanic activity, and analysing the variation in amplitude of the seasonal signal. The geophysical events situated within a radius of 30 km from the epicentre showed a higher seasonal value than when the timespan did not contain a geophysical event. The presence of flicker and random walk noise was computed using overlapping Hadamard variance (OHVAR) and the non-stationary behaviour of the time series of the CORS coordinates in the time frequency analysis was done using continuous wavelet transform (CWT). Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Figure 1

Figure 1
<p>Seasonal amplitude for the (<b>a</b>) East component and (<b>b</b>) North component of all stations.</p> Full article ">Figure 1 Cont.
<p>Seasonal amplitude for the (<b>a</b>) East component and (<b>b</b>) North component of all stations.</p> Full article ">Figure 2
<p>Seasonal amplitude for the Up component of all stations.</p> Full article ">Figure 3
<p>Geophysical events which occurred between 2000 and 2020.</p> Full article ">Figure 4
<p>Seasonal signals for the East component in the presence of geophysical events using the four above-mentioned computational strategies.</p> Full article ">Figure 5
<p>Seasonal signal values for the North component in the presence of a geophysical event using the four above-mentioned computational strategies.</p> Full article ">Figure 6
<p>Seasonal signal values for the Up component in the presence of a geophysical event using the four above-mentioned computational strategies.</p> Full article ">Figure 7
<p>(<b>a</b>–<b>i</b>) OHVAR of each coordinate component for the three periods analysed: 1995–1999 (left column), 2000–2004 (centre) and 2005–2009 (right column).</p> Full article ">Figure 8
<p>(<b>a</b>–<b>c</b>) Mean values of the OHVAR (Y-axis) as a function of τ (averaging time, X-axis) for each of the components and periods in the time series analysed.</p> Full article ">Figure 9
<p>(<b>a</b>–<b>h</b>) Time–frequency spectra using CWT of the North and East components of the ZARA, ONSA and ESCO stations and the East component of the BAIA and BACA stations. The white dash-dot lines correspond to the tropical year and its 2nd, 3rd and 4th harmonics (bottom to top).</p> Full article ">
23 pages, 7132 KiB  
Article
Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites
by Xingxing Li, Hongmin Zhang, Keke Zhang, Yongqiang Yuan, Wei Zhang and Yujie Qin
Remote Sens. 2021, 13(15), 3046; https://doi.org/10.3390/rs13153046 - 3 Aug 2021
Cited by 8 | Viewed by 4237
Abstract
Earth rotation parameters (ERP) are one of the key parameters in realization of the International Terrestrial Reference Frames (ITRF). At present, the International Laser Ranging Service (ILRS) generates the satellite laser ranging (SLR)-based ERP products only using SLR observations to Laser Geodynamics Satellite [...] Read more.
Earth rotation parameters (ERP) are one of the key parameters in realization of the International Terrestrial Reference Frames (ITRF). At present, the International Laser Ranging Service (ILRS) generates the satellite laser ranging (SLR)-based ERP products only using SLR observations to Laser Geodynamics Satellite (LAGEOS) and Etalon satellites. Apart from these geodetic satellites, many low Earth orbit (LEO) satellites of Earth observation missions are also equipped with laser retroreflector arrays, and produce a large number of SLR observations, which are only used for orbit validation. In this study, we focus on the contribution of multiple LEO satellites to ERP estimation. The SLR and Global Positioning System (GPS) observations of the current seven LEO satellites (Swarm-A/B/C, Gravity Recovery and Climate Experiment (GRACE)-C/D, and Sentinel-3A/B) are used. Several schemes are designed to investigate the impact of LEO orbit improvement, the ERP quality of the single-LEO solutions, and the contribution of multiple LEO combinations. We find that ERP estimation using an ambiguity-fixed orbit can attain a better result than that using ambiguity-float orbit. The introduction of an ambiguity-fixed orbit contributes to an accuracy improvement of 0.5%, 1.1% and 15% for X pole, Y pole and station coordinates, respectively. In the multiple LEO satellite solutions, the quality of ERP and station coordinates can be improved gradually with the increase in the involved LEO satellites. The accuracy of X pole, Y pole and length-of-day (LOD) is improved by 