This paper adresses the problem of simultaneously estimating the state and the fault of nonlinear discrete-time stochastic systems in light of the unknown input filtering framework. The fault and unknown disturbances which may cause great estimate errors and even divergence of conventional filters, affect both the system state and the measurements. Inspired by the robust two stage Kalman filter for linear discrete-time system, a nonlinear robust state and fault estimator is derived. In order to achieve the aim, the nonlinear system with fault and unknown disturbances is first transformed into an equivalent descriptor system. Next, it is shown that the previously proposed robust two stage Kalman filter can be applied to yield a robust state and fault estimation. Simulation results for a robotic manipulator show the effectiveness of the proposed method.