# Validation of the EGSIEM-REPRO GNSS Orbits and Satellite Clock Corrections

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Generation of GNSS Orbits

#### 2.2. Generation of Gnss Clock Products

## 3. Results

#### 3.1. ERP Misclosures

#### 3.2. GNSS Satellite Clock Corrections Analysis

- GPS + GLONASS kinematic solution;
- GPS only kinematic solution;
- GLONASS only kinematic solution.

#### 3.3. Validation of GNSS Orbits by Satellite Laser Ranging

#### 3.4. Quality Assessment Using GRACE Precise Orbit Determination

## 4. Discussion and Outlook

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Jäggi, A.; Weigelt, M.; Flechtner, F.; Güntner, A.; Mayer-Gürr, T.; Martinis, S.; Bruinsma, S.; Flury, J.; Bourgogne, S.; Steffen, H.; et al. European Gravity Service for Improved Emergency Management (EGSIEM)-from concept to implementation. Geophys. J. Int.
**2019**, 218, 1572–1590. [Google Scholar] [CrossRef] - Tapley, B.; Bettadpur, S.; Ries, J.; Watkins, M. GRACE measurements of mass variability in the Earth system. Science
**2004**, 305, 503–505. [Google Scholar] [CrossRef][Green Version] - Jean, Y.; Meyer, U.; Jäggi, A. Combination of GRACE monthly gravity field solutions from different processing strategies. J. Geod.
**2018**, 92, 1313–1328. [Google Scholar] [CrossRef][Green Version] - Meyer, U.; Jean, Y.; Kvas, A.; Dahle, C.; Lemoine, J.-M.; Jäggi, A. Combination of GRACE monthly gravity fields on the normal equation level. J. Geod.
**2019**, 93, 1645–1658. [Google Scholar] [CrossRef][Green Version] - Zumberge, J.F.; Heflin, M.B.; Jefferson, D.C.; Watkins, M.M.; Webb, F.H. Precise point positioning for the efficient and robust analysis of GPS data from large networks. J. Geo. Res.
**1997**, 102, 5005–5017. [Google Scholar] [CrossRef][Green Version] - Dach, R.; Schaer, S.; Arnold, D.; Orliac, E.; Prange, L.; Sušnik, A.; Villiger, A.; Jäggi, A.; Beutler, G.; Brockmann, E.; et al. Center of Orbit Determination in Europe: IGS Technical Report 2017. In International GNSS Service: Technical Report 2017; Villiger, A., Dach, R., Eds.; (AIUB), IGS Central Bureau and University of Bern, Bern Open Publishing: Bern, Switzerland, 2018; pp. 32–44. [Google Scholar]
- Bock, H.; Beutler, G.; Schaer, S.; Springer, T.A.; Rothacher, M. Processing aspects related to permanent GPS arrays. Earth Planets Space
**2000**, 52, 657–662. [Google Scholar] [CrossRef][Green Version] - Bock, H.; Dach, R.; Jäggi, A.; Beutler, G. High-rate GPS clock corrections from CODE: Support of 1 Hz applications. J. Geod.
**2009**, 83, 1083–1094. [Google Scholar] [CrossRef][Green Version] - Beutler, G.; Rothacher, M.; Schaer, S.; Springer, T.A.; Kouba, J.; Neilan, R.E. The international GPS service (IGS): An interdisciplinary service in support of Earth sciences. Adv. Space Res.
**1999**, 23, 631–653. [Google Scholar] [CrossRef] - Dow, J.; Neilan, R.; Rizos, C. The International GNSS service in a changing landscape of Global Navigational Satellite Systems. J. Geod.
**2009**, 82, 191–198. [Google Scholar] [CrossRef] - Steigenberger, P.; Hugentobler, U.; Lutz, S.; Dach, R. CODE Contribution to the first IGS Reprocessing Campaign. Tech. Rep.
**2011**. 1/2011. Available online: http://www.bernese.unibe.ch/publist/2011/artproc/CODE_Repro1.pdf (accessed on 25 May 2020). - Fritsche, M.; Sosnica, K.; Rodriguez-Solano, C.; Steigenberger, P.; Dietrich, R.; Dach, R.; Wang, K.; Hugentobler, U.; Rothacher, M. Homogeneous reprocessing of GPS, GLONASS and SLR observations. J. Geod.
**2014**, 88, 625–642. [Google Scholar] [CrossRef] - Griffiths, J. Combined orbits and clocks from IGS 2nd reprocessing. J. Geod.
**2018**, 93, 177–195. [Google Scholar] [CrossRef] [PubMed][Green Version] - Altamimi, Z.; Rebischung, P.; Metivier, L.; Collilieux, X. ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J. Geophys. Res. Solid Earth
**2016**, 121, 6109–6131. [Google Scholar] [CrossRef][Green Version] - Arnold, D.; Meindl, M.; Beutler, G.; Dach, R.; Schaer, S.; Lutz, S.; Prange, L.; Sosnica, K.; Mervart, L.; Jäggi, A. CODE’s new solar radiation pressure model for GNSS orbit determination. J. Geod.
**2015**, 89, 775–791. [Google Scholar] [CrossRef][Green Version] - Rebischung, P.; Griffiths, J.; Ray, J.; Schmid, R.; Collilieux, X.; Garayt, B. IGS08: The IGS realization of ITRF2008. GPS Solut.
**2012**, 16, 483–494. [Google Scholar] [CrossRef] - Schmid, R.; Dach, R.; Collilieux, X.; Jäggi, A.; Schmitz, M.; Dilssner, F. Absolute IGS antenna phase center model igs08.atx: Status and potential improvements. J. Geod.
**2016**, 90, 343–364. [Google Scholar] [CrossRef][Green Version] - Dach, R.; Lutz, S.; Walser, P.; Fridez, P. (Eds.) The Bernese GNSS Software Version 5.2. User Manual; Astronomical Institute, University of Bern, Bern Open Publishing: Bern, Switzerland, 2015. [Google Scholar]
- The IGSMail Archives. Available online: https://lists.igs.org/pipermail/igsmail/2015/000869.html (accessed on 25 May 2020).
- Mervart, L.; Beutler, G.; Rothacher, M. Ambiguity resolution strategies using the results of the International GPS Geodynamics Service (IGS). Bull. Géodésique
**1994**, 68, 29–38. [Google Scholar] [CrossRef] - Dach, R.; Schaer, S.; Lutz, S.; Meindl, A.; Bock, H.; Orliac, E.; Prange, L.; Thaller, D.; Mervart, L.; Jäggi, A.; et al. Center for Orbit Determination in Europe. IGS Technical Report 2011. In International GNSS Service: Technical Report 2011; Dach, R., Yean, Y., Eds.; IGS Central Bureau and University of Bern, Bern Open Publishing: Bern, Switzerland, 2012; pp. 21–34. [Google Scholar]
- Beutler, G.; Brockmann, E.; Hugentobler, U.; Mervart, L.; Rothacher, M.; Weber, R. Combining consecutive short arcs into long arcs for precise and efficient GPS orbit determination. J. Geod.
**1996**, 70, 287–299. [Google Scholar] [CrossRef] - Caissy, M.; Agrotis, L.; Weber, G.; Hermandez-Pajares, M.; Hugentobler, U. The International GNSS Real-Time Service. GPS World
**2012**, 23, 52–58. [Google Scholar] - Gurtner, W. RINEX: The receiver-independent exchange format. GPS World
**1994**, 5, 48–52. Available online: ftp://igs.org/pub/data/format/rinex2.txt (accessed on 15 May 2020). - Lutz, S.; Meindl, M.; Steigenberger, P.; Beutler, G.; Sosnica, K.; Schaer, S.; Dach, R.; Arnold, D.; Thaller, D.; Jäggi, A. Impact of the arc length on GNSS analysis results. J. Geod.
**2015**, 90, 365–378. [Google Scholar] [CrossRef] - Allan, D. Time and Frequency (Time-Domain) Characterization, Estimation, and Prediction of Precision Clocks and Oscillators. IEEE Trans. Ultrason. Ferroelectr.
**1987**, 34, 647–654. [Google Scholar] [CrossRef] [PubMed] - Sosnica, K.; Thaller, D.; Dach, R.; Steigenberger, P.; Beutler, G.; Arnold, D.; Jäggi, A. Satellite laser ranging to GPS and GLONASS. J. Geod.
**2015**, 89, 725–743. [Google Scholar] [CrossRef][Green Version] - Rodriguez-Solano, C.; Hugentobler, U.; Steigenberger, P.; Blossfeld, M.; Fritsche, M. Reducing the draconitic errors in GNSS geodetic products. J. Geod.
**2014**, 88, 559–574. [Google Scholar] [CrossRef] - Grahsl, A.; Sušnik, A.; Prange, L.; Arnold, D.; Dach, R.; Jäggi, A. GNSS orbit validation activites at the Astronomical Institute in Bern. In International Laser Ranging Service, Workshop 2016, 9–14 October 2016; Potsdam, Germany. Available online: https://cddis.nasa.gov/lw20/docs/2016/papers/P15-Maier_paper.pdf (accessed on 10 July 2020).
- Neubert, R.; Grunwaldt, L.; Neubert, J. The retroreflector for the CHAMP satellite: Final design and realization. In Proceedings of the 11th International Workshop on Laser Ranging, Deggendorf, Germany, 12–25 September 1998; pp. 260–270. [Google Scholar]

