{"ID":2848654,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.03740","arxiv_id":"2511.03740","title":"Kalman-Bucy Filtering with Randomized Sensing: Fundamental Limits and Sensor Network Design for Field Estimation","abstract":"Stability analysis of the Kalman filter under randomly lost measurements has been widely studied. We revisit this problem in a general continuous-time framework, where both the measurement matrix and noise covariance evolve as random processes, capturing variability in sensing locations. Within this setting, we derive a closed-form upper bound on the expected estimation covariance for continuous-time Kalman filtering. We then apply this framework to spatiotemporal field estimation, where the field is modeled as a Gaussian process observed by randomly located, noisy sensors. Using clarity, introduced in our earlier work as a rescaled form of the differential entropy of a random variable, we establish a grid-independent lower bound on the spatially averaged expected clarity. This result exposes fundamental performance limits through a composite sensing parameter that jointly captures the effects of the number of sensors, noise level, and measurement frequency. Simulations confirm that the proposed bound is tight for the discrete-time Kalman filter, approaching it as the measurement rate decreases, while avoiding the recursive computations required in the discrete-time formulation. Most importantly, the derived limits provide principled and efficient guidelines for sensor network design problem prior to deployment.","short_abstract":"Stability analysis of the Kalman filter under randomly lost measurements has been widely studied. We revisit this problem in a general continuous-time framework, where both the measurement matrix and noise covariance evolve as random processes, capturing variability in sensing locations. Within this setting, we derive...","url_abs":"https://arxiv.org/abs/2511.03740","url_pdf":"https://arxiv.org/pdf/2511.03740v2","authors":"[\"Xinyi Wang\",\"Devansh R. Agrawal\",\"Dimitra Panagou\"]","published":"2025-10-29T16:07:19Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"cs.MA\"]","methods":"[]","has_code":false}