Finite-interval kernel-based identification and state estimation for LTI systems with noisy output data
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Bibliographic record
Abstract
This note extends previous results pertaining to algebraic state and parameter estimation of linear systems based on a special construction of kernel system representations that incorporate system differential invariants. Main results include explicit expressions for the kernel functions for single-input, single-output LTI systems of arbitrary order. A recursive regression type algorithm is also proposed for the purpose of joint system identification and finite interval filtering. As compared with previous results the proposed non-asymptotic estimation method proves remarkably robust to Gaussian noise in output measurements. The approach has been shown to extend to linear time-varying and linear parameter-varying systems in a multivariate setting. The idea of system-related kernels can further be employed to enhance convergence properties of moving-window and minimum energy nonlinear filtering methods.
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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