**Figure 1.**Success rate of the ambiguity resolution for Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) (blue color) and Global Positioning System (GPS) (red color) observations for the period 2000–2015.

**Figure 2.**Number of stations delivering high-rate Receiver Independent Exchange Format (RINEX2) data for the period 2003–2015.

**Figure 3.**Geographical distribution of stations providing high-rate RINEX2 data on January 1, 2003 (black dots), and on January 1, 2014 (red stars).

**Figure 4.**(

**a**) Time series of polar motion misclosures referring to the 2nd IGS reprocessing campaign (IGS-repro02). (

**b**) Time series of polar misclosures referring to the reprocessing campaign carried out in the frame of the EGSIEM project (EGSIEM-REPRO). The top shows misclosures in the x coordinates and the bottom shows misclosures in the y coordinates, plotted with a shift along the vertical axis for clarity. Polar motion misclosures referring to the 1-day solution are shown with red, while polar motion misclosures referring to the 3-day solution are presented in blue.

**Figure 5.**(

**a**) Power spectrum of polar motion misclosures referring to the 2nd IGS reprocessing campaign (IGS-repro02). (

**b**) Power spectrum of polar misclosures referring to the reprocessing campaign carried out in the frame of the EGSIEM project (EGSIEM-REPRO). Misclosures in x coordinates are shown on the top and misclosures in the y coordinates are shown on the bottom, plotted with a shift along the vertical axis for clarity. Polar motion misclosures referring to the 1-day solution are shown in red, while polar motion misclosures referring to the 3-day solution are presented in blue. In both cases, the chosen time interval is 2000–2014.

**Figure 6.**(

**a**) Power spectrum of polar motion misclosures for the 3-day solution referring to IGS-repro02. (

**b**) Power motion of polar misclosures for the 3-day solution referring to EGSIEM-REPRO. The x coordinates are shown on the top and y coordinates are shown on the bottom. In both cases, the chosen time interval is 2000–2013.

