An Adaptive Kalman Filter for Spacecraft Formation Navigation using Maximum Likelihood Estimation with Intrinsic Smoothing
Bibliographic record
Abstract
In the interests of enhancing autonomous navigation capabilities for Low Earth Orbit formation flying, this work presents the development of an Adaptive Extended Kalman Filter (AEKF) that estimates relative position and velocity states between two spacecraft. A standard EKF based on the nonlinear dynamics of relative motion is used to provide preliminary state estimates of the formation, which are then corrected through a fixed-window smoothing routine. Since uncertainties in the process and measurement noise covariances within the filter inherently limit the final accuracy of the EKF, an online tuning mechanism is derived using Maximum Likelihood Estimation (MLE) to optimize the noise covariances given an available set of measurements. Inclusion of these adaptations improves filter robustness by allowing the filter to handle situations where noise characteristics of the system are unknown or subject to change, while simultaneously eliminating the need for the initial manual covariance tuning process that accompanies EKF design. Numerical validation of the proposed algorithm is completed by comparing navigation solutions from the AEKF with those obtained from the non-adaptive EKF, using a realistic in-plane elliptical spacecraft formation.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".