  Disturbance noises are always bounded in a practical system, while fusion
estimation is to best utilize multiple sensor data containing noises for the
purpose of estimating a quantity--a parameter or process. However, few results
are focused on the information fusion estimation problem under bounded noises.
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 are unknown
but bounded. When considering linear time-varying fusion systems with bounded
noises, a new local Kalman-like estimator is designed such that the square
error of the estimator is bounded as time goes to $\infty$. 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, according to the
design method of linear time-varying fusion systems, 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. Finally, target tracking system and
localization of a mobile robot are given to show the advantages and
effectiveness of the proposed methods.
