A Novel Robust Kalman Filter Based on Normal-Bernoulli Distribution for Non-Stationary Heavy-Tailed Measurement Noise
Bibliographic record
Abstract
In this paper, the state estimation problem with non-stationary heavy-tailed measurement noise (NHMN) is considered. The mixture of two Gaussian distributions, with a Bernoulli random variable, is expressed as an exponential multiplication form, which we refer to as the Normal-Bernoulli (NB) distribution. We utilize the marginalization of the NB (MNB) distribution to model NHMN, leading to the derivation of a robust NB-based Kalman filter that does not require any iterative process. In contrast to conventional algorithms, the analytical closed-form solutions for the states and modeling distribution parameters are derived by using Bayes’ rule and minimizing the Kullback-Leibler divergence. The first two order moments of MNB-distributed state posterior are then calculated as filtering outputs. Simulation results demonstrate the superiority of the proposed filter in terms of estimation accuracy, consistency, and computational complexity under NHMN.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".