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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, therelative measurements are difficult to deal with, and the SMFs highly rely onspecific set descriptions. As a result, establishing the general distributedSMFing framework having relative measurements is still an open problem. Tosolve this problem, first, we provide the set description based on uncertainvariables determined by the relative measurements between two agents as thefoundation. Surprisingly, the accurate description requires only a singlecalculation step rather than multiple iterations, which can effectively reducecomputational complexity. Based on the derived set description, called theuncertain range, we propose two distributed SMFing frameworks: one calculatesthe joint uncertain range of the agent itself and its neighbors, while theother only computes the marginal uncertain range of each local system.Furthermore, we compare the performance of our proposed two distributed SMFingframeworks and the benchmark -- centralized SMFing framework. A rigorous setanalysis reveals that the distributed SMF can be essentially considered as theprocess of computing the marginal uncertain range to outer bound the projectionof the uncertain range obtained by the centralized SMF in the correspondingsubspace. Simulation results corroborate the effectiveness of our proposeddistributed frameworks and verify our theoretical analysis.

Distributed Set-membership Filtering Frameworks For Multi-agent Systems With Absolute and Relative Measurements