Distributed Zonotopic Fusion Estimation for Multi-sensor Systems
Yuchen Zhang, Bo Chen, Zheming Wang, Wen-An Zhang, Li Yu, Lei Guo
TL;DR
The paper addresses robust state estimation in multi-sensor networks under bounded, possibly non-Gaussian noise by developing distributed zonotopic fusion estimators (DZFEs). It introduces a batch zonotopic fusion criterion with an analytical solution for the optimal fusion matrices $M^{\mathrm{opt}}(k)$, and an improved criterion that tightens the enclosure by constructing strips for the intersection, both guaranteeing the state inclusion property. To reduce computational load, a sequential zonotope fusion approach fuses local estimates in time order with its own optimal gains, while preserving inclusion and improving performance. A stability analysis shows ultimate boundedness under mild conditions, and two numerical examples (2D zonotopes and multi-sensor target tracking) demonstrate that the DZFEs outperform local estimates and that the sequential approach reduces computation time. These results offer a practical, scalable framework for robust distributed fusion in networked sensing applications, with potential extensions to cooperative localization and cyber-physical systems.
Abstract
Fusion estimation is often used in multi-sensor systems to provide accurate state information which plays an important role in the design of efficient control and decision-making. This paper is concerned with the distributed zonotopic fusion estimation problem for multi-sensor systems. The objective is to propose a zonotopic fusion estimation approach using different zonotope fusion criteria. We begin by proposing a novel zonotope fusion criterion to compute a distributed zonotopic fusion estimate (DZFE). The DZFE is formulated as a zonotope enclosure for the intersection of local zonotopic estimates from individual sensors. Then, the optimal parameter matrices for tuning the DZFE are determined by the analytical solution of an optimization problem. To reduce the conservatism of the DZFE with optimal parameters, we enhance our approach with an improved zonotope fusion criterion, which further improves the estimation performance of this DZFE by constructing tight strips for the intersection. In addition, we tackle the problem of handling sequentially arrived local estimates in realistic communication environments with a sequential zonotope fusion criterion. This sequential zonotope fusion offers reduced computational complexity compared to batch zonotope fusion. Notice that the proposed zonotope fusion criteria are designed to meet the state inclusion property and demonstrate performance superiority over local zonotopic estimates. We also derive stability conditions for these DZFEs to ensure their generator matrices are ultimately bounded. Finally, two illustrative examples are employed to show the effectiveness and advantages of the proposed methods.