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

Authors

Ligang Sun, Leibniz University HannoverFollow
Hamza Alkhatib, Leibniz University HannoverFollow
Boris Kargoll, Leibniz University HannoverFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Ingo Neumann, Leibniz University HannoverFollow

Publication Date

2-2018

Comments

Technical Report: UTEP-CS-18-10

Abstract

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.