Interpretable Gradient Descent for Kalman Gain
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908461049053184 |
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| author | Belabbas, M. A. Olshevsky, A. |
| author_facet | Belabbas, M. A. Olshevsky, A. |
| contents | We derive a decomposition for the gradient of the innovation loss with respect to the filter gain in a linear time-invariant system, decomposing as a product of an observability Gramian and a term quantifying the ``non-orthogonality" between the estimation error and the innovation. We leverage this decomposition to give a convergence proof of gradient descent to the optimal Kalman gain, specifically identifying how recovery of the Kalman gain depends on a non-standard observability condition, and obtaining an interpretable geometric convergence rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpretable Gradient Descent for Kalman Gain Belabbas, M. A. Olshevsky, A. Optimization and Control Systems and Control We derive a decomposition for the gradient of the innovation loss with respect to the filter gain in a linear time-invariant system, decomposing as a product of an observability Gramian and a term quantifying the ``non-orthogonality" between the estimation error and the innovation. We leverage this decomposition to give a convergence proof of gradient descent to the optimal Kalman gain, specifically identifying how recovery of the Kalman gain depends on a non-standard observability condition, and obtaining an interpretable geometric convergence rate. |
| title | Interpretable Gradient Descent for Kalman Gain |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2507.14354 |