# Determination of Global Geodetic Parameters Using Satellite Laser Ranging Measurements to Sentinel-3 Satellites

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## Abstract

**:**

## 1. Introduction

#### 1.1. Satellite Laser Ranging to Low Earth Orbiters

#### 1.2. Goal and Objectives of This Study

## 2. Materials and Methods

#### 2.1. Sentinel-3A/3B Mission Overview

#### 2.2. Sentinel-3A/3B Orbits

#### 2.3. Methodology

#### 2.4. Solution Constraining Scenarios

#### 2.5. The Issue of Reference Frame Differences

## 3. Results

#### 3.1. Solution Statistics

#### 3.2. Significance of Proper Handling of Station Biases

#### 3.3. Sentinel-3 Solution Scenario Tests

#### 3.3.1. Station Coordinates

#### 3.3.2. Influence of the Number of NPs on Coordinate Residual Values

#### 3.4. Different Numbers of Stacked 1-day Solutions

#### 3.4.1. Station Coordinates

#### 3.4.2. Geocenter Coordinates

#### 3.4.3. Earth Rotation Parameters

#### 3.5. Combined Sentinel+LAGEOS Solutions

#### 3.5.1. Geocenter from the Combined LAGEOS+Sentinel Solutions

#### 3.5.2. ERP from the Combined LAGEOS+Sentinel Solutions

#### 3.5.3. Station Coordinates from the Combined LAGEOS+Sentinel Solutions

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

S3A/B | Sentinel-3A/3B |

SLR | Satellite Laser Ranging |

GPS | Global Positioning System |

ERPs | Earth Rotation Parameters |

GNSS | Global Navigational Satellite Systems |

LEOs | Low Earth Orbiters |

MEO | Medium Earth Orbiters |

DORIS | Doppler Orbitography and Radiopositioning Integrated by Satellite |

ILRS | International Laser Ranging Service |

POD | Precise Orbit Determination |

AIUB | Astronomical Institute of the University of Bern |

LRR | Laser Retroreflectors |

CPOD | Copernicus POD Service |

IGS | International GNSS Service |

SLRF | Satellite Laser Ranging Frame |

ITRF | International Terrestrial Reference Frame |

NPs | Normal Points |

CoM | Center of Mass |

CoF | Center of Figure |

NNR | No Net Rotation |

NNT | No Net Translation |

PPP | Precise Point Positioning |

LAG | LAGEOS |

IQR | Interquartile Range |

RMS | Root Mean Square Error |

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**Figure 2.**Residual histograms for solutions with uncorrected (

**left**) and corrected (

**right**) range biases for all sites.

**Figure 3.**Dependency of residuals on S3A as a function of $\beta $ and $\Delta $u angles for solutions with uncorrected (

**left**) and corrected (

**right**) range biases.

**Figure 4.**Residual dependency on Monument Peak station azimuth angles for solutions with uncorrected (

**left**) and corrected (

**right**) range biases.

**Figure 5.**SLR site coordinate repeatabilities in SLRF2014 based on SLR-to-S3A/B data for scenario 1 (green), scenario 2 (red), scenario 3 (blue). Minimum, maximum, 1st and 3rd quartiles and the median value are shown as elements of box-plots. Stations are sorted starting from that with the highest number of 7-day solutions (

**left**) to the lowest number of solutions (

**right**).

**Figure 6.**Time series (with error bars) of estimated station coordinates for Potsdam (

**left**) and Yarragadee (

**right**) using SLR observations to S3A/B w.r.t a priori SLRF2014 coordinates for scenario 1 (green), 2 (red), 3 (blue).

**Figure 7.**Absolute of residuals of estimated SLR station coordinates based on S3A/B data referred to the a priori values from SLRF2014 as the function of the number of observations collected by all SLR stations for scenario 1 (green), 2 (red), 3 (blue).

**Figure 8.**Coordinate comparison to SLR2014 results from S3A/B when using different numbers of 1-day normal equations: 1-day (green), 3-day (red), 7-day (blue), 15-day (cyan). Minimum, maximum, 1st and 3rd quartiles and the median value are shown as elements of box-plots. Stations are sorted according to the number of 7-day solutions, starting with the highest number (

**left**) to the lowest number of solutions (

**right**).

**Figure 9.**Geocenter coordinates based on SLR observations to S3A/B from 3-day (green), 5-day (blue), 7-day (red) solutions all of which are based on stacking a different number of 1-day orbit solutions.

**Figure 10.**Pole coordinates and the UT1-UTC from S3A/B w.r.t the IERS-14-C04 series for the tests using 3-day (green), 5-day (blue), and 7-day (red) solutions.

**Figure 11.**Comparison of geocenter coordinates (

**left**) and the spectral analysis (

**right**) for LAG (green), Sent (blue), and LAG+Sent (red) solutions.

**Figure 12.**Differences of pole coordinates and UT1-UTC w.r.t. IERS-14-C04 series and the spectral analysis of differences for LAG (green), Sent (blue), and LAG+Sent (red) solutions.

**Figure 13.**Differences of estimated SLR station coordinates w.r.t. SLR2014 for LAG (green), Sent (blue), and LAG+Sent (red) solutions represented as box-plots with max., min., 1st, 3rd quartiles, and median values.

**Figure 14.**Time series (error bars) for Arequipa (

**left**) and Potsdam (

**right**) site coordinates w.r.t SLRF2014 for LAG (green), Sent (blue), LAG+Sent (red) solutions.

**Table 1.**Constraints in tests of different network realization scenarios and different sets of estimated global parameters for S3A/B and LAG.