57.5%, 57.6% and 43.8%, respectively, when the LEO number increases from three to seven. Moreover, the combination of multiple LEO satellites is able to weaken the orbit-related signal existing in the single-LEO solution. We also investigate the combination of LEO satellites and LAGEOS satellites in the ERP estimation. Compared to the LAGEOS solution, the combination leads to an accuracy improvement of 0.6445 ms, 0.6288 ms and 0.0276 ms for X pole, Y pole and LOD, respectively. In addition, we explore the feasibility of a one-step method, in which ERP and the orbit parameters are jointly determined, based on SLR and GPS observations, and present a detailed comparison between the one-step solution and two-step solution. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Figure 1

Figure 1
<p>Flowchart of two-step method and one-step method.</p> Full article ">Figure 2
<p>Time series of pole coordinates and the length-of-day differences with respect to finals2000A.data series for the GRACE-D solutions based on the ambiguity-float orbit and ambiguity-fixed orbit. Values in the top right corner indicate the mean and RMS of differences for these two schemes.</p> Full article ">Figure 3
<p>Number of observations in 3-day solution for GRACE-D, Sentinel-3A, Swarm-A, Swarm-B, and LAGEOS (LAGEOS-1 + LAGEOS-2) collected by all stations (left) and core stations (right).</p> Full article ">Figure 4
<p>Spectral analysis for GRACE-C, Sentinel-3A, LAGEOS (LAGEOS-1 and LAGEOS-2), Swarm-C and Swarm-B solutions.</p> Full article ">Figure 5
<p>Differences of all SLR station and core station coordinates w.r.t. SLRF2014.</p> Full article ">Figure 6
<p>(<b>a</b>) Percentage of observations to LAGEOS satellites from core stations and non-core stations; (<b>b</b>) number of core stations and non-core stations in 3-day solutions.</p> Full article ">Figure 7
<p>Time series of pole coordinates and the length-of-day differences with respect to finals2000A.data series for the 3-LEO, 5-LEO and 7-LEO solutions. Values in the top right corner indicate the mean and RMS of differences for these three schemes.</p> Full article ">Figure 8
<p>Spectral analysis for the 3-LEO, 5-LEO and 7-LEO solutions.</p> Full article ">Figure 9
<p>Differences in all estimated SLR station coordinates w.r.t. SLRF2014 for the 3-LEO, 5-LEO and 7-LEO solutions.</p> Full article ">Figure 10
<p>Time series of pole coordinates and the length-of-day differences with respect to finals2000A.data series for the LAGEOS solution, 7-LEO solution and combined solution. Values in the top right corner indicate the mean and RMS of differences for these three schemes.</p> Full article ">Figure 11
<p>Spectral analysis for the LAGEOS solution, the 7-LEO solution and the combined solution.</p> Full article ">Figure 12
<p>Differences in all estimated SLR station coordinates w.r.t. SLRF2014 for the LAGEOS solution, the 7-LEO solution and the combined solution.</p> Full article ">Figure 13
<p>Time series of station coordinate of a station in Monument Peak (7110) from LAGEOS solutions and the combination solutions.</p> Full article ">Figure 14
<p>Time series of pole coordinates and the length-of-day differences with respect to finals2000A.data series for the two-step solution and one-step solution. Values in the top right corner indicate the mean and RMS of differences for these two methods.</p> Full article ">Figure 15
<p>Differences in all estimated SLR station coordinates w.r.t. SLRF2014 for the two-step solution and one-step solution.</p> Full article ">Figure 16
<p>Average RMS of Sentinel-3A orbit difference with respect to the CNES product for the two-step solution and one-step solution. Values in the top right corner indicate the mean of RMS for the whole processing period.</p> Full article ">
21 pages, 2849 KiB  
Article
An Improved Single-Epoch Attitude Determination Method for Low-Cost Single-Frequency GNSS Receivers
by Xinzhe Wang, Yibin Yao, Chaoqian Xu, Yinzhi Zhao and Huan Zhang
Remote Sens. 2021, 13(14), 2746; https://doi.org/10.3390/rs13142746 - 13 Jul 2021
Cited by 10 | Viewed by 2727
Abstract
GNSS attitude determination has been widely used in various navigation and positioning applications, due to its advantages of low cost and high efficiency. The navigation positioning and attitude determination modules in the consumer market mostly use low-cost receivers and face many problems such [...] Read more.
