# Initial Tracking, Fast Identification in a Swarm and Combined SLR and GNSS Orbit Determination of the TUBIN Small Satellite

^{*}

## Abstract

**:**

## 1. Introduction

^{2}to 0.22 m

^{2}for a 23 kg mass) and low-altitude orbit (approximately 530 km) and without a controlled attitude most of the time, represents one of most challenging cases for orbit predictions within the ILRS network to the authors’ knowledge. Thanks to its GPS receiver, the amount of tracking data is sufficient for ensuring convergence of an orbit estimator, but the issue lies in the rapid degradation of the orbit prediction accuracy.

## 2. Tubix20 Platform and TUBIN Mission

#### 2.1. Previous Missions of the TUBiX20 Platform

#### 2.2. Goals and Spacecraft Development

#### 2.3. On-Ground Verification

#### 2.3.1. Characterization and Binning of Laser Retroreflectors

#### 2.3.2. GPS Receiver Verification by Spoofing

## 3. Leop and Spacecraft Identification after Launch

#### 3.1. TLE Generation for Ground Station Tracking

#### 3.2. GPS Receiver Commissioning

#### 3.3. LEOP Orbit Determination from GPS Data

#### 3.3.1. Orbit Determination Model

Model or Parameter | Description |
---|---|

Earth gravity | EIGEN-6S (truncated to 120 × 120) |

Earth tides | IERS conventions 2010 |

Ocean tides | FES2004 |

Third-body attraction | Moon and Sun from DE430 |

Atmospheric density model | NRLMSISE-00 |

Drag coefficient | Constant or estimated |

Space weather data | 3-hourly CSSI data [13] |

Spacecraft shape | Box-wing model (when attitude available) |

Spherical (when no attitude data available) | |

Earth albedo | Knocke model [15] |

Solar radiation pressure | Lambertian diffusion on each satellite’s facet, Equations (8)–(45) in [16] (when attitude available) |

Cannonball model, Equations (8)–(44) in [16] (when no attitude data available) | |

Radiation coefficient | Constant or estimated |

Relativistic corrections | Post-Newtonian (Schwarzschild, Lense-Thirring, de Sitter) [17] |

Inertial reference system | True of Date |

Precession and nutation | IAU 2000 |

Polar motion | C04 IERS |

GPS data | From TUBIN’s Phoenix receiver, quantity and frequency variable |

GPS antenna—CoG position bias | Applied when attitude data available |

Numerical integration | Dormand-Prince 853 |

Integration step size | Variable, max 300 s |

Orbit determination method | Batch least squares |

Optimizer | Gauss–Newton with QR decomposer |

#### 3.3.2. Verification of the GPS-Based Orbit Determination

- OD3 was performed using a few tens of GPS measurements over one hour. This explains why this prediction drifted faster than OD2 in Figure 3 above.
- OD4 was performed using continuous GPS measurements from two orbits separated by one day. This orbit determination had the best distribution of measurement data, and therefore, the prediction drifted very little over time.
- OD5 only had 10 min of GPS data at its disposal, which explains why this prediction drifted faster than OD4.

#### 3.4. Identification in a Swarm

#### 3.4.1. Method

#### 3.4.2. Results

#### 3.5. Conclusions on LEOP

## 4. Operational Orbit Determination from SLR and GPS Data

#### 4.1. Models and Parameters for SLR and GPS Orbit Determination

#### 4.2. Verification of SLR-Only Orbit Determination

#### 4.3. Quality of the Orbit Determination Products

#### 4.3.1. Residuals

#### 4.3.2. Comparison of Successive CPF Predictions

#### 4.3.3. Time Bias of Orbit Predictions

#### 4.3.4. Improvement of Orbit Prediction Using GPS Time Bias

#### 4.4. SLR Data Statistics

#### 4.5. Effect of the Attitude on the Atmospheric Drag

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CDDIS | Crustal Dynamics Data Information System |

CoG | Center of gravity |

CPF | Consolidated Prediction Format |

CRD | Consolidated Laser Ranging Data Format |

CSpOC | Combined Space Operations Center |

DLR | Deutsches Zentrum für Luft- und Raumfahrt |

ECEF | Earth-centered Earth-fixed |

EDC | EUROLAS Data Center |

FOV | Field Of view |

GFZ | GeoForschungsZentrum |

GNSS | Global navigation satellite system |

GPS | Global positioning system |

ILRS | International Laser Ranging Service |

LEO | Low-Earth orbit |

LEOP | Launch and early orbit phase |

LRR | Laser retroreflector |

LVLH | Local-vertical local-horizontal |

MEMS | Microelectromechanical systems |

MSAFE | MSFC Solar Activity Future Estimation |

MSFC | Marshall Space Flight Center |

NERC | Natural Environment Research Council |

NORAD | North American Aerospace Defense Command |

NPT | Normal point data |

POD | Precise orbit determination |

PVT | Position velocity and time |

QUEEN | QUantentechnologien für den Einsatz auf Einem Nanosatelliten |

SDR | Software-defined radio |

SGF | Space Geodesy Facility |

SGP4 | Simplified general perturbations |

SINEX | Solution Independent Exchange |

SLR | Satellite laser ranging |

TLE | Two-line elements |

TOD | True of date |

TTFF | Time to first fix |

TUBIN | TU Berlin Infrared Nanosatellite |

UHF | Ultra-high frequency |

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**Figure 1.**(

**Left**) Representation of the TUBIN spacecraft in flight configuration. (

**Right**) Retroreflector pyramid as it was mounted on nadir and zenith sides.

**Figure 2.**Comparison of data and atmospheric density from the CSSI and MSAFE space weather files for an SSO orbit at a 515 km altitude with an 18 h local time of ascending node (LTAN). (

**Top**) Three-hour Kp geomagnetic index. (

**Middle**) F10.7 daily solar flux (interpolated). (

**Bottom**) NRLMSISE-00 atmospheric density model resulting from both data sources.

**Figure 3.**Evolution over time of the along-track error between each prediction and subsequent GPS data.

**Figure 4.**Position residuals (GPS data minus estimated orbit) in LVLH frame from the second orbit determination “OD2”.

