Invariant Trapezoidal Kalman Filter for Application to Attitude Estimation
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Bibliographic record
Abstract
This paper incorporates formal concepts of invariance of numerical integration schemes into the design of Kalman filters. In general terms, invariant discretizations of dynamical systems can form the basis for the derivation of the covariance propagation during the prediction and update phases of a Kalman filter, and this paper presents a framework to that effect. Specifically, natural invariants of angular motion are introduced, as part of a symmetry-preserving trapezoidal integration rule, to form the basis for the derivation of a discrete-time invariant Kalman filter for an attitude estimation problem. The proposed filter is realized by expressing all zero-mean random variables in the Lie algebra, while the state manipulations are performed in special orthogonal group 3. Simulation and experimental results are obtained using a neutrally buoyant spherical blimp to validate the proposed method against state-of-the-art Kalman filters in a broad range of angular speeds and sampling rates. Furthermore, the results support claims of invariance of the estimator with respect to angular speed, as well as the preservation of the system’s symmetries through the covariance calculations.
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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