Multi-Sensor Multi-Source Localization under Clutter and Uncertainty

Multi-source localization from time difference of arrival measurements in sensor networks is challenging in the presence of clutter, timing uncertainty, missed detections, and an unknown number of sources. We propose a combinatorial framework that jointly addresses these challenges by evaluating feasible subsets of detections, referred to as coalitions. Each coalition is assigned an associated cost defined as the ℓ∞-norm of the time difference of arrival residuals. We retain coalitions whose residual lies below a user-specified pseudorange threshold, providing a physically interpretable control of coalition feasibility. Coalition selection is performed using a family of set packing algorithms, including greedy and binary integer linear programming formulations with cost-based and lexicographic objectives. The lexicographic variants maximize sensor consensus by prioritizing, from largest to smallest cardinality, the number of selected disjoint detection coalitions, and break ties by minimizing the sum of coalition costs. This provides a unified, geometrically consistent framework for joint data association based on maximized sensor consensus, clutter suppression, source counting, and localization. The methods are benchmarked using Monte Carlo simulations under varying levels of clutter, time jitter, and missed detections, as well as using an acoustic dataset recorded in an urban environment.