Consistent Fusion of Correlated Pose Estimates on Matrix Lie Groups
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Pose fusion on the Special Euclidean groups ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$SE(n)$</tex-math></inline-formula> ) plays a key role in the localization of ground/aerial vehicles. However, for consistent fusion of pose estimates, the enduring correlation problem due to the observation of a common noise-corrupted process is yet to be addressed. We develop a methodology for the consistent fusion of correlated pose estimates that optimizes a quadratic cost function encompassing both self- and cross-correlation of local pose estimates. The error terms are calculated relative to a reference estimate and approximated using the Baker-Campbell-Hausdorff formula to obtain a non-iterative solution on the Lie algebra. The dependency of the fusion on the cross-covariance matrices is addressed via explicitly computing them through a recursive propagation of estimation errors at local extended Kalman filters. The efficacy of the proposed methodology is demonstrated by several numerical experiments conducted to (i) rigorously investigate the effect of correlation degree between local estimates on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$SE(3)$</tex-math></inline-formula> and (ii) solve the localization problem of a rover on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$SE(2)$</tex-math></inline-formula> with available pseudo pose measurements.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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