Orbit Determination for Continuously Maneuvering Starlink Satellites Based on an Unscented Batch Filtering Method
Abstract
1. Introduction
2. Materials and Methods
2.1. Orbital Dynamics Model
2.1.1. General Model
2.1.2. Reduced Dynamics Model for Climbing Starlink Satellites
2.2. Orbit Estimation with an Unscented Batch Filtering Method
2.2.1. Sigma Points Sampling Strategy
- Choose the tuning parameter ω0 such that 0 < ω0 < 1;
- Determine the weight matrix W with ωi, i = 1, …, n
- 3.
- Construct the sigma set
2.2.2. Orbit Estimation Based on an Unscented Batch Filtering Method
3. Simulations and Results
3.1. Observation Simulations
3.2. Orbit Determination Simulation
3.2.1. Effects of the Measurement Errors
- Case 1: Δr0 = [−195.4272, 915.1713, −364.8435] m, Δv0 = [0.4716, −3.7691, −1.9408];
- Case 2: Δr0 = [1295.5440 −863.3109 −1545.5358] m, Δv0 = [−6.1658 3.6929 6.2951];
- Case 3: Δr0 = [585.9460 2818.3729 −1410.7564] m, Δv0 = [2.6370 −14.4218 −18.6149].
3.2.2. Effects of the Initial State Covariance
- Case A: (100 m)2 for position, (0.1 m/s)2 for velocity;
- Case B: (1000 m)2 for position, (1 m/s)2 for velocity;
- Case C: (5000 m)2 for position, (5 m/s)2 for velocity;
- Case D: (10,000 m)2 for position, (10 m/s)2 for velocity;
- Case E: (50,000 m)2 for position, (50 m/s)2 for velocity;
- Case F: (100,000 m)2 for position, (100 m/s)2 for velocity.
3.2.3. Statistical Analysis with Various Satellites
3.2.4. Effects of a Higher-Fidelity Dynamics Model
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Station Number | Longitude (deg) | Latitude (deg) | Altitude (m) |
---|---|---|---|
1 | 75.99 E | 39.47 N | 0 |
2 | 109.5 E | 18.4 N | 0 |
3 | 125.31 E | 44.88 N | 0 |
Arc ID | Starting Time | Ending Time |
---|---|---|
1 | 7 February 2024 20:31:42 | 7 February 2024 20:35:42 |
2 | 7 February 2024 22:05:42 | 7 February 2024 22:12:42 |
3 | 7 February 2024 23:42:42 | 7 February 2024 23:48:12 |
4 | 8 February 2024 01:21:42 | 8 February 2024 01:23:42 |
5 | 8 February 2024 02:57:42 | 8 February 2024 03:02:12 |
6 | 8 February 2024 04:32:42 | 8 February 2024 04:39:42 |
7 | 8 February 2024 06:09:42 | 8 February 2024 07:14:12 |
Case | RMS Position Error (m) | Maximum Position Error (m) |
---|---|---|
1-E | 1274 | 2768 |
1-E′ | 900 | 2057 |
1-F | 1395 | 3085 |
1-F′ | 1217 | 2408 |
3-E | 2080 | 5143 |
3-E′ | 1060 | 2690 |
3-F | 2308 | 5725 |
3-F′ | 1508 | 3424 |
Dynamics Model | RMS Position Error of 24 h OP (m) | |||||
---|---|---|---|---|---|---|
A | B | C | D | E | F | |
Equation (4) | 1776 | 1837 | 1354 | 1148 | 2080 | 2308 |
Equation (21) | 1380 | 942 | 950 | 820 | 1835 | 1911 |
Dynamics Model | Maximum Position Error of 24 h OP (m) | |||||
---|---|---|---|---|---|---|
A | B | C | D | E | F | |
Equation (4) | 5333 | 3615 | 3052 | 3092 | 5143 | 5725 |
Equation (21) | 3383 | 2645 | 2541 | 2074 | 3946 | 4160 |
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Lang, A.; Jiang, Y. Orbit Determination for Continuously Maneuvering Starlink Satellites Based on an Unscented Batch Filtering Method. Sensors 2025, 25, 4079. https://doi.org/10.3390/s25134079
Lang A, Jiang Y. Orbit Determination for Continuously Maneuvering Starlink Satellites Based on an Unscented Batch Filtering Method. Sensors. 2025; 25(13):4079. https://doi.org/10.3390/s25134079
Chicago/Turabian StyleLang, Anqi, and Yu Jiang. 2025. "Orbit Determination for Continuously Maneuvering Starlink Satellites Based on an Unscented Batch Filtering Method" Sensors 25, no. 13: 4079. https://doi.org/10.3390/s25134079
APA StyleLang, A., & Jiang, Y. (2025). Orbit Determination for Continuously Maneuvering Starlink Satellites Based on an Unscented Batch Filtering Method. Sensors, 25(13), 4079. https://doi.org/10.3390/s25134079