Dual Set Membership Filter with Minimizing Nonlinear Transformation of Ellipsoid

TL;DR

This paper introduces a dual set membership filter for nonlinear systems that uses semi-infinite programming to find tight ellipsoids, improving computational efficiency and accuracy in state estimation.

Contribution

The paper proposes a novel dual set membership filter leveraging semi-infinite programming and Frank-Wolfe method for nonlinear systems, enhancing efficiency and accuracy.

Findings

Effective in mobile robot localization

Computationally efficient with lower complexity

Provides tighter ellipsoid bounds

Abstract

In this paper, we propose a dual set membership filter for nonlinear dynamic systems with unknown but bounded noises, and it has three distinctive properties. Firstly, the nonlinear system is translated into the linear system by leveraging a semi-infinite programming, rather than linearizing the nonlinear function. In fact, the semi-infinite programming is to find an ellipsoid bounding the nonlinear transformation of an ellipsoid, which aims to compute a tight ellipsoid to cover the state. Secondly, the duality result of the semi-infinite programming is derived by a rigorous analysis, then a first order Frank-Wolfe method is developed to efficiently solve it with a lower computation complexity. Thirdly, the proposed filter can take advantage of the linear set membership filter framework and can work on-line without solving the semidefinite programming problem. Furthermore, we apply the dual set membership filter to a typical scenario of mobile robot localization. Finally, two illustrative examples in the simulations show the advantages and effectiveness of the dual set membership filter.