An Extended Kalman Filter for Systems with Infinite-Dimensional Measurements
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912601528598528 |
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| author | Varley, Maxwell M. Molloy, Timothy L. Nair, Girish N. |
| author_facet | Varley, Maxwell M. Molloy, Timothy L. Nair, Girish N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Extended Kalman Filter for Systems with Infinite-Dimensional Measurements Varley, Maxwell M. Molloy, Timothy L. Nair, Girish N. Systems and Control Robotics 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. |
| title | An Extended Kalman Filter for Systems with Infinite-Dimensional Measurements |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2509.18749 |