DC programming based ellipsoid bounding algorithm for guaranteed state estimation

This paper presents a new ellipsoid bounding algorithm in the framework of the set-membership filter for real-time state estimation of nonlinear systems with bounded-error assumptions. The nonlinear model of the system is linearized as the normal extended Kalman filter does, but the linearization errors are taken into account and outer bounded strictly by DC programming approach, which will be propagated to the model errors with ellipsoidal approximations. An ellipsoid bounding algorithm composed of ellipsoid summing and iterative ellipsoid-strip intersection steps is proposed to give the feasible set estimation of the states in which they are guaranteed to lie, with some approximations to keep the trade-off between the computation complexity and conservativeness of the whole algorithm. Simulation results are given by comparing our proposed algorithm to the extended set-membership algorithm to show the performance improvements of the new algorithm.