We discuss the localization of radiation sources whose number and other relevant parameters are not known in advance. The data collection is ensured by an autonomous mobile robot that performs a survey in a defined region of interest populated with static obstacles. The measurement trajectory is information-driven rather than pre-planned, and the localization exploits a regularized particle filter estimating the sources' parameters continuously. Regarding the dynamic robot control, this switches between two modes, one attempting to minimize the Shannon entropy and the other aiming to reduce the variance of expected measurements in unexplored parts of the target area; both of the modes maintain safe clearance from the obstacles. The performance of the algorithms was tested in a simulation study based on real-world data acquired previously from three radiation sources exhibiting various activities. Our approach reduces the time necessary to explore the region and to find the sources by approximately 40~\%; at present, however, the method is unable to reliably localize sources that have a relatively low intensity. In this context, additional research has been planned to increase the credibility and robustness of the procedure and to improve the robotic platform autonomy.