Continuous-time batch trajectory estimation using temporal basis functions
Bibliographic record
Abstract
Roboticists often formulate estimation problems in discrete time for the practical reason of keeping the state size tractable; however, the discrete-time approach does not scale well for use with high-rate sensors, such as inertial measurement units, rolling-shutter cameras, or sweeping laser imaging sensors. The difficulty lies in the fact that a pose variable is typically included for every time at which a measurement is acquired, rendering the dimension of the state impractically large for large numbers of measurements. This issue is exacerbated for the simultaneous localization and mapping problem, which further augments the state to include landmark variables. To address this tractability issue, we propose to move the full Maximum-a-Posteriori estimation problem into continuous time and use temporal basis functions to keep the state size manageable. We present a full probabilistic derivation of the continuous-time estimation problem, derive an estimator based on the assumption that the densities and processes involved are Gaussian and show how the coefficients of a relatively small number of basis functions can form the state to be estimated, making the solution efficient. Our derivation is presented in steps of increasingly specific assumptions, opening the door to the development of other novel continuous-time estimation algorithms through the application of different assumptions at any point. We use the simultaneous localization and mapping problem as our motivation throughout the paper, although the approach is not specific to this application. Results from two experiments are provided to validate the approach: (i) self-calibration involving a camera and a high-rate inertial measurement unit, and (ii) perspective localization with a rolling-shutter camera.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".