Angular Velocity Estimation From the Angular Acceleration Matrix
Bibliographic record
Abstract
Computing the angular velocity ω from the angular acceleration matrix is a nonlinear problem that arises when one wants to estimate the three-dimensional angular velocity of a rigid-body from point-acceleration measurements. In this paper, two new methods are proposed, which compute estimates of the angular velocity from the symmetric part WS of the angular acceleration matrix. The first method uses a change of coordinate frame of WS prior to performing the square-root operations. The new coordinate frame is an optimal representation of WS with respect to the overall error amplification. In the second method, the eigenvector spanning the null space of WS is estimated. As ω lies in this space, and because its magnitude is proportional to the absolute value of the trace of WS, it is a simple matter to obtain ω. A simulation shows that, for this example, the proposed methods are more accurate than those existing methods that use only centripetal acceleration measurements. Moreover, their errors are comparable to other existing methods that combine tangential and centripetal acceleration measurements. In addition, errors of 2.15% in the accelerometer measurements result in errors of approximately 3% in the angular-velocity estimates. This shows that accelerometers are competitive with angular-rate sensors for motions of the type of the simulated example, provided that position and orientation errors of the accelerometers are accounted for.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".