Bibliographic record
Abstract
This chapter covers the Kalman filter and its variants. Kalman filter is the optimal Bayesian filter in the sense of minimizing the mean-square estimation error for linear systems with Gaussian noise. Algorithms that extend the applicability of the Kalman filter to nonlinear systems either use power series to approximate the nonlinear functions in the state-space model or use numerical methods to approximate the corresponding probability distributions. While the extended Kalman filter and the divided-difference filter belong to the former category of algorithms, the unscented Kalman filter and the cubature Kalman filter belong to the latter. Information filter and extended information filter provide alternative formulations of the Kalman filter and the extended Kalman filter by recursively updating the inverse of the estimation error covariance matrix. Using a mixture of Gaussians to approximate the posterior, the Gaussian-sum filter extends the applicability of the Kalman filter to non-Gaussian systems. In the Kalman filter algorithm, the corrective term is reminiscent of the proportional controller. The generalized proportional-integral-derivative (PID) filter uses a more sophisticated corrective term inspired by the PID controller. Finally, a number of applications of Kalman filtering algorithms are reviewed including information fusion, augmented reality, urban traffic network, cybersecurity of power systems, incidence of influenza, and COVID-19 pandemic.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.026 | 0.022 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".