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Finding the source of an accidental or deliberate release of a toxic substance into the atmosphere is of great importance for national security. The paper presents a search algorithm for turbulent environments which falls into the class of cognitive (infotaxi) algorithms. Bayesian estimation of the source parameter vector is carried out using the Rao–Blackwell dimension-reduction method, while the robots are controlled autonomously to move in a scalable formation. Estimation and control are carried out in a centralised replicated fusion architecture assuming all-to-all communication. The paper presents a comprehensive numerical analysis of the proposed algorithm, including the search-time and displacement statistics.