This paper addresses the challenges of Simultaneous Localization and Mapping (SLAM) in robotics, focusing on the development and implementation of a Particle Filter SLAM (PF-SLAM) method. The authors, from various institutions in the United States and Spain, leverage encoded data, fiber optic gyro (FOG) information, and lidar technology to enhance the accuracy of vehicle motion estimation and environmental perception. The PF-SLAM framework integrates these data streams to effectively navigate and map dynamic environments, overcoming the "chicken-and-egg" dilemma where accurate mapping and localization are interdependent. The paper details the problem formulation, implementation, and technical approach, including the motion and observation models, and demonstrates the effectiveness of the PF-SLAM algorithm through real-world experiments. The results show promising performance in map construction and localization, highlighting the practical implications and potential applications in autonomous navigation and robotics.This paper addresses the challenges of Simultaneous Localization and Mapping (SLAM) in robotics, focusing on the development and implementation of a Particle Filter SLAM (PF-SLAM) method. The authors, from various institutions in the United States and Spain, leverage encoded data, fiber optic gyro (FOG) information, and lidar technology to enhance the accuracy of vehicle motion estimation and environmental perception. The PF-SLAM framework integrates these data streams to effectively navigate and map dynamic environments, overcoming the "chicken-and-egg" dilemma where accurate mapping and localization are interdependent. The paper details the problem formulation, implementation, and technical approach, including the motion and observation models, and demonstrates the effectiveness of the PF-SLAM algorithm through real-world experiments. The results show promising performance in map construction and localization, highlighting the practical implications and potential applications in autonomous navigation and robotics.