Unknown input observer is one of the most famous strategies for robust fault diagnosis of linear systems, but studies on nonlinear cases are not sufficient. On the other hand, the extended Kalman filter (EKF) is wellknown in nonlinear estimation, and its convergence as an observer of nonlinear deterministic system has been derived recently. By combining the EKF and the unknown input Kalman filter, we propose a robust nonlinear estimator called unknown input EKF (UIEKF) and prove its convergence as a nonlinear robust observer under some mild conditions using linear matrix inequality (LMI). Simulation of a three-tank system "DTS200", a benchmark in process control, demonstrates the robustness and effectiveness of the UIEKF as an observer for nonlinear systems with uncertainty, and the fault diagnosis based on the UIEKF is found successful.