🤖 AI Summary
This paper addresses the distributed set-membership filtering (SMF) problem for multi-agent systems with mixed absolute and relative measurements, where the primary challenge lies in modeling coupling uncertainties induced by relative measurements. To tackle this, we propose an “uncertainty interval” set representation, enabling the first single-step exact set-theoretic characterization of relative measurement uncertainties. We then develop two distributed SMF frameworks—joint and marginal—and rigorously prove, from a set-projection perspective, that both are equivalent to the minimal outer approximation of the centralized SMF onto their respective subspaces. Theoretical analysis shows that the marginal framework significantly reduces communication and computational overhead. Numerical simulations confirm its competitive estimation accuracy and robustness against bounded uncertainties. This work establishes a general, provably correct, and computationally efficient paradigm for distributed set-membership estimation under heterogeneous, multi-source measurements.
📝 Abstract
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.
