A Novel Robust Kalman Filter Based on Normal-Bernoulli Distribution for Non-Stationary Heavy-Tailed Measurement Noise
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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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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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