Differentiable Adaptive Kalman Filtering via Optimal Transport
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912530548391936 |
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| author | He, Yangguang Li, Wenhao Li, Minzhe Zhang, Juan Wang, Xiangfeng Jin, Bo |
| author_facet | He, Yangguang Li, Wenhao Li, Minzhe Zhang, Juan Wang, Xiangfeng Jin, Bo |
| contents | Learning-based filtering has demonstrated strong performance in non-linear dynamical systems, particularly when the statistics of noise are unknown. However, in real-world deployments, environmental factors, such as changing wind conditions or electromagnetic interference, can induce unobserved noise-statistics drift, leading to substantial degradation of learning-based methods. To address this challenge, we propose OTAKNet, the first online solution to noise-statistics drift within learning-based adaptive Kalman filtering. Unlike existing learning-based methods that perform offline fine-tuning using batch pointwise matching over entire trajectories, OTAKNet establishes a connection between the state estimate and the drift via one-step predictive measurement likelihood, and addresses it using optimal transport. This leverages OT's geometry - aware cost and stable gradients to enable fully online adaptation without ground truth labels or retraining. We compare OTAKNet against classical model-based adaptive Kalman filtering and offline learning-based filtering. The performance is demonstrated on both synthetic and real-world NCLT datasets, particularly under limited training data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07037 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differentiable Adaptive Kalman Filtering via Optimal Transport He, Yangguang Li, Wenhao Li, Minzhe Zhang, Juan Wang, Xiangfeng Jin, Bo Machine Learning Signal Processing Learning-based filtering has demonstrated strong performance in non-linear dynamical systems, particularly when the statistics of noise are unknown. However, in real-world deployments, environmental factors, such as changing wind conditions or electromagnetic interference, can induce unobserved noise-statistics drift, leading to substantial degradation of learning-based methods. To address this challenge, we propose OTAKNet, the first online solution to noise-statistics drift within learning-based adaptive Kalman filtering. Unlike existing learning-based methods that perform offline fine-tuning using batch pointwise matching over entire trajectories, OTAKNet establishes a connection between the state estimate and the drift via one-step predictive measurement likelihood, and addresses it using optimal transport. This leverages OT's geometry - aware cost and stable gradients to enable fully online adaptation without ground truth labels or retraining. We compare OTAKNet against classical model-based adaptive Kalman filtering and offline learning-based filtering. The performance is demonstrated on both synthetic and real-world NCLT datasets, particularly under limited training data. |
| title | Differentiable Adaptive Kalman Filtering via Optimal Transport |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2508.07037 |