A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

TL;DR

This paper develops a novel distributed fusion estimation framework for linear and nonlinear systems with bounded noises, providing bounded error guarantees and optimal fusion criteria without relying on statistical noise models.

Contribution

It introduces a new local Kalman-like estimator for linear systems and a Taylor series-based nonlinear estimator, along with convex optimization methods for optimal fusion under bounded noise conditions.

Findings

Bounded estimation error achieved for linear systems.

Effective nonlinear fusion estimator derived using Taylor expansion.

Validated on target tracking and robot localization tasks.

Abstract

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.