GNSS attitude determination has been widely used in various navigation and positioning applications, due to its advantages of low cost and high efficiency. The navigation positioning and attitude determination modules in the consumer market mostly use low-cost receivers and face many problems such as large multipath effects, frequent cycle slips and even loss of locks. Ambiguity fixing is the key to GNSS attitude determination and will face more challenges in the complex urban environment. Based on the CLAMBDA algorithm, this paper proposes a CLAMBDA-search algorithm based on the multi-baseline GNSS model. This algorithm improves the existing CLAMBDA method through a fixed geometry constraint among baselines in the vehicle coordinate system. A fixed single-baseline solution reduces two degrees of freedom of vehicle rigid body, and a global minimization search for the ambiguity objective function in the other degree of freedom is conducted to calculate the baseline vector and its Euler angles. In addition, in order to make up for the shortcomings of short baseline ambiguity in complex environments, this paper proposes different validation strategies. Using three low-cost receivers (ublox M8T) and patch antennas, static and dynamic on-board experiments with different baseline length set-ups were carried out in different environments. Both the experiments prove that the method proposed in this paper has greatly improved the ambiguity fixing performance and also the Euler angle calculation accuracy, with an acceptable calculation burden. It is a practical vehicle-mounted attitude determination algorithm. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Baselines layout and body coordinate system definition.</p> Full article ">Figure 2
<p>Procedure of CLAMBDA-search method for attitude determination.</p> Full article ">Figure 3
<p>Open-sky (<b>a</b>) and degraded (<b>b</b>) observation environments, recorded with Ublox M8T, patch antenna on 8 March 2020.</p> Full article ">Figure 4
<p>(<b>a</b>) Multi-receiver setup. (<b>b</b>) Number of observed satellites and PDOP values with cutoff satellite elevation of 10°.</p> Full article ">Figure 5
<p>The statistical results of the GPS/BDS attitude solution under five baseline lengths by CLAMBDA-search method, each group of data has a total of six histograms. Three on the left are open-sky results, three on the right are degraded results, where blue is yaw, green is pitch, red is roll. The three panels, respectively, show the average error, maximum error and error RMS of the experiment; the unit of the <span class="html-italic">x</span>-axis is meters.</p> Full article ">Figure 6
<p>(<b>a</b>) Observed satellite number, PDOP values. (<b>b</b>) C/N0 cumulative distribution function (CDF), residuals for group 1.5 m in the degraded environment.</p> Full article ">Figure 7
<p>Dynamic experiment. <b>Top left panel:</b> heavily degraded (Taiyuan roundabout). <b>Top right panel:</b> lightly degraded (Peacefully Plaza). <b>Bottom left panel:</b> open-sky (Development Avenue turntable). <b>Bottom right panel:</b> the antennae configuration. Recorded with Ublox M8T, patch antenna on 19 March 2020.</p> Full article ">Figure 8
<p>Dynamic experiment. (<b>a</b>) trajectory expressed in horizontal East–North coordinates as a function of time. The purple and red star lines are baseline one case, while the yellow and purple star lines are baseline two case. (<b>b</b>)baseline solutions expressed in horizontal East–North plane, with blue line for rover 1 and red line for rover 2. The unit of the x-axis and y-axis is meters.</p> Full article ">
22 pages, 5960 KiB  
Article
TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere
by Di Zhang, Jiming Guo, Tianye Fang, Na Wei, Wensheng Mei, Lv Zhou, Fei Yang and Yinzhi Zhao
Remote Sens. 2021, 13(13), 2568; https://doi.org/10.3390/rs13132568 - 30 Jun 2021
Cited by 5 | Viewed by 3445
Abstract
Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity [...] Read more.
Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay’s accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Procedure for determination of TMF.</p> Full article ">Figure 2
<p>The ray-tracing land cover area.</p> Full article ">Figure 3
<p>Distribution of the IGS stations used, the color of a circle denotes the station’s height. Please note that each dot only represents the position of a station, and there is no meaning for its size here.</p> Full article ">Figure 4
<p>Interpolation of the meteorological parameters.</p> Full article ">Figure 5
<p>The hydrostatic and wet gradients mapping functions using equations given by Chen, et al. [<a href="#B44-remotesensing-13-02568" class="html-bibr">44</a>].</p> Full article ">Figure 6
<p>Tilting of the tropospheric zenith.</p> Full article ">Figure 7
<p>The asymmetry of ray-tracing slant delays calculated by removal of the mean value of each elevation on all azimuths, for the IGS station SHAO located in Shanghai on 21 July 2018 (<b>a</b>) SHDs at 00:00 UTC, (<b>b</b>) SHDs at 05:00 UTC, (<b>c</b>) SWDs at 00:00 UTC, (<b>d</b>) SWDs at 05:00 UTC. Please note the difference between the bound of the colour bar on the right side of each subfigure.</p> Full article ">Figure 8
<p>The asymmetry of ray-tracing slant delays calculated by removal of the mean value of each elevation, for the IGS station SHAO located in Shanghai on 26 December 2018. (<b>a</b>) SHDs at 00:00 UTC, (<b>b</b>) SHDs at 05:00 UTC, (<b>c</b>) SWDs at 00:00 UTC, (<b>d</b>) SWDs at 05:00 UTC. Please note the difference between the bound of the colorbar.</p> Full article ">Figure 9
<p>The RMS of various mapping functions at the 5° elevation angle without or with gradients estimation for the 12 IGS stations on doy 74, 202, 246, and 360 in 2018. The size and the color of a circle denote the RMS<sub>5°</sub> value of the station, of which digit is also marked inside the circle.</p> Full article ">Figure 9 Cont.
