Nonlinear state estimation under bounded noises

Abstract

Most of the existing nonlinear state estimation methods require to know the statistical information of noises. However, the statistical information may not be accurately obtained or satisfied in practical applications. Actually, the noises are always bounded in a practical system. In this paper, we study the nonlinear state estimation problem under bounded noises, where the addressed noises do not provide any statistical information, and the bounds of noises are also unknown. By using matrix analysis and second-order Taylor series expansion, a novel constructive method is proposed to find an upper bound of the square error of the nonlinear estimator. Then, a convex optimization problem on the design of an optimal estimator gain is established in terms of linear matrix inequalities, which can be solved by standard software packages. Moreover, stability conditions are derived such that the square error of the designed nonlinear estimator is asymptotically bounded. Finally, two illustrative examples are employed to show the advantages and effectiveness of the proposed methods.