Performance diagnosis of local filters in state estimation of nonlinear systems

The paper deals with state estimation of nonlinear stochastic discrete-time systems with a special focus on filters providing a point estimate of the state. The aim is concentrated on performance diagnosis of the filters, which should inform about a possible decrease of estimate quality provided by the filter. The paper proposes a diagnostics of the filter performance using the non-Gaussianity measures. More specifically, the paper focuses on a third-order moment based non-Gaussianity measure and provides relations for its recursive computation. It is shown that this measure can effectively be used for the performance diagnosis of the filters, which is illustrated using a numerical example. The example considers tracking motion of a ship using the extended Kalman filter.