A Geometric Approach For Pose and Velocity Estimation Using IMU and Inertial/Body-Frame Measurements
Bibliographic record
Abstract
This paper addresses accurate pose estimation (orientation and position) and linear velocity for a rigid body using a combination of generic inertial-frame and/or body-frame measurements along with an Inertial Measurement Unit (IMU). By embedding the original state space SO(3)× ℝ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>× ℝ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> into the higher-dimensional Lie group SE<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf>(3), we reformulate the state dynamics and measurement models within a structured geometric framework. This embedding enables a natural decoupling of the geometric error dynamics, where the translational error dynamics exhibit a structure analogous to that of a continuous-time Kalman filter, allowing for a time-varying gain design based on the continuous Riccati equation. Under the assumption of uniform observability, we establish that the proposed observer on SE<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf>(3) guarantees almost-global asymptotic stability. The effectiveness of the approach is demonstrated in simulations for a practical scenario of GPS-aided inertial navigation systems (INS). Overall, the proposed method significantly simplifies the design of nonlinear geometric observers for INS, offering a unified and robust approach to state estimation.
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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 | 0.001 | 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 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".