1cSolution Scenario | Network and Parameter Constraints | ||||||
---|---|---|---|---|---|---|---|

NNT [m] | NNR [rad] | Scale [mm] | Geocenter crd [m] | UT1-UTC [ms] | Pole Crds [µas] | Range Bias [m] | |

1. NNT/NNR parameters est. | $1\xb7{10}^{-5}$ | $1\xb7{10}^{-6}$ | - | - | 2 | 30 | $1\xb7{10}^{-4}$ |

2. NNT/NNR no parameters est. | $1\xb7{10}^{-5}$ | $1\xb7{10}^{-6}$ | - | $1\xb7{10}^{-6}$ | $1\xb7{10}^{-7}$ | $1\xb7{10}^{-5}$ | $1\xb7{10}^{-4}$ |

3. no NNT/NNR no parameters est. | - | - | - | $1\xb7{10}^{-6}$ | $1\xb7{10}^{-7}$ | $1\xb7{10}^{-5}$ | $1\xb7{10}^{-4}$ |

LAGEOS | $1\xb7{10}^{-5}$ | $1\xb7{10}^{-6}$ | - | $1\xb7{10}^{-6}$ | $1\xb7{10}^{-7}$ | $1\xb7{10}^{-5}$ | - |

**Table 2.**SLR station coordinate repeatability for the North, East, and Up components for tested S3A/B solutions for all and top SLR sites (in mm).

Sites | Solution Scenario | North | East | Up | |||
---|---|---|---|---|---|---|---|

Median | IQR | Median | IQR | Median | IQR | ||

All sites | 1. NNT/NNR, all parameters est. | 0.0 | 11.7 | 0.2 | 13.4 | -0.8 | 16.3 |

2. NNT/NNR, no global par. est. | 0.3 | 11.5 | 1.1 | 15.2 | −0.3 | 16.9 | |

3. no NNT/NNR, no global par. est. | 1.7 | 14.4 | 1.4 | 19.8 | 0.0 | 18.3 | |

Top sites | 1. NNT/NNR, all parameters est. | 0.5 | 7.8 | −0.4 | 9.1 | −1.6 | 11.9 |

2. NNT/NNR, no global par. est. | 1.1 | 8.5 | 0.2 | 11.4 | −0.6 | 12.3 | |

3. no NNT/NNR, no global par. est. | 3.2 | 11.6 | 0.4 | 16.9 | −0.7 | 13.4 |

**Table 3.**Mean offsets and RMS values of the estimated X, Y, Z geocenter coordinates (in mm). The mean values are calculated with respect to the ITRF2014/SLRF2014.

Solution | X | Y | Z | |||
---|---|---|---|---|---|---|

Mean | RMS | Mean | RMS | Mean | RMS | |

LAG | 1.0 | 4.3 | 0.5 | 3.1 | −1.6 | 6.8 |

Sent | −1.0 | 6.2 | 0.3 | 4.0 | −1.2 | 6.0 |

LAG+Sent | 0.0 | 4.5 | 0.9 | 3.4 | −2.3 | 5.9 |

**Table 4.**Mean offsets and RMS values of the estimated X, Y pole coordinates (in mas) and UT1-UTC (in ms) in reference to the a priori IERS-CO4-14 series.

1cSolution | X pole | Y pole | UT1-UTC | |||
---|---|---|---|---|---|---|

mean | RMS | mean | RMS | Mean | RMS | |

LAG | 0.128 | 0.134 | 0.047 | 0.166 | −0.098 | 0.107 |

Sent | 0.109 | 0.320 | 0.040 | 0.314 | −0.002 | 0.063 |

LAG+Sent | 0.134 | 0.138 | 0.044 | 0.189 | −0.011 | 0.067 |

**Table 5.**Statistics of summarized station coordinate repeatability for 7-day LAG, Sent, and LAG+Sent solutions with all SLR sites and top performing SLR sites decomposed into the North, East, and Up components (in mm).

2cSolution | North | East | Up | ||||
---|---|---|---|---|---|---|---|

median | IQR | median | IQR | median | IQR | ||

All sites | LAG | −0.9 | 12.7 | 0.5 | 11.1 | −0.8 | 24.6 |

Sent | 0.0 | 11.7 | 0.2 | 13.4 | −0.8 | 16.3 | |

LAG+Sent | −1.0 | 12.4 | 0.3 | 11.4 | −1.3 | 26.3 | |

Top sites | LAG | −0.1 | 5.3 | 0.0 | 5.0 | −0.4 | 12.5 |

Sent | 0.5 | 7.8 | −0.4 | 9.1 | −1.6 | 11.9 | |

LAG+Sent | −0.2 | 5.2 | −0.1 | 5.2 | −0.7 | 12.3 |

© 2019 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**

Strugarek, D.; Sośnica, K.; Arnold, D.; Jäggi, A.; Zajdel, R.; Bury, G.; Drożdżewski, M.
Determination of Global Geodetic Parameters Using Satellite Laser Ranging Measurements to Sentinel-3 Satellites. *Remote Sens.* **2019**, *11*, 2282.
https://doi.org/10.3390/rs11192282

**AMA Style**

Strugarek D, Sośnica K, Arnold D, Jäggi A, Zajdel R, Bury G, Drożdżewski M.
Determination of Global Geodetic Parameters Using Satellite Laser Ranging Measurements to Sentinel-3 Satellites. *Remote Sensing*. 2019; 11(19):2282.
https://doi.org/10.3390/rs11192282

**Chicago/Turabian Style**

Strugarek, Dariusz, Krzysztof Sośnica, Daniel Arnold, Adrian Jäggi, Radosław Zajdel, Grzegorz Bury, and Mateusz Drożdżewski.
2019. "Determination of Global Geodetic Parameters Using Satellite Laser Ranging Measurements to Sentinel-3 Satellites" *Remote Sensing* 11, no. 19: 2282.
https://doi.org/10.3390/rs11192282