A hierarchical wavelet decomposition for continuous-time SLAM
Bibliographic record
Abstract
This paper proposes using hierarchical wavelets as a basis in parametric continuous-time batch estimation. The need for a continuous-time robot pose in the simultaneous localization and mapping (SLAM) problem has arisen as state-of-the-art batch SLAM algorithms attempt to handle more challenging hardware; specifically, the continuous-time framework is particularly beneficial when using high-rate sensors, multiple unsynchronized sensors, or scanning sensors, such as lidar and rolling-shutter cameras, during motion. Although the traditional discrete-time SLAM formulation can be adapted by using temporal pose interpolation, approaches using the continuous-time framework are able to generate smooth robot trajectories with less state variables. In this paper, we focus on the parametric approach using temporal basis functions to develop a finite-element representation of the continuous-time robot trajectory. While the majority of current implementations have utilized a uniformly spaced B-spline basis, we note that trajectory richness is often quite variable; in this paper, we show how a hierarchical system of wavelet basis functions can be used to increase the resolution of the solution only in the temporally local regions of the trajectory that require additional detail. We validate our approach by contrasting uniform B-splines and wavelets in a six-dimensional pose-graph SLAM experiment, using both simulated and real data.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".