Nonlinear Explicit Stochastic Attitude Filter on SO(3)
Bibliographic record
Abstract
This work proposes a nonlinear stochastic filter evolved on the Special Orthogonal Group SO(3) as a solution to the attitude filtering problem. One of the most common potential functions for nonlinear deterministic attitude observers is studied and reformulated to address the noise attached to the attitude dynamics. The resultant estimator and correction factor demonstrate convergence properties and remarkable ability to attenuate the noise. The stochastic dynamics of the attitude problem are mapped from SO(3) to Rodriguez vector. The proposed stochastic filter evolved on SO(3) guarantees that errors in the Rodriguez vector and estimates steer very close to the neighborhood of the origin and that the errors are semi-globally uniformly ultimately bounded in mean square. Simulation results illustrate the robustness of the proposed filter in the presence of high uncertainties in measurements. Keywords: Attitude, estimate, estimator, observer, filter, stochastic differential equations, SDEs, Ito, Rodriguez vector, special orthogonal group, Euler angles, Brownian motion process, Angle-axis, Mapping, Parameterization, Representation, Partial derivative, asymptotic, unknown, time-varying, global, stable, stability, uncertain, white noise, Gaussian, colored, bias, vectorial, vector measurement, angular velocity, rotational matrix, identity, orientation, body frame, inertial frame, rigid body, three dimensional, micro electromechanical systems, Gyroscope, sensor, Inertial measurement units, IMUs, MEMS, Roll, Pitch, Yaw, autonomous, Robotic System, Spacecraft, submarine, Vehicles, Robot, Underwater vehicle, derivative, explicit complementary filter.
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How this classification was reachedexpand
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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".