Three-stage unscented Kalman filter for state and fault estimation of nonlinear system with unknown input

As the fault and unknown inputs may cause great estimate errors and even divergence for conventional filters when dealing with nonlinear discrete-time systems, this paper proposed a three-stage unscented Kalman filter (ThSUKF) and robust three-stage unscented Kalman filter (RThSUKF) to improve the performance by estimating the state and fault simultaneously. The detail derivation of the filters is illustrated in the paper. The proposed filters are available when the statistic models of the fault and unknown inputs are perfectly known. But if there is no prior knowledge about the fault and unknown input, RThSUKF can also have a great performance. Their performance and effectiveness are demonstrated by the numerical simulation of two-dimensional target tracking. And the results show that ThSUKF and RThSUKF can achieve superior performances with low estimation errors if the nonlinear systems are in presence of fault and unknown inputs.