## 1 Introduction  
Simultaneous Localization and Mapping (SLAM) technology [1] is a pivotal component in the realms of autonomous driving and mobile robotics, endowing robots with the capability for autonomous navigation in uncharted environments and forming the foundation for advanced robotic functionalities such as environmental comprehension, decision-making, and path planning. By fusing data from a variety of sensors, including LiDAR, cameras, and Inertial Measurement Units (IMUs) [2], SLAM technology enables the real-time construction of detailed maps of the surrounding environment while precisely localizing the robot itself. This capability is essential for the long-term autonomous operation of robots in dynamic environments. As technology continues to evolve, SLAM is becoming an indispensable part of intelligent infrastructure, propelling innovation and development across the automation industry [3]. Consequently, research and optimization of SLAM technology have profound implications for the future development of intelligent systems. Despite the vast potential of SLAM technology, its implementation in dynamic, complex, and unknown environments poses significant technical challenges. Particularly in highly dynamic settings, the rapid changes in the environment demand greater adaptability and robustness from SLAM algorithms. Additionally, ensuring algorithmic precision while enhancing its responsiveness to environmental alterations is an issue that urgently needs addressing in current SLAM research [4]. Therefore, developing SLAM algorithms that maintain high accuracy and robustness across various environments is crucial for propelling the field forward. FastSLAM [5], recognized as an efficient solution for the SLAM problem, adeptly manages nonlinear and non-Gaussian noise challenges by harnessing the combined power of particle filtering and the Extended Kalman Filter (EKF) [6]. Gaussian noise, also known as white noise, is a type of noise that follows a Gaussian distribution, which is characterized by a bell-shaped curve and is widely used in signal processing due to its simple and predictable properties. However, in many real-world applications, the noise encountered is non-Gaussian, meaning it does not adhere to a Gaussian distribution, thereby presenting more complex challenges for SLAM algorithms. This algorithm strategically divides the SLAM problem into two core components: the estimation of the pose of the robot and the estimation of environmental landmarks. Particle filtering is tasked with addressing the nonlinear aspects of pose estimation while the EKF independently processes each landmark, a decomposition that substantially reduces computational complexity and enables scalability in large-scale environments. However, FastSLAM encounters particle degradation issues under conditions of large-scale environments and high noise, which can diminish the diversity of particles and potentially hinder the ability to effectively explore the entire state space [7]. This degradation phenomenon, characterized by increasing insignificance of the weights of most particles over filtering iterations, with only a few particles retaining substantial weight, leads to a posterior probability that is predominantly represented by these few particles. Consequently, this not only results in a waste of computational resources but also poses a risk to the estimation accuracy, thereby limiting the broader applicability of FastSLAM. This contribution is significant for applications where traditional Gaussian-based models fall short of capturing the true nature of the underlying processes. Another method is the fractional \(\alpha\)-stable filter [8], which introduces an adaptive filtering structure grounded in \(\alpha\)-stable statistics and fractional-order calculus to address the state estimation problem in the presence of non-Gaussian noise, effectively enhancing the estimation accuracy of rapidly changing systems.