Set-Membership Filtering with Quadratic Inequality Constraints

This paper investigates the problem of set membership filtering for nonlinear dynamic systems with general nonconvex inhomogeneous quadratic inequality constraints. We propose an ellipsoidal state bounding estimation in the setting of unknown but bounded noise. To guarantee the on-line usage, at each time step, the nonlinear function is linearized by Taylor expansion, where the bounding ellipsoid of the remainder is updated on-line based on the current state bounding ellipsoid. Moreover, based on the remainder bounds and the constraints, both the state prediction and measurement update of the filtering can be transformed to a semidefinite programming problem which can be solved efficiently. A typical numerical example demonstrates the effectiveness of this filtering.