Confidence regions for multi-sensor state estimation under faulty measurements

The paper deals with state estimation of nonlinear dynamic stochastic systems under faulty measurements. The special focus is laid on defining and constructing a confidence region for the state estimate. The construction of the region is motivated by traditional approaches to fault detection based on parity equations and the region is designed by using a geometry perspective to provide a hyper-sphere centered at the state estimate. Consequently, it is proven that the proposed confidence region contains the state with a probability that serves as a design parameter of the region. The construction of the confidence region is illustrated in an example dealing with positioning a moving object using bearing measurements.