Interpretable Gradient Descent for Kalman Gain

M. A. Belabbas; A. Olshevsky

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arXiv · 2507.14354

Interpretable Gradient Descent for Kalman Gain

M. A. Belabbas·A. Olshevsky

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Abstract

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.

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BibTeX RIS

M. A. Belabbas, A. Olshevsky. 2025-07-18. Interpretable Gradient Descent for Kalman Gain. https://arxiv.org/abs/2507.14354

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