This paper presents a framework addressing the challenge of global localization in autonomous mobile robotics by integrating LiDAR-based descriptors and Wi-Fi fingerprinting in a pre-mapped environment. This is motivated by the increasing demand for reliable localization in complex scenarios, such as urban areas or underground mines, requiring robust systems able to overcome limitations faced by traditional Global Navigation Satellite System (GNSS)-based localization methods. By leveraging the complementary strengths of LiDAR and Wi-Fi sensors used to generate predictions and evaluate the confidence of each prediction as an indicator of potential degradation, we propose a redundancy-based approach that enhances the system's overall robustness and accuracy. The proposed framework allows independent operation of the LiDAR and Wi-Fi sensors, ensuring system redundancy. By combining the predictions while considering their confidence levels, we achieve enhanced and consistent performance in localization tasks.