Non-Asymptotic State and Input Estimation for Smooth Linear Parameter Varying Systems
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Bibliographic record
Abstract
This note explains the advantage of employing integral system representations of linear systems in application to state and input estimation for a broad class of LPV systems. Integral (kernel) representations of linear systems are seen as vehicles for retaining local information about the system's input-output behaviour in which the notion of initial or boundary conditions play no role. An important by-product of kernel system representations is their capacity for reconstruction of time derivatives of the measured system output by using the kernel derivatives. These attributes immediately lead to the construction of kernel-based dead-beat state and parameter estimators for linear systems. The approach is extended here to LPV systems with measured scheduling parameters, or else LPV systems in which the scheduling parameters cannot be measured directly, but whose values may be inferred from the output observations of other, possibly nonlinear, dynamical systems. It is shown that the lack of knowledge of the system input does not prejudice successful state estimation provided that the system has strong observability properties that effectively permit input reconstruction in a suitable B-spline basis. The method also applies to nonlinear smooth systems that can be transformed to LPV systems with dynamically varying parameters. An example of a strongly nonlinear system is presented for which the extended Kalman filter is known to fail.
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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