{"ID":2893251,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.14354","arxiv_id":"2507.14354","title":"Interpretable Gradient Descent for Kalman Gain","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.","short_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 giv...","url_abs":"https://arxiv.org/abs/2507.14354","url_pdf":"https://arxiv.org/pdf/2507.14354v2","authors":"[\"M. A. Belabbas\",\"A. Olshevsky\"]","published":"2025-07-18T20:20:06Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}