Three examples of the stability properties of the invariant extended Kalman filter
Bibliographic record
Abstract
In the aerospace industry the (multiplicative) extended Kalman filter (EKF) is the most common method for sensor fusion for guidance and navigation. However, from a theoretical point of view, the EKF has been shown to possess local convergence properties only under restrictive assumptions. In a recent paper, we proved a slight variant of the EKF, namely the invariant extended Kalman filter (IEKF), when used as a nonlinear observer, possesses local convergence properties under the same assumptions as those of the linear case, for a class of systems defined on Lie groups. This is especially interesting as the IEKF also retains all the desirable features of the standard EKF, especially its relevant tuning in the presence of noises. In the present paper we provide three examples of engineering interest where the theory is shown to apply, yielding three EKF-like algorithms with guaranteed local convergence properties. Beyond those contributions, the present article is sufficiently accessible to help the practitioner understand through concrete examples the general IEKF theory, and to provide him with guidelines for the design of IEKFs.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".