## 1 Introduction
[13] presented a multi-hypothesis, multi-rule, adaptive trajectory initialization algorithm that filters clutter with a density clustering algorithm, retains historical information, and utilizes an adaptive initial period to suppress false targets. [PERSON] et al. [14] proposed a trajectory initialization algorithm based on adaptive gates and a fuzzy Hough transform, effectively reducing false alarms and achieving high-quality trajectory initialization. [PERSON] et al. [15] introduced a density-based random sample consensus (DB-RANSAC) algorithm for trajectory initialization in dense clutter environments, leveraging spatiotemporal domain information to enhance initialization efficiency. [PERSON] et al. [16] introduced a TSEPM algorithm that integrates multi-hypothesis tracking with a modified logic-based trajectory initialization method. This approach aims to enhance detection rates and decrease false alarms. In scenarios where trajectory initialization for weak targets in cluttered environments is challenging, conventional algorithms are often hindered by noise, frequent target ID changes, and difficulties in trajectory synthesis. These issues can lead to unstable initial feature parameters for the target, ultimately impacting the accuracy, stability, and robustness of subsequent tracking processes. The accuracy of these methods relies heavily on precise initial conditions and parameter settings, necessitating a comprehensive understanding of algorithms and application contexts for practical adjustments. Trajectory initialization is vital for obtaining trajectory parameters early and resolving issues from incorrect initial conditions. By optimizing these initial conditions and parameters, trajectory initialization helps mitigate the impact of environmental noise and other disturbances. As such, trajectory initialization not only enhances the accuracy and efficiency of target tracking but also serves as a fundamental strategy to overcome limitations in existing tracking methods and enhance algorithm adaptability and generalization. Recent advancements in predictive modeling, particularly in complex physical systems, have introduced methods that integrate domain knowledge with data-driven models. One such approach is the Kolmogorov-Arnold Network (KAN), which has shown great promise in improving the robustness and accuracy of systems operating in dynamic and noisy environments. KAN enables the incorporation of expert knowledge into the learning process, allowing for better handling of uncertainty and noise. This has been particularly effective in tasks such as trajectory initialization and human-robot interaction, where the system needs to adapt rapidly to changing conditions and high levels of environmental clutter. The field of target tracking has seen significant progress in recent years, especially in tackling challenges posed by cluttered environments and dynamic target behaviors. Current research demonstrates a growing emphasis on improving the robustness and adaptability of tracking algorithms. Techniques have become more sophisticated in handling noise interference and adapting to varying target motions. However, many approaches still face challenges in maintaining consistency across different environments. For instance, algorithms often perform well under controlled conditions but encounter difficulties when applied to more unpredictable or real-world scenarios. Furthermore, while accuracy has improved, issues related to false alarms and initialization delays persist. These limitations highlight the need for further advancements in achieving reliable, real-time tracking, especially in environments with high levels of clutter and target maneuverability. Despite these challenges, the continuous refinement of existing algorithms shows promising potential for future developments. This paper presents a trajectory initialization algorithm using multi-dimensional fuzzy clustering to solve challenges in cluttered environments and target maneuvers.