Estimation for nonlinear discrete-time systems with uncertain linearization and noises statistics

This paper presents an extended Kalman filter for discrete-time nonlinear systems subject to uncertainties. The proposed filter considers that the linearization of the nonlinear functions are unknown, but within a known set. The nonlinear functions are assumed to belong to a conic region. This condition is characterized as a Lipschitz condition on the system state, control signal and the noise residuals. The proposed design also allows dynamic and measurement noises to have unknown time-varying expected values, covariances and cross-covariances. The filter furnishes upper bounds for the variances of the a priori and a posteriori estimation errors for all allowed uncertainties.