Localization of Wireless Sensors via Nuclear Norm for Rank Minimization
Bibliographic record
Abstract
The low rank feature of location estimation in Wireless Sensor Networks (WSNs) makes it feasible to use nuclear norm minimization as an accurate and fast solution for low-dimensional embedding problems. In this paper, a novel localization algorithm for WSNs is proposed by using nuclear norm for rank minimization. We formulate the location finding problem from only a small fraction of random entries of Euclidean Distance Matrix (EDM) as a low-rank matrix recovery problem, subject to a set of linear equality constraints. We show that a measurement matrix using orthogonal projection obeys the RIP and thus, supports a sufficient condition for the recovery of the low-rank matrix with overwhelming probability. For simplicity, Singular Value Thresholding (SVT) algorithm, a standard convex optimization approach, is used for the nuclear norm minimization. Simulation results demonstrate that in a 100 m × 100 m area, for a small scale network with 100 nodes, only 20% of measurements is needed to achieve a 0.5 m localization error, while 3% needed to achieve a 0.05 m error for a comparatively large scale network with 1000 nodes.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| 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".