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The complexity of agent localization increases significantly when unique identification of the agents is not possible. Corresponding application cases include multiple-source localization, in which the agents do not have identification sequences at all, and scenarios in which it is infeasible to send sufficiently long identification sequences, e.g., for highly resource-limited agents. The complexity increase is due to the need to solve an additional optimization problem to resolve the indifferentiability of the agents and thus to enable their localization. In this work, we present a thorough analysis of this problem and propose a maximum a posteriori (MAP)-optimal algorithm based on graph decompositions and expression trees. The proposed algorithm efficiently exploits the fixed-parameter tractability of the underlying graph-theoretical problem and employs dynamic programming and backtracking. We show that the proposed algorithm is able to reduce the run time by up to 88.3% compared with a corresponding MAP-optimal integer linear programming formulation.

Backtracking-based dynamic programming for resolving transmit ambiguities in WSN localization