<p>The RMS of various mapping functions at the 5° elevation angle without or with gradients estimation for the 12 IGS stations on doy 74, 202, 246, and 360 in 2018. The size and the color of a circle denote the RMS<sub>5°</sub> value of the station, of which digit is also marked inside the circle.</p> Full article ">Figure 10
<p>The difference of RMS<sub>5°</sub> computed by w-TMFabc minus w-WHU-SMFabc_gg for station SHAO (Shanghai, China) for doy 202, 2018.</p> Full article ">Figure 11
<p>The RMS scatters of MF-derived total delays at the 5° elevation angle (units: cm).</p> Full article ">
22 pages, 2180 KiB  
Article
Enhanced Neural Network Model for Worldwide Estimation of Weighted Mean Temperature
by Fengyang Long, Chengfa Gao, Yuxiang Yan and Jinling Wang
Remote Sens. 2021, 13(12), 2405; https://doi.org/10.3390/rs13122405 - 19 Jun 2021
Cited by 5 | Viewed by 2657
Abstract
Precise modeling of weighted mean temperature (Tm) is critical for realizing real-time conversion from zenith wet delay (ZWD) to precipitation water vapor (PWV) in Global Navigation Satellite System (GNSS) meteorology applications. The empirical Tm models developed by neural network [...] Read more.
Precise modeling of weighted mean temperature (Tm) is critical for realizing real-time conversion from zenith wet delay (ZWD) to precipitation water vapor (PWV) in Global Navigation Satellite System (GNSS) meteorology applications. The empirical Tm models developed by neural network techniques have been proved to have better performances on the global scale; they also have fewer model parameters and are thus easy to operate. This paper aims to further deepen the research of Tm modeling with the neural network, and expand the application scope of Tm models and provide global users with more solutions for the real-time acquisition of Tm. An enhanced neural network Tm model (ENNTm) has been developed with the radiosonde data distributed globally. Compared with other empirical models, the ENNTm has some advanced features in both model design and model performance, Firstly, the data for modeling cover the whole troposphere rather than just near the Earth’s surface; secondly, the ensemble learning was employed to weaken the impact of sample disturbance on model performance and elaborate data preprocessing, including up-sampling and down-sampling, which was adopted to achieve better model performance on the global scale; furthermore, the ENNTm was designed to meet the requirements of three different application conditions by providing three sets of model parameters, i.e., Tm estimating without measured meteorological elements, Tm estimating with only measured temperature and Tm estimating with both measured temperature and water vapor pressure. The validation work is carried out by using the radiosonde data of global distribution, and results show that the ENNTm has better performance compared with other competing models from different perspectives under the same application conditions, the proposed model expanded the application scope of Tm estimation and provided the global users with more choices in the applications of real-time GNSS-PWV retrival. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Figure 1

Figure 1
<p>The distribution of IGRA stations used in this work.</p> Full article ">Figure 2
<p>The model structures of three different modeling schemes. The red solid circles denote the direct input parameter of BPNN models.</p> Full article ">Figure 3
<p>Box-whisker plot of MD for different modeling schemes with different BPNN structures. The small circle denotes the results after combination, the red ‘+’ is the outlier.</p> Full article ">Figure 4
<p>The MAD of different modeling schemes with different BPNN structures.</p> Full article ">Figure 5
<p>The RMSE of different modeling schemes with different BPNN structures.</p> Full article ">Figure 6
<p>The STD of different modeling schemes with different BPNN structures.</p> Full article ">Figure 7
<p>The Pearson correlation coefficient (R) of different modeling schemes with different BPNN structures.</p> Full article ">Figure 8
<p>The scattergram of MD (mean deviation) for (<b>a</b>) GTrop-Tm model; (<b>b</b>) ENNTm-A model; (<b>c</b>) NN-II model; (<b>d</b>) ENNTm-B model and (<b>e</b>) ENNTm-C model at each test IGRA station; and (<b>f</b>) their statistics in different geographical zones validated by radiosonde data during 2017 and 2018.</p> Full article ">Figure 9
<p>The scattergram of RMSE (root-mean-square error) for (<b>a</b>) GTrop-Tm model, (<b>b</b>) ENNTm-A model, (<b>c</b>) NN-II model, (<b>d</b>) ENNTm-B model and (<b>e</b>) ENNTm-C model at each test IGRA station, and (<b>f</b>) their statistics in different geographical zones validated by radiosonde data during 2017 and 2018.</p> Full article ">Figure 10
<p>The statistics of RMSE reductions in (<b>a</b>) ENNTm-A w.r.t. GTrop-Tm; (<b>b</b>) ENNTm-B w.r.t. NN-II; (<b>c</b>) ENNTm-C w.r.t. NN-II; and (<b>d</b>) ENNTm-C w.r.t. ENNTm-B. w.r.t = with respect to.</p> Full article ">Figure 11
<p>The statistics of MDs at different height layers in the (<b>a</b>) NFZ; (<b>b</b>) NTZ; (<b>c</b>) TZ; (<b>d</b>) STZ; and (<b>e</b>) SFZ.</p> Full article ">Figure 12
<p>The statistics of RMSEs at different height layers in the (<b>a</b>) NFZ; (<b>b</b>) NTZ; (<b>c</b>) TZ; (<b>d</b>) STZ; and (<b>e</b>) SFZ.</p> Full article ">Figure 13
<p>The statistics of MD for each model in different months in the (<b>a</b>) NFZ; (<b>b</b>) NTZ; (<b>c</b>) TZ; (<b>d</b>) STZ; and (<b>e</b>) SFZ.</p> Full article ">Figure 14
<p>The statistics of RMSE for each model in different months in the (<b>a</b>) NFZ; (<b>b</b>) NTZ; (<b>c</b>) TZ; (<b>d</b>) STZ; and (<b>e</b>) SFZ.</p> Full article ">
23 pages, 5737 KiB  
Article
Analysis of the Impact of Multipath on Galileo System Measurements
by Dominik Prochniewicz and Maciej Grzymala
Remote Sens. 2021, 13(12), 2295; https://doi.org/10.3390/rs13122295 - 11 Jun 2021
Cited by 23 | Viewed by 4028
Abstract
Multipath is one of the major source of errors in precise Global Navigation Satellite System positioning. With the emergence of new navigation systems, such as Galileo, upgraded signals are progressively being used and are expected to provide greater resistance to the effects of [...] Read more.
