Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems
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Bibliographic record
Abstract
We present the Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of control-affine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference computational cost that is independent of the number of training points. We lift the original nonlinear system into a higher-dimensional Reproducing Kernel Hilbert Space (RKHS), where the system becomes bilinear. The time-invariant model matrices can be learned by solving a least-squares problem on training trajectories. At test time, the system is algebraically manipulated into a linear time-varying system, where standard batch linear state estimation techniques can be used to efficiently compute state means and covariances. Random Fourier Features (RFF) are used to combine the computational efficiency of Koopman-based methods and the generality of kernel-embedding methods. KoopSE is validated experimentally on a localization task involving a mobile robot equipped with ultra-wideband receivers and wheel odometry. KoopSE estimates are more accurate and consistent than the standard model-based extended Rauch-Tung-Striebel (RTS) smoother, despite KoopSE having no prior knowledge of the system’s motion or measurement models.
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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