In this paper, we focus on the distributed set-membership filtering (SMFing) problem for a multi-agent system with absolute (taken from agents themselves) and relative (taken from neighbors) measurements. In the literature, the relative measurements are difficult to deal with, and the SMFs highly rely on specific set descriptions. As a result, establishing the general distributed SMFing framework having relative measurements is still an open problem. To solve this problem, first, we provide the set description based on uncertain variables determined by the relative measurements between two agents as the foundation. Surprisingly, the accurate description requires only a single calculation step rather than multiple iterations, which can effectively reduce computational complexity. Based on the derived set description, called the uncertain range, we propose two distributed SMFing frameworks: one calculates the joint uncertain range of the agent itself and its neighbors, while the other only computes the marginal uncertain range of each local system. Furthermore, we compare the performance of our proposed two distributed SMFing frameworks and the benchmark -- centralized SMFing framework. A rigorous set analysis reveals that the distributed SMF can be essentially considered as the process of computing the marginal uncertain range to outer bound the projection of the uncertain range obtained by the centralized SMF in the corresponding subspace. Simulation results corroborate the effectiveness of our proposed distributed frameworks and verify our theoretical analysis.

翻译：本文聚焦于具有绝对测量（来源于智能体自身）与相对测量（来源于邻居）的多智能体系统的分布式集员滤波问题。现有文献中，相对测量难以处理，且集员滤波高度依赖特定的集合描述方式。因此，建立包含相对测量的一般性分布式集员滤波框架仍是一个开放性问题。为解决该问题，我们首先以基于两智能体间相对测量所确定的不确定变量为基础，构建集合描述方法。令人惊讶的是，精确描述仅需单步计算而非多次迭代，这能有效降低计算复杂度。基于所推导的集合描述（称为不确定范围），我们提出两种分布式集员滤波框架：一种计算智能体自身与其邻居的联合不确定范围，另一种仅计算各局部系统的边际不确定范围。此外，我们将所提出的两种分布式集员滤波框架与基准——集中式集员滤波框架进行性能比较。严格的集合分析表明，分布式集员滤波本质上可视为计算边际不确定范围以在对应子空间中外逼近集中式集员滤波所得不确定范围投影的过程。仿真结果验证了所提分布式框架的有效性，并证实了我们的理论分析。