**Figure 7.**(

**a**) The completeness of 30 s GLONASS (where each GLONASS satellite is shown with their pseudorandom noise numbers (PRN) number on the y axis) satellite clock corrections. (

**b**) The completeness of 5 s GLONASS (where each GLONASS satellite is shown with their pseudorandom noise numbers (PRN) number on the y axis) satellite clock corrections. Note that the 5 s GLONASS clock corrections are only available from the end of 2010 onwards.

**Figure 8.**(

**a**) Allan deviations for satellites with space vehicle number (SVN) R747, G063, and G036 satellite clock corrections with different sampling corrections. (

**b**) Allan deviations for satellites with space vehicle number (SVN) R724, G063, and G036 satellite clock corrections with different samplings. Both figures refer to October 27, 2013.

**Figure 10.**(

**a**) RMS in mm of the kinematic coordinates in the up (top), north (middle), and east (bottom) components for WTZR (Wettzell, Germany) station. (

**b**) RMS in mm of the kinematic coordinates in the up (top), north (middle), and east (bottom) components for KIRU (Kiruna, Sweden) station. For both stations, the selected period is from December 11, 2013, to December 17, 2013.

**Figure 11.**(

**a**) Estimated kinematic coordinates in the north for two different sampling types, referring to the GPS+GLONASS solution. (

**b**) Estimated kinematic coordinates in the north for two different sampling types, referring to the GPS solution. (

**c**) Estimated kinematic coordinates in the north for two different sampling types, referring to the GLONASS solution. All three solutions refer to the first hour on December 17, 2013.

**Figure 12.**(

**a**) Allan deviations of estimated kinematic coordinates in the east component for two different samplings using GLONASS (indicated with GLO) only observations and satellite clock corrections. (

**b**) Allan deviations of estimated kinematic coordinates in the north component for two different samplings using GLONASS only observations and satellite clock corrections. (

**c**) Allan deviations of estimated kinematic coordinates in the up component for two different samplings using GLONASS only observations and satellite clock corrections. In all three figures, the Allan deviations were calculated over the entire day.

**Figure 13.**(

**a**) SLR residuals to GLONASS-M orbits from IGS-repro02 using the original Empirical CODE Orbit Model (ECOM). (

**b**) SLR residuals to GLONASS-M orbits from EGSIEM-REPRO using the extended ECOM. For both figures, residuals between January 2003 and December 2013 are shown. Observations for four GLONASS satellites (space vehicle number (SVN) 723, 725, 736, 737) were excluded due to anomalous patterns. Residuals of these GLONASS satellites increased after a certain time after launch [29]. Furthermore, residuals with absolute beta angles smaller than 15◦ are not shown due to unmodeled attitude behavior during eclipses. The black line indicates the linear regression of the SLR residuals as a function of the elongation angle.

**Figure 14.**(

**a**) RMS of ionosphere-free carrier-phase residuals of kinematic precise orbit determination (POD) for GRACE-A. (

**b**) RMS of ionosphere-free carrier-phase residuals of kinematic precise orbit determination (POD) for GRACE-B. The numbers indicate the average RMS values over the entire year. In both figures values in red were calculated using the GPS orbits and clocks from CODE’s contribution to the first IGS reprocessing campaign (repro1), while the values in green present the results obtained with EGSIEM-REPRO products.

**Figure 15.**(

**a**) SLR residuals as a function of the solar beta angle with respect to microwave-based orbits of GLONASS satellite SVN 747 over a three-year time span (January 2012 to December 2014): computed using the D0B1 parametrization of the ECOM model; (

**b**) computed using the D4B1 parametrization of the ECOM model; (

**c**) computed using D2B1 parametrization of the ECOM model.

**Table 1.**Estimated empirical parameters in satellite–Sun direction (D), direction along the satellite’s solar panels axis (Y), and completion of the orthogonal right-handed system (B) for the original Empirical CODE Orbit Model (ECOM) and the extended Empirical CODE Orbit Model (ECOM2). Cycles-per-revolution is denoted as cpr.

