This article investigates the issue of distributed state estimation for a nonlinear hydraulic system. Our objective is to propose a distributed algorithm that enables individual nodes to obtain a global state estimation by utilizing local measurements and information gathered from neighboring nodes. We ensure global optimality by designing a mechanism for information exchange between neighboring nodes. The state estimation acquired by our distributed algorithm is equivalent to that of the centralized extended Kalman filter within a finite time. Our proposed algorithm is effective for acyclic network graphs and can be applied to cyclic network graphs through the loop removal approach. In addition, we provide a stability analysis of the proposed distributed algorithm. Finally, experiments on the practical platform are conducted to verify the feasibility and merits of the proposed algorithm.