This study proposes a new Gaussian Mixture Filter (GMF) to improve the estimation performance for the autonomous robotic radio signal source search and localization problem in unknown environments. The proposed filter is first tested with a benchmark numerical problem to validate the performance with other state-of-the-practice approaches such as Particle Filter (PF) and Particle Gaussian Mixture (PGM) filters. Then the proposed approach is tested and compared against PF and PGM filters in real-world robotic field experiments to validate its impact for real-world applications. The considered real-world scenarios have partial observability with the range-only measurement and uncertainty with the measurement model. The results show that the proposed filter can handle this partial observability effectively whilst showing improved performance compared to PF, reducing the computation requirements while demonstrating improved robustness over compared techniques.