State estimation under operational uncertainty in water distribution systems

Effective management of water distribution systems (WDSs) requires timely knowledge of system-wide hydraulic conditions. As utilities deploy increasing numbers of pressure and flow sensors, state estimation (SE) has emerged as a powerful tool for inferring hydraulic states in WDSs, including at unmonitored locations, by integrating sensor measurements with hydraulic models. However, most existing studies consider smoothly varying uncertainties, such as pipe roughness and customer demands, while overlooking uncertainties associated with control devices and operational control rules. Because these operational factors induce strong, system-wide hydraulic changes, existing SE approaches struggle to generalize across varying operating conditions. To address this challenge, we propose a correlation-aware covariance formulation within the Extended Kalman Filter (Corr-EKF) that leverages hydraulic connectivity and spatial correlations among hydraulic states to propagate measurement information throughout the WDS. Corr-EKF incorporates operational information as soft information within the estimation process, enabling both smoothly varying and operational sources of uncertainty to be represented in a unified estimation framework. We systematically compare Corr-EKF with alternative EKF approaches based on uncorrelated uncertainty assumptions and hard boundary constraints. Tested on a complex WDS benchmark using synthetic observations, Corr-EKF substantially improves head and flow estimation accuracy relative to existing EKF approaches. The results demonstrate the importance of accounting for operational uncertainty in state estimation under varying operating conditions.