Distributed Zonotopic Fusion Estimation for Multisensor Systems

Fusion estimation is widely applied in multi-sensor systems to provide accurate state information, which is crucial for designing efficient control and decision-making strategies. Despite their ability to accommodate unknown noise statistics, set-membership approaches to fusion estimation are still in an early stage of development, especially zonotopic fusion estimation, which is highly advantageous given its computational efficiency and superior representational granularity. 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 based on several zonotope fusion criteria. We first propose 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 through the analytical solution of an optimization problem. To reduce the conservatism of the DZFE with optimal parameters, we introduce an improved zonotope fusion criterion, which further improves the estimation performance by constructing tight strips for the intersection. In addition, we tackle the problem of handling sequentially arrived local estimates in realistic communication environments by introducing a sequential zonotope fusion criterion. This sequential zonotope fusion offers reduced computational complexity compared to batch zonotope fusion. The proposed zonotope fusion criteria are designed to meet the state inclusion property and to achieve superior performance compared with 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 demonstrate the effectiveness and advantages of the proposed methods.