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Of growing concern for the security of many nations are numerous incidents of lost or stolen radioactive sources or materials. The detection of and search for these abnormal radioactive sources plays an important role in monitoring nuclear safety and disposal of nuclear waste. In this paper, a method for autonomously searching for radioactive sources in a flat open rectangular-shaped field through mobile platforms was proposed. In this method, by using the possibility particle filter, the search for radioactive sources was realized according to a series of radiation information measured by the mobile platform carrying a Geiger–Müller counter. According to the inverse square law and the radiation counting governed by Poisson distribution, a radioactive source localization model was constructed. Then, a mobile platform controlled by an information entropy strategy constantly moved within the search area and detected radiation at specific points. The possibility filter algorithm, implemented via the sequential Monte Carlo method, is used to update posterior probability distributions of the source parameters. The performance of the proposed search algorithm, including a comparison with a standard particle filter algorithm, is studied by simulations. The simulation experiment proves that the possibility particle filter algorithm has good robustness. The successful application of the experimental dataset collected in the simulations verifies the measurement model and theoretical consideration.