{"ID":2867002,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.18749","arxiv_id":"2509.18749","title":"An Extended Kalman Filter for Systems with Infinite-Dimensional Measurements","abstract":"This article examines state estimation in discrete-time nonlinear stochastic systems with finite-dimensional states and infinite-dimensional measurements, motivated by real-world applications such as vision-based localization and tracking. We develop an extended Kalman filter (EKF) for real-time state estimation, with the measurement noise modeled as an infinite-dimensional random field. When applied to vision-based state estimation, the measurement Jacobians required to implement the EKF are shown to correspond to image gradients. This result provides a novel system-theoretic justification for the use of image gradients as features for vision-based state estimation, contrasting with their (often heuristic) introduction in many computer-vision pipelines. We demonstrate the practical utility of the EKF on a public real-world dataset involving the localization of an aerial drone using video from a downward-facing monocular camera. The EKF is shown to outperform VINS-MONO, an established visual-inertial odometry algorithm, in some cases achieving mean squared error reductions of up to an order of magnitude.","short_abstract":"This article examines state estimation in discrete-time nonlinear stochastic systems with finite-dimensional states and infinite-dimensional measurements, motivated by real-world applications such as vision-based localization and tracking. We develop an extended Kalman filter (EKF) for real-time state estimation, with...","url_abs":"https://arxiv.org/abs/2509.18749","url_pdf":"https://arxiv.org/pdf/2509.18749v1","authors":"[\"Maxwell M. Varley\",\"Timothy L. Molloy\",\"Girish N. Nair\"]","published":"2025-09-23T07:47:32Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"cs.RO\"]","methods":"[]","has_code":false}