A Koopman Operator-Based Finite Impulse Response Filter for Nonlinear Systems
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Bibliographic record
Abstract
This paper proposes a novel Koopman operator-based finite impulse response (KFIR) filter for nonlinear dynamic systems. This filter is generalized from the minimum variance unbiased (MVU) FIR filter for linear systems by using a global linear approximation of the nonlinear dynamics obtained from Koopman operator theory and the extended dynamic mode decomposition (EDMD) algorithm. Based on the recursive linear model, a reduced-order FIR filtering structure is proposed, and the optimal gain is derived to minimize the trace of the estimation error covariance. Unlike traditional methods, the KFIR filter requires no prior knowledge of the initial state and fully utilizes the data of a moving horizon. Simulation results show that the proposed filter has excellent robustness against unexpected modeling uncertainties and inaccurate noise information, making it suitable for real applications.
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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