Multipath is one of the major source of errors in precise Global Navigation Satellite System positioning. With the emergence of new navigation systems, such as Galileo, upgraded signals are progressively being used and are expected to provide greater resistance to the effects of multipath compared to legacy Global Positioning System (GPS) signals. The high quality of Galileo observations along with recent development of the Galileo space segment can therefore offer significant advantages to Galileo users in terms of the accuracy and reliability of positioning. The aim of this paper is to verify this hypothesis. The multipath impact was determined both for code and phase measurements as well as for positioning results. The code multipath error was determined using the Code-Minus-Carrier combination. The influence of multipath on phase observations and positioning error was determined using measurements on a very short baseline. In addition, the multipath was classified into two different types: specular and diffuse, using wavelet transform. The results confirm that the Galileo code observations are more resistant to the multipath effect than GPS observations. Among all of the observations examined, the lowest values of code multipath errors were recorded for the Galileo E5 signal. However, no advantage of Galileo over GPS was observed for phase observations and for the analysis of positioning results. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Environment at the WUT antennas site (in the foreground is WUT2 station).</p> Full article ">Figure 2
<p>Standard deviation of code multipath error versus elevation at the WUT2 site.</p> Full article ">Figure 3
<p>Standard deviation of pseudorange noise versus elevation at the WUT2 site.</p> Full article ">Figure 4
<p>A model of the code multipath error as a function of satellite elevation for (<b>a</b>) Galileo and (<b>b</b>) GPS.</p> Full article ">Figure 5
<p>Three-dimensional distribution of a code multipath error at the WUT2 site for (<b>a</b>) E1C Galileo and (<b>b</b>) L1 C/A GPS observations.</p> Full article ">Figure 6
<p>Standard deviation of phase multipath error versus elevation.</p> Full article ">Figure 7
<p>Standard deviation of phase noise error versus elevation.</p> Full article ">Figure 8
<p>A model of the phase multipath error as a function of satellite elevation for (<b>a</b>) Galileo and (<b>b</b>) GPS.</p> Full article ">Figure 9
<p>Skyplot for satellites E18 and G09.</p> Full article ">Figure 10
<p>CMC observables and scalograms for (<b>a</b>) Galileo E18 and (<b>b</b>) GPS G09 satellites at the WUT2 site.</p> Full article ">Figure 11
<p>Double-difference phase residuals and scalograms for (<b>a</b>) Galileo E18 and (<b>b</b>) GPS G09 satellites.</p> Full article ">Figure 12
<p>CMC observable signal extractions using wavelets for (<b>a</b>) specular, (<b>b</b>) diffuse, and (<b>c</b>) specular and diffuse multipaths.</p> Full article ">Figure 13
<p>DD phase residual signal extraction using wavelets for (<b>a</b>) specular, (<b>b</b>) diffuse, and (<b>c</b>) specular and diffuse multipaths.</p> Full article ">Figure 14
<p>Vertical components (<b>a</b>), skyplot (<b>b</b>) and scalograms for Galileo (<b>c</b>) and GPS (<b>d</b>).</p> Full article ">Figure 15
<p>Vertical component signal extraction using wavelets for (<b>a</b>) specular, (<b>b</b>) diffuse, and (<b>c</b>) specular and diffuse multipaths.</p> Full article ">
18 pages, 3948 KiB  
Article
An Improved Multipath Mitigation Method and Its Application in Real-Time Bridge Deformation Monitoring
by Ruicheng Zhang, Chengfa Gao, Qing Zhao, Zihan Peng and Rui Shang
Remote Sens. 2021, 13(12), 2259; https://doi.org/10.3390/rs13122259 - 9 Jun 2021
Cited by 4 | Viewed by 2783
Abstract
A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to [...] Read more.
A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to the influence of observation noise and the multipath differences between different satellites. Aiming at the insufficiency of MHM in dealing with the adverse impact of observation noise, we proposed the MHM_V model, based on Variational Mode Decomposition (VMD) and the MHM algorithm. Utilizing the VMD algorithm to extract the multipath from single-difference (SD) residuals, and according to the principle of the closest elevation and azimuth, the original observation of carrier phase in the few days following the implementation are corrected to mitigate the influence of the multipath. The MHM_V model proposed in this paper is verified and compared with the traditional MHM algorithm by using the observed data of the Forth Road Bridge with a seven day and 10 s sampling rate. The results show that the correlation coefficient of the multipath on two adjacent days was increased by about 10% after residual denoising with the VMD algorithm; the standard deviations of residual error in the L1/L2 frequencies were improved by 37.8% and 40.7%, respectively, which were better than the scores of 26.1% and 31.0% for the MHM algorithm. Taking a ratio equal to three as the threshold value, the fixed success rates of ambiguity were 88.0% without multipath mitigation and 99.4% after mitigating the multipath with MHM_V. The MHM_V algorithm can effectively improve the success rate, reliability, and convergence rate of ambiguity resolution in a bridge multipath environment and perform better than the MHM algorithm. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>SD residuals in a 12° × 26° grid. (<b>a</b>) SD residuals of G05 from DOY 295 to 297; (<b>b</b>) SD residuals of G05/06/08/26 on DOY 297.</p> Full article ">Figure 2
<p>The algorithm flow of the MHM_V model.</p> Full article ">Figure 3
<p>The distribution of the monitoring stations and base station.</p> Full article ">Figure 4
<p>The SD residuals in L1/L2 of G14 and G32 with the SHM1–SHM2 baseline on DOY 2019:297.</p> Full article ">Figure 5
<p>The SD residuals in L1 and L2 of G14 and G32 satellites with the SHM1–SHM2 baseline on DOY 2019:297. (<b>Upper panel</b>): G14; (<b>Bottom panel</b>): G32.</p> Full article ">Figure 6
<p>The correlation coefficients of two adjacent days for all satellites. (<b>Upper panel</b>): L1; (<b>Bottom panel</b>): L2.</p> Full article ">Figure 7
<p>Sky map of the MHM grid. The azimuth angle is measured clockwise from the north. The elevation angle is measured upwards from the ground plane. The center represents an elevation angle of 90°, and the largest circle represents an elevation angle of 0°. (<b>a</b>) L1; (<b>b</b>) L2.</p> Full article ">Figure 8
<p>The residual time series of G14 L1 and L2 before and after multipath mitigation with MHM_V or MHM during a complete observation period. (<b>Left panel</b>): L1; (<b>Right panel</b>): L2.</p> Full article ">Figure 9
<p>The residual statistical histogram of G14 L1 and L2 before and after multipath mitigation with MHM_V or MHM during a complete observation period. (<b>Upper panel</b>): L1; (<b>Bottom panel</b>): L2.</p> Full article ">Figure 10
<p>Multipath reduction percentage after multipath model correction (MHM_V and MHM).</p> Full article ">Figure 11
<p>The SD residual standard deviations of all satellites corrected with MHM_V and MHM. (<b>Upper panel</b>): L1; (<b>Bottom panel</b>): L2.</p> Full article ">Figure 12
<p>(<b>a</b>) The SD residual improvement of all satellites sorted by elevation. (<b>b</b>) SD residual fitting results. Upper panel: L1; Bottom panel: L2.</p> Full article ">Figure 13
<p>The ratio test result of ambiguity resolution with and without the multipath correction.</p> Full article ">Figure 14
<p>The float ambiguity bias with and without multipath mitigation.</p> Full article ">
25 pages, 15587 KiB  
Article
Algorithm for Real-Time Cycle Slip Detection and Repair for Low Elevation GPS Undifferenced Data in Different Environments
by Ning Liu, Qin Zhang, Shuangcheng Zhang and Xiaoli Wu
Remote Sens. 2021, 13(11), 2078; https://doi.org/10.3390/rs13112078 - 25 May 2021
Cited by 8 | Viewed by 3566
Abstract
Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, [...] Read more.
Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, cycle slip detection and repair in low elevation GPS observation data are more complicated than those in normal environments. For low elevation GPS undifferenced carrier phase data in different environments, a combined cycle slip detection algorithm is proposed. This method uses the first-order Gauss–Markov stochastic process to model the pseudorange multipath in the wide-lane phase minus narrow-lane pseudorange observation equation, and establishes the state equation of the wide-lane ambiguity with the pseudorange multipath as a parameter, and it uses the Kalman filter for real-time estimation and detects cycle slips based on statistical hypothesis testing with a predicted residual sequence. Meanwhile, considering there are certain correlations among low elevation, observation epoch interval, and ionospheric delay error, a second-order difference geometry-free combination cycle slip test is constructed that takes into account the elevation. By combining the two methods, real-time cycle slip detection for GPS low elevation satellite undifferenced data is achieved. A cycle slip repair method based on spatial search and objective function minimization criterion is further proposed to determine the correct solution of the cycle slips after they are detected. The whole algorithm is experimentally verified using the static and kinematic measured data of low elevation satellites under four different environments: normal condition, high-voltage transmission lines, dynamic condition in the sea, and ionospheric disturbances. The experimental results show that the algorithm can detect and repair cycle slips accurately for low elevation GPS undifferenced data, the difference between the float solution and the true value for the cycle slip does not exceed 0.5 cycle, and the differences obey the normal distribution overall. At the same time, the wide-lane ambiguity and second-order difference GF combination sequence calculated by the algorithm is smoother, which give further evidence that the algorithm for cycle slip detection and repair is feasible and effective, and has the advantage of being immune to the special observation environments. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>(<b>a</b>) Elevation and pseudorange measurement error sequence of satellite G26; (<b>b</b>) elevation and pseudorange measurement error sequence of satellite G08.</p> Full article ">Figure 2
<p>Results of conventional MW combination detection of small cycle slips.</p> Full article ">Figure 3
<p>Elevation and pseudorange measurement error sequence of satellite G09.</p> Full article ">Figure 4
<p>GPS station TB06 under high-voltage transmission line environment (the latitude and longitude of station TB06 are 34°08′01″ and 107°54′38″, respectively).</p> Full article ">Figure 5
<p>Elevation and pseudorange measurement error sequence of satellite G03.</p> Full article ">Figure 6
<p>GPS trajectory on buoy.</p> Full article ">Figure 7
<p>Elevation and pseudorange measurement error sequence of satellite G10.</p> Full article ">Figure 8
<p>Elevation and pseudorange measurement error sequence of satellite G26.</p> Full article ">Figure 9
<p>Cycle slip detection results of satellite G09 at different epochs under normal environment.</p> Full article ">Figure 9 Cont.
<p>Cycle slip detection results of satellite G09 at different epochs under normal environment.</p> Full article ">Figure 9 Cont.
<p>Cycle slip detection results of satellite G09 at different epochs under normal environment.</p> Full article ">Figure 10
<p>Cycle slip detection results of satellite G03 at different epochs under high-voltage transmission line environment.</p> Full article ">Figure 10 Cont.
<p>Cycle slip detection results of satellite G03 at different epochs under high-voltage transmission line environment.</p> Full article ">Figure 10 Cont.
<p>Cycle slip detection results of satellite G03 at different epochs under high-voltage transmission line environment.</p> Full article ">Figure 11
<p>Cycle slip detection results of satellite G10 at different epochs under dynamic sea environment.</p> Full article ">Figure 11 Cont.
<p>Cycle slip detection results of satellite G10 at different epochs under dynamic sea environment.</p> Full article ">Figure 11 Cont.
<p>Cycle slip detection results of satellite G10 at different epochs under dynamic sea environment.</p> Full article ">Figure 12
<p>Cycle slip detection results of satellite G26 at different epochs in ionospheric disturbance environment.</p> Full article ">Figure 12 Cont.
<p>Cycle slip detection results of satellite G26 at different epochs in ionospheric disturbance environment.</p> Full article ">Figure 13
<p>Statistics of difference between float solution and true value for cycle slip.</p> Full article ">Figure 14
<p>Wide-lane ambiguity and second-order difference GF combination sequence of satellite G10 under dynamic sea environment.</p> Full article ">Figure 15
<p>Wide-lane ambiguity and second-order difference GF combination sequence of satellite G26 in ionospheric disturbance environment.</p> Full article ">

Other

Jump to: Research

15 pages, 83382 KiB  
Technical Note
Performance of Multi-GNSS Real-Time UTC(NTSC) Time and Frequency Transfer Service Using Carrier Phase Observations
by Pengfei Zhang, Rui Tu, Xiaochun Lu, Lihong Fan and Rui Zhang
Remote Sens. 2021, 13(20), 4184; https://doi.org/10.3390/rs13204184 - 19 Oct 2021
Viewed by 2240
Abstract
The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and [...] Read more.
