  In this paper, a new filter model called set-membership Kalman filter for
nonlinear state estimation problems was designed, where both random and unknown
but bounded uncertainties were considered simultaneously in the discrete-time
system. The main loop of this algorithm includes one prediction step and one
correction step with measurement information, and the key part in each loop is
to solve an optimization problem. The solution of the optimization problem
produces the optimal estimation for the state, which is bounded by ellipsoids.
The new filter was applied on a highly nonlinear benchmark example and a
two-dimensional simulated trajectory estimation problem, in which the new
filter behaved better compared with extended Kalman filter results. Sensitivity
of the algorithm was discussed in the end.
