In this article, a rapid sensor fault diagnosis (SFD) method is presented for a class of nonlinear systems. First, by exploiting the linear adaptive observer technology and the deterministic learning method (DLM), an adaptive neural network (NN) observer is constructed to capture the information of the unknown sensor fault function. Second, when the NN input orbit is a period or recurrent one, the partial persistent excitation (PE) condition of the NNs can be guaranteed through the DLM. Based on the partial PE condition and the uniformly completely observable property of a linear time-varying system, the accurate state estimation and the sensor fault identification can be achieved by properly choosing the observer gain. Third, a bank of dynamical observers utilizing the experiential knowledge is constructed to achieve rapid SFD and data recovery. The attractions of the proposed approach are that accurate approximations of sensor faults can be achieved through the DLM, and the data that are destroyed by the sensor faults can be recovered by using the learning results. Simulation studies of a robot system are utilized to show the effectiveness of the proposed method.