The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and clock determinations has enabled GNSS time and frequency transfer using the CP technique to be performed in real-time mode, without any issues associated with latency. In this contribution, we preliminarily built the prototype system of real-time multi-GNSS time and frequency transfer service in National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS), which undertakes the task to generate, maintains and transmits the national standard of time and frequency UTC(NTSC). The comprehensive assessment of the availability and quality of the service system were provided. First, we assessed the multi-GNSS state space representation (SSR) correction generated in real-time multi-GNSS prototype system by combining broadcast ephemeris through a comparison with the GeoForschungsZentrum (GFZ) final products. The statistical results showed that the orbit precision in three directions was smaller than 6 cm for global positioning system (GPS) and smaller than approximately 10 cm for BeiDou satellite system (BDS). The root mean square (RMS) values of clock differences for GPS were approximately 2.74 and 6.74 ns for the GEO constellation of BDS, 3.24 ns for IGSO, and 1.39 ns for MEO. The addition, the GLObal NAvigation Satellite System (GLONASS) and Galileo satellite navigation system (Galileo) were 4.34 and 1.32 ns, respectively. In order to assess the performance of real-time multi-GNSS time and frequency transfer in a prototype system, the four real-time time transfer links, which used UTC(NTSC) as the reference, were employed to evaluate the performance by comparing with the solution determined using the GFZ final products. The RMS could reach sub-nanosecond accuracy in the two solutions, either in the SSR or GFZ solution, or in GPS, BDS, GLONASS, and Galileo. The frequency stability within 10,000 s was 3.52 × 10?12 for SSR and 3.47 × 10?12 for GFZ and GPS, 3.63 × 10?12 for SSR and 3.53 × 10?12 for GFZ for BDS, 3.57 × 10?12 for SSR and 3.52 × 10?12 for GFZ for GLONASS, and 3.56 × 10?12 for SSR and 3.48 × 10?12 for GFZ for Galileo. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Figure 1

Figure 1
<p>Prototype system of real-time multi-GNSS time transfer service.</p> Full article ">Figure 2
<p>Distribution of real-time GNSS stations in NTSC time and frequency transfer prototype system for products determine.</p> Full article ">Figure 3
<p>Average RMS of orbits in three directions, calculated for real-time multi-GNSS compared to GFZ’s final products: (<b>a</b>) GPS; (<b>b</b>) BDS; (<b>c</b>) GLONASS; (<b>d</b>) GALILEO.</p> Full article ">Figure 4
<p>Average RMS and STD values real-time calculation compared with GFZ final products for DOY 346 to 349, 2019. (<b>a</b>) GPS; (<b>b</b>) BDS; (<b>c</b>) GLONASS; (<b>d</b>) Galileo.</p> Full article ">Figure 5
<p>GPS results for SSR and GFZ solutions.</p> Full article ">Figure 6
<p>GPS Allan deviation (ADEV) for SSR and GFZ solutions.</p> Full article ">Figure 7
<p>BDS results for SSR and GFZ solutions.</p> Full article ">Figure 8
<p>BDS Allan deviation (ADEV) for SSR and GFZ solutions.</p> Full article ">Figure 9
<p>GLONASS results for SSR and GFZ solutions.</p> Full article ">Figure 10
<p>GLONASS Allan deviation (ADEV) for SSR and GFZ solutions.</p> Full article ">Figure 11
<p>Galileo results for SSR and GFZ solutions.</p> Full article ">Figure 12
<p>Galileo Allan deviation (ADEV) for SSR and GFZ solutions.</p> Full article ">
17 pages, 3087 KiB  
Technical Note
A Method to Accelerate the Convergence of Satellite Clock Offset Estimation Considering the Time-Varying Code Biases
by Shuai Liu and Yunbin Yuan
Remote Sens. 2021, 13(14), 2714; https://doi.org/10.3390/rs13142714 - 9 Jul 2021
Cited by 7 | Viewed by 2254
Abstract
Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time [...] Read more.
Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior. Full article
(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)
►▼ Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Overview of the experimental stations. Red circles denote 70 stations for satellite clock estimation, and blue triangles denote 57 stations for PPP experiment. The observation data are obtained from the IGS MGEX networks.</p> Full article ">Figure 2
<p>Time series of RMS of the code residuals for different models on DOY 031.</p> Full article ">Figure 3
<p>Time series of RMS of the phase residuals for different models on DOY 031.</p> Full article ">Figure 4
<p>Time series of SCBs extracted by Undifferenced-SCB model on DOY 031.</p> Full article ">Figure 5
<p>Time series of SCBs extracted by Undifferenced-SRCB model on DOY 031.</p> Full article ">Figure 6
<p>Time series of RCBs extracted by Undifferenced-RCB model on DOY 031.</p> Full article ">Figure 7
<p>Time series of RCBs extracted by Undifferenced-SRCB model on DOY 031.</p> Full article ">Figure 8
<p>RMS and STD values of clock estimates compared with the IGS final products on DOY 031. The mean values are also plotted near the right edge of each panel. G01 is the reference satellite.</p> Full article ">Figure 9
<p>Time series of the clock biases with respect to the IGS final products on DOY 031. Different colors correspond to different satellites, and mean values are removed.</p> Full article ">Figure 10
<p>Comparison of positioning accuracy and convergence time with different ratio values on DOY 031.</p> Full article ">Figure 11
<p>Time series of the positioning errors using different satellite clocks for station ABPO on DOY 031.</p> Full article ">Figure 12
<p>RMS of positioning errors for different PPP solutions when compared to IGS weekly solutions at 57 stations from DOY 031 to 037.</p> Full article ">Figure 13
<p>The mean convergence time for various PPP solutions from DOY 031 to 037.</p> Full article ">Figure 14
<p>Time series of all GPS SCBs extracted using Undifferenced-SCB model on DOY 031.</p> Full article ">
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-15
Back to TopTop