An Efficient Global Optimality Certificate for Landmark-Based SLAM
Bibliographic record
Abstract
Modern state estimation is often formulated as an optimization problem and solved using efficient local search methods. These methods at best guarantee convergence to local minima, but, in some cases, global optimality can also be certified. Although such global optimality certificates have been well established for 3Dpose-graph optimization, the details have yet to be worked out for the 3D landmark-based SLAM problem, in which estimated states include both robot poses and map landmarks. In this letter, we address this gap by using a graph-theoretic approach to cast the subproblems of landmark-based SLAM into a form that yields a sufficient condition for global optimality. Efficient methods of computing the optimality certificates for these subproblems exist, but first require the construction of a large data matrix. We show that this matrix can be constructed with complexity that remains linear in the number of landmarks and does not exceed the state-of-the-art computational complexity of one local solver iteration. We demonstrate the efficacy of the certificate on simulated and real-world landmark-based SLAM problems. We also integrate our method into the state-of-the-art SE-Sync pipeline to efficiently solve landmark-based SLAM problems to global optimality. Finally, we study the robustness of the global optimality certificate to measurement noise, taking into consideration the effect of the underlying measurement graph.
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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 | 0.003 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 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".