The deployment of mobile robots to conduct search for radioactive sources plays a crucial role in preventing radiation pollution and safeguarding public health. And it is a significant challenge to accurately locate radioactive sources in unknown environments. Herein, a particle filter based on mobile robot search method is proposed to localize radiation sources. By applying an angle constraint technique, the complexity of this algorithm is reduced, the high accuracy of source estimation is maintained, and the range of search is expanded. Additionally, a particle diffusion technology is applied to address particle loss that occurs during filtering. Furthermore, an adaptive gradient descent strategy is adopted to enhance the search efficiency. Experimental results demonstrate that this method achieves a success rate of over 95 % within a rectangular area (e.g., 40m by 40m), outperforming traditional methods, and it could perform effectively in dual radioactive source search tasks.