Effect of Sensor Noise on Estimation of Diffusion**The financial support of the National Science and Engineering Research Council of Canada Discovery Grant program for the research discussed in this article is gratefully acknowledged.
Bibliographic record
Abstract
A Kalman filter is commonly used for state estimation. It is optimal in that the variance of the error is minimized by the estimator. In this paper the problem of optimal sensor location is combined with estimator design to obtain a sensor placement that minimizes the error variance. The question of whether of a larger number of inaccurate sensors, that is those with large noise variance, can provide as good an estimate as a single highly accurate (but probably more expensive) sensor. This question can be investigated with the assumption that all the selected sensors are placed optimally. Estimation of the state of a one-dimensional diffusion equation with three different disturbances is examined in this context. Despite the difference among disturbances, similar proportional relations between the sensor noise variance and the estimation error are observed in numerical simulations. Furthermore, it appears that multiple low quality sensors can lead to better estimation than a single high quality sensor, provided that enough sensors are used.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".