In this paper, we propose a tighter set-membership filter for some nonlinear dynamic systems by using an analytic method and a boundary sampling technique. The nonlinear dynamic systems can be linearized about the current estimate, then the remainder term is bounded in real time by an optimization ellipsoid, other than a priori remainder bound. For a 2-D radar system and a quadratic system, some regular properties can be derived for the remainder term, which helps us obtain a tighter bounding ellipsoid to cover the remainder. Moreover, the prediction step and the measurement update step are derived based on the recent optimization method and the on-line bounding ellipsoid of the remainder, so that a tighter set-membership filter can be achieved. The numerical examples demonstrate the effectiveness of the proposed filter.