Batch Bayesian auto-tuning for nonlinear Kalman estimators
Bibliographic record
Abstract
The optimal performance of nonlinear Kalman estimators (NKEs) depends on properly tuning five key components: process noise covariance, measurement noise covariance, initial state noise covariance, initial state conditions, and dynamic model parameters. However, the traditional auto-tuning approaches based on normalized estimation error squared or normalized innovation squared cannot efficiently estimate all NKE components because they rely on ground truth state models (usually unavailable) or on a subset of measured data used to compute the innovation errors. Furthermore, manual tuning is labor-intensive and prone to errors. In this work, we introduce an approach called batch Bayesian auto-tuning (BAT) for NKEs. This novel approach enables using all available measured data (not just those selected for generating innovation errors) during the tuning process of all NKE components. This is done by defining a comprehensive posterior distribution of all NKE components given all available measured data outside of the NKE recursive process based on the equivalence between the posterior distributions used in batch and recursive Bayesian inference. Our empirical validation on a synthetic bioprocess dataset demonstrates that BAT significantly improves the consistency and accuracy of NKE estimations compared to baseline methods. These findings indicate that BAT can effectively optimize NKE tuning, improving performance and reliability in practical applications.
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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 | 0.004 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".