Distributed ToA Localization of Acoustic Sources with Unknown Time of Emission via Operator Splitting
Localization of non-cooperative acoustic sources using multiple spatially distributed receivers is critical for applications such as marine-life tracking, search-and-rescue operations, and maritime security in underwater environments. In conventional Time of Arrival (ToA) systems, the emission time is typically known explicitly or implicitly through clock synchronization or two-way communication, so the problem reduces to range-based localization. In passive settings, however, only reception timestamps are available. Thus, the emission time must be eliminated through Time Difference of Arrival (TDoA) preprocessing or estimated jointly with the source position. For the case of a single source, we address the distributed localization problem over a receiver network by reformulating passive localization directly as a ToA problem with unknown time of signal emission. This yields a distributed consensus optimization problem, which we solve using an operator-splitting method, namely an edge-based Distributed Alternating Direction Method of Multipliers (DADMM) scheme that decomposes the estimation task into local subproblems coupled through agreement constraints. We derive closed-form local update equations for the local DADMM subproblems and establish convergence properties for a smoothed approximation of the measurement model. Numerical simulations illustrate the efficacy of the proposed approach.