Optimal sensor design for infinite-time Kalman filters
Why this work is in the frame
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Bibliographic record
Abstract
This paper is concerned with state estimation for systems governed by partial differential equations. Kalman filters are optimal state estimators in that they minimize the estimation error variance for given measurements. The focus of this paper is the achievement of additional minimization of the error variance by also optimizing over the sensor design. The optimal sensor design problem is thus incorporated into the estimation problem. Not only the sensor location but also other factors such as sensor shape and the effect of the sensors on system dynamics are included in the optimization criteria. The problem is first stated formally, and then it is shown to be well-posed and to possess an optimal solution. Applications to a one-dimensional diffusion equation and also to a two-dimensional wave equation are given. A computational framework for calculation of optimal shape is described.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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 it