Algorithms are proposed for real-time state estimation of nonlinear systems with unknown disturbances. An optimal estimate of the state is determined so as to minimize a receding-horizon performance index that includes estimate of unknown disturbances. Application of the stabilized continuation method results in algorithms that do not involve any successive approximation methods. One of the proposed algorithms is examined in numerical simulation of a two-wheeled mobile robot. Simulation results clarify characteristics of the algorithm. The performance of the present algorithm is compared with that of an algorithm that does not take disturbances into account.