A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and is unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local stable Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to ∞. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Moreover, a stability condition is also derived for the designed nonlinear estimator. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods.