Invariant Momentum-tracking Kalman Filter for attitude estimation
Why this work is in the frame
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Bibliographic record
Abstract
This paper presents the development, simulation and experimental testing of a non-linear Kalman filter for attitude estimation. This non-linear filter is able to conserve the invariants of the Kalman filter, i.e., the expectations on state estimates and their covariances, by operating in the Lie algebra of SO(3) and along the trajectory of evolving angular momentum. The main feature of this novel discrete-time filter is that the linearization of the Gaussian uncertainty around these permanent trajectories leads to a locally optimal Kalman gain matrix. Results confirm that this Invariant Momentum-tracking Kalman Filter (IMKF) out-performs state-of-the-art approaches such as the Extended Kalman Filter (EKF), and Invariant Extended Kalman Filter (IEKF). At very-low sampling rates, EKFs suffer from divergence as the uncertainty propagation is corrupted by the underlying system approximations. The IMKF suffers no such problems according to the theoretical developments and results reported here.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it