Empirical CODE Orbit Model (ECOM) | D | Y | B |
---|---|---|---|

D0B1 | constant | constant | constant, 1-cpr |

D2B1 | constant, 2-cpr | constant | constant, 1-cpr |

D4B1 | constant, 2-cpr, 4-cpr | constant | constant, 1-cpr |

**Table 2.**Root-Mean-Squared (RMS) values of polar motion misclosures for the interval 2000–2014, resulting in IGS-repro02 (indicated with R-02 in the Table) and EGSIEM-REPRO (indicated with R-15 in the Table) in the x and y coordinates of the poles for the 1- and 3-day solutions, referring to different period intervals in microarcsecond (μas).

Solution | Periods (Days) | X | Y | ||
---|---|---|---|---|---|

R-02 | R-15 | R-02 | R-15 | ||

1-day | All | 194.2 | 174.9 | 255.7 | 240.2 |

<30 | 138.1 | 137.2 | 173.7 | 183.8 | |

30 < P < 600 | 135.5 | 106.9 | 182.2 | 153.1 | |

3-day | All | 28.7 | 29.5 | 29.9 | 29.6 |

<30 | 26.9 | 28 | 28.3 | 28.7 | |

30 < P < 600 | 9.1 | 8.1 | 9.0 | 7.1 |

**Table 3.**Mean and standard deviation in mm of Satellite Laser Ranging (SLR) residuals for reduced-dynamic orbits over the entire year 2008. The number of used normal points in the analysis is given in brackets.

Product Identifier | GRACE-A | GRACE-B |
---|---|---|

repro1 | 1.99 ± 18.14 (32,587) | 0.09 ± 18.51 (31,008) |

EGSIEM-REPRO | 2.21 ± 12.93 (32,639) | 0.70 ± 14.14 (31,030) |

**Table 4.**Mean and standard deviation in mm of Satellite Laser Ranging (SLR) residuals of kinematic orbits over the entire year 2008. The number of used normal points in the analysis is given in brackets.

Product Identifier | GRACE-A | GRACE-B |
---|---|---|

repro1 | 1.24 ± 19.98 (32,358) | 0.44 ± 23.00 (30,343) |

EGSIEM-REPRO | 2.11 ± 17.00 (32,409) | 1.24 ± 19.75 (30,456) |

**Table 5.**Median and interquartile range (IQR) of SLR residuals with respect to GLONASS orbits between January 2012 and December 2014. The orbits were computed using three different orbit parametrizations, namely D0B1, D4B1, and D2B1. The observations for eclipsing satellites (absolute value of solar beta angle smaller than 15°) and for SVN 721, 723, 725, 730, 736, and 737 satellites were excluded due to anomalous patterns [15,29].

Solution | Median (mm) | IQR (mm) |
---|---|---|

D0B1 | 5.0 | 38.0 |

D2B1 | −2.4 | 32.8 |

D4B1 | −2.6 | 33.3 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sušnik, A.; Grahsl, A.; Arnold, D.; Villiger, A.; Dach, R.; Beutler, G.; Jäggi, A. Validation of the EGSIEM-REPRO GNSS Orbits and Satellite Clock Corrections. *Remote Sens.* **2020**, *12*, 2322.
https://doi.org/10.3390/rs12142322

**AMA Style**

Sušnik A, Grahsl A, Arnold D, Villiger A, Dach R, Beutler G, Jäggi A. Validation of the EGSIEM-REPRO GNSS Orbits and Satellite Clock Corrections. *Remote Sensing*. 2020; 12(14):2322.
https://doi.org/10.3390/rs12142322

**Chicago/Turabian Style**

Sušnik, Andreja, Andrea Grahsl, Daniel Arnold, Arturo Villiger, Rolf Dach, Gerhard Beutler, and Adrian Jäggi. 2020. "Validation of the EGSIEM-REPRO GNSS Orbits and Satellite Clock Corrections" *Remote Sensing* 12, no. 14: 2322.
https://doi.org/10.3390/rs12142322