Magnetic-Only Orbit and Attitude Estimation Using the Square-Root Unscented Kalman Filter: Application to the PROBA-2 Spacecraft
Bibliographic record
Abstract
In this paper a new technique to estimate simultaneously the orbit and the attitude of a spacecraft based solely on the magnetic field is described. This magnetic-only orbital and attitude estimation scheme uses a Square-Root Unscented Kalman Filter algorithm and is applied to a sun-synchronous low-Earth orbit spacecraft. The resulting software, to be validated in orbit as a flight technology-demonstration experiment on board the European PROBA-2 spacecraft, is validated in this paper using a high-fidelity real-world software simulator. This paper describes the estimation filter algorithm, the dynamic models and the measurement models required to implement the algorithm. The high-fidelity simulator is quickly reviewed and the critical functions (e.g. Earth magnetic field model and magnetometer) are analyzed and described in detail. All model uncertainties are addressed and defined for realistic scenarios relevant to sun-synchronous low-Earth orbits. Next, the computation of the tuning parameters of the estimation filter is detailed for the proposed scenarios and the numerical simulations results are analyzed. Two realistic scenarios are defined for the validation: (A) bias-type errors are assumed calibrated and compensated and (B) a nominal scenario for the PROBA-2 mission in which the biases are only approximately calibrated. The results obtained for the Scenario A demonstrate that the technique can achieve RSS position error of less than 2 km, a RSS attitude error of less than 1.4 degree and a time of convergence of less than 2 orbits. Finally, further improvements, expected to be implemented prior to the PROBA-2 launch, are proposed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".