A New Nonlinear Set Membership Filter Based on Guaranteed Bounding Ellipsoid Algorithm

Abstract

The framework of set membership filter (SMF) with unknown-but-bounded noise assumption provides an attractive alternative for probabilistic filters. However, the potential computational burden and conservation consideration may seriously limit the usage of this filter in practical applications. In this paper, based on guaranteed bounding ellipsoid approximation, a new enhanced set membership filter with better real-time property and reduced conservation is proposed for state estimation problem of nonlinear systems. The nonlinear model is firstly linearized and the DC programming method is used to outer-bound the linearization error, which is incorporated to the model noise with ellipsoidal approximations. A classical two-step prediction-correction procedure consisting vector sum computation between ellipsoids and an iterative outer-bounding ellipsoid algorithm to intersect ellipsoid with strip is presented to compute the ellipsoidal feasible set of the estimated states. Simulation results with comparisons to the nonlinear extended set membership filter are given to demonstrate the effectiveness and improved performances of our proposed algorithm.