Towards Optimal Beacon Placement for Range-Aided Localization
Bibliographic record
Abstract
Range-based localization is ubiquitous: global navigation satellite systems (GNSS) power mobile phone-based navigation, and autonomous mobile robots can use range measurements from a variety of modalities including sonar, radar, and even WiFi signals. Many of these localization systems rely on fixed anchors or beacons with known positions acting as transmitters or receivers. In this work, we answer a fundamental question: given a set of positions we would like to localize, how should beacons be placed so as to minimize localization error? Specifically, we present an information-theoretic method for optimally selecting an arrangement consisting of a few beacons from a large set of candidate positions. By formulating localization as maximum a posteriori (MAP) estimation, we can cast beacon arrangement as a submodular set function maximization problem. This approach is probabilistically rigorous, simple to implement, and extremely flexible. Furthermore, we prove that the submodular structure of our problem formulation ensures that a greedy algorithm for beacon arrangement has suboptimality guarantees. We compare our method with a number of benchmarks on simulated data and release an open source Python implementation of our algorithm and experiments.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".