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

A New Kalman Filter Model for Nonlinear Systems Based on Ellipsoidal Bounding