In practical applications within a Water-Energy Nexus, achieving full-state measurement is often infeasible due to limited sensor placement and the presence of measurement noise. This work proposes a robust framework for state estimation and control to overcome these real-world constraints. By leveraging Moving Horizon Estimation (MHE), the system is able to reconstruct unmeasured states, such as pressure head at nodes, and filter sensor noise in battery state-of-charge and water tank levels over a sliding past window. The proposed strategy integrates this MHE-based state reconstruction with a coordinated Model Predictive Control (MPC) to manage the coupled dynamics of Water Distribution Systems (WDS) and Power Distribution Systems (PDS). The MHE component utilizes a strategic measurement selection matrix to map available sensor data to the full state vector, providing a reliable initial condition for the MPC. The controller then optimizes an Optimal Water and Power Flow (OWPF) objective, ensuring hydraulic demand compliance and electrical voltage regulation while minimizing operational costs. This presentation details the mathematical formulation of the estimator and controller, focusing on ensuring feasibility and coordination in complex, partially observable nexus environments.