Navigating with highly precise odometry and noisy GPS: a case study**This work is supported by the company Safran.
Bibliographic record
Abstract
: For linear systems, the Kalman filter perfectly handles rank deficiencies in the process noise covariance matrix, i.e., deterministic information. Yet, in a nonlinear setting this poses great challenges to the extended Kalman filter (EKF). In this paper we consider a simplified nonlinear car model with deterministic dynamics, i.e., perfect odometry, and noisy position measurements. Simulations evidence the EKF, when used as a nonlinear observer, 1- fails to correctly encode the physical implications of the deterministic dynamics 2- fails to converge even for arbitrarily small initial estimation errors. On the other hand, the invariant (I)EKF, a variant of the EKF that accounts for the symmetries of the problem 1- correctly encodes the physical implications of the deterministic information 2-is mathematically proved to (almost) globally converge, with explicit convergence rates, whereas the EKF does not even locally converge in our simulations. This study more generally suggests the IEKF is way more natural than the EKF, for high precision navigation purposes.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".