**Figure 5.**Mean position residuals (log scale) between the TLE of each cataloged object in launch and GPS measurements from TUBIN. TLE are from 9 July 2021 at 12:00 a.m. UTC. A green dot means the corresponding spacecraft was already identified on Space-Track at that time, and a red dot means otherwise.

**Figure 6.**Illustration of the concept of satellite laser ranging (SLR) from Kim et al. (2015) [24] (CC BY-NC 3.0).

**Figure 8.**SLR range (

**left**) and GPS position residuals (

**right**) for a mixed SLR+GPS orbit determination on TUBIN on 25 June 2022 from a 42 h measurement arc.

**Figure 9.**SLR range (

**left**) and GPS position residuals (

**right**) for a mixed SLR+GPS orbit determination on TUBIN on 25 June 2022 from a 24 h measurement arc.

**Figure 10.**Position difference between an estimated orbit and two sets of TLE for an orbit determination on 25 June 2022 with a 42 h arc. The darker gray area on the left of each figure represents the orbit determination window. (

**Left**) Original TLE from Space-Track. (

**Right**) TLE optimized by differential correction. The along-track error of the optimized TLE remained mostly periodic and within a ±1 km range in the time interval represented.

**Figure 11.**Position difference between the estimated orbit and the previous CPF prediction for an orbit determination on 25 June 2022 with a 42 h arc. The darker gray area on the left represents the orbit determination window.

**Figure 12.**Evolution of time bias of TUB17901 CPF orbit prediction generated on 28 June 2022. Teal represents time bias computed from GPS measurements, dark red represents time bias from SLR data (from GFZ website), and the red line represents the polynomial fit from SLR time bias to predict the time bias trend (from GFZ website).

**Figure 13.**Evolution of time bias of multiple predictions with different drag coefficients ${C}_{D}$ for TUBIN on 6 September 2022, measured by comparison to subsequent GPS data. (

**Left**) First 36 h after the prediction epoch. (

**Right**) First 5 days after the prediction epoch.

**Figure 14.**Cumulated number of normal points since the beginning of mission until 4 July 2022 for TechnoSat (

**left**) and TUBIN (

**right**).

**Figure 15.**Simulated along-track drift between two initially identical orbits but with different pointing laws, converted to a time difference in milliseconds, as a function of the number of days since epoch. The orbit was TUBIN’s Sun-synchronous orbit at a 530 km altitude. The spacecrafts were pointing nadir with each having a different offset that ensured the minimum and maximum cross-sections, respectively, with regard to atmospheric drag.

Mission | TechnoSat | TUBIN |
---|---|---|

Objective | Technology demonstration | Technology demonstration |

Earth observation | ||

Initial orbit | 620 km SSO | 530 km SSO |

Design lifetime | 1 year | 1 year |

Launch date | 14 July 2017 | 30 June 2021 |

Spacecraft mass | 20 kg | 23 kg |

Spacecraft volume | 465 × 465 × 305 mm^{3} | 465 × 465 × 305 mm^{3} |

Orbit determination | Satellite laser ranging (SLR) | SLR |

GPS receiver |

**Table 2.**Overview of perturbation forces on TUBIN, averaged over a 4 day period with ${F}_{10.7}=120$, ${C}_{D}=2.2$, and ${C}_{R}=1.0$ in nadir pointing.

Perturbation Force | Acceleration in Along-Track Direction (Absolute Value, Mean) (m/s${}^{2}$) |
---|---|

Earth gravity harmonics 120 × 120 | 7.25 × 10^{−3} |

Sun third-body attraction | 1.77 × 10^{−7} |

Moon third-body attraction | 1.68 × 10^{−7} |

Atmospheric drag | 1.39 × 10^{−7} |

Solid tides | 5.57 × 10^{−8} |

Ocean tides | 1.95 × 10^{−8} |

Sun radiation pressure | 1.37 × 10^{−8} |

Earth albedo | 3.44 × 10^{−10} |

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**MDPI and ACS Style**

Jonglez, C.; Bartholomäus, J.; Werner, P.; Stoll, E.
Initial Tracking, Fast Identification in a Swarm and Combined SLR and GNSS Orbit Determination of the TUBIN Small Satellite. *Aerospace* **2022**, *9*, 793.
https://doi.org/10.3390/aerospace9120793

**AMA Style**

Jonglez C, Bartholomäus J, Werner P, Stoll E.
Initial Tracking, Fast Identification in a Swarm and Combined SLR and GNSS Orbit Determination of the TUBIN Small Satellite. *Aerospace*. 2022; 9(12):793.
https://doi.org/10.3390/aerospace9120793

**Chicago/Turabian Style**

Jonglez, Clément, Julian Bartholomäus, Philipp Werner, and Enrico Stoll.
2022. "Initial Tracking, Fast Identification in a Swarm and Combined SLR and GNSS Orbit Determination of the TUBIN Small Satellite" *Aerospace* 9, no. 12: 793.
https://doi.org/10.3390/aerospace9120793