2025/10/29 by Xinyi Wang, Wang, Xinyi, Devansh R. Agrawal +3
Computer Science · #Distributed Control Multi-Agent Systems #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #Multiagent Systems (cs.MA) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2511.03740
openalex publication_date 2025/10/29 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28
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.