## 5 Conclusions  
A novel multidimensional fuzzy clustering algorithm (MDF-clustering) is proposed for initializing point target trajectories in complex environments. The algorithm effectively determines the trajectory's affiliation degree by extracting the multidimensional features of the target, integrating the clustering center and weight assignment, and subsequently updating the clustering center and weights. Experimental results demonstrate that this method significantly enhances the accuracy and robustness of trajectory initialization when compared to traditional approaches in environments characterized by high clutter and target maneuvers. This improvement is evidenced by enhancements in the average number of stable initialization frames, the rate of correct trajectory initialization, and a minimal false trajectory occupancy rate. Consequently, the MDF-clustering algorithm elevates the performance of trajectory initialization, thereby improving the overall efficiency and reliability of the tracking system. This advancement holds substantial practical significance for target tracking in complex environments. While the MDF-clustering algorithm achieves notable improvements, several limitations remain. One key limitation is its sensitivity to the initialization of clustering centers, which could impact performance in highly dynamic environments with varying clutter densities. Additionally, although the algorithm integrates an adaptive clustering mechanism, further enhancements may be needed to better handle extreme clutter conditions or highly dense target environments. Moreover, when applying the algorithm to larger datasets or real-time systems, there could be some challenges. In particular, the computational complexity may result in a slight increase in processing time, leading to occasional delays in real-time applications. However,  
Figure 13: Miss rate of various algorithms with different false alarm rates in cloud background scenarios. this delay is not expected to be overly significant but may cause minor latency in systems that require very rapid updates. Similarly, while the memory usage remains efficient for moderate datasets, processing large-scale multi-dimensional data could result in increased memory consumption, particularly in environments with limited computational resources. Though these impacts are not critical, they warrant consideration when deploying the algorithm in real-time, high-demand environments. Future research could explore optimizing the algorithm to address these challenges and ensure better performance in such scenarios. For future research, we propose the following directions:  
1. Real-time system optimization: While the algorithm shows strong performance in experimental conditions, further optimization is needed to enhance its efficiency for real-time applications, particularly in scenarios involving fast-moving, closely spaced targets. 2. Improving robustness under dense clutter: We plan to explore techniques that further reduce false alarm rates in environments where the density of noise or clutter is exceptionally high. 3. Advanced error handling in multi-target scenarios: Extending the algorithm's capability to handle more complex multi-target tracking problems, where targets frequently cross paths or exhibit highly erratic movement, will be a focus of future work. 4. Integration of KAN for improved trajectory initialization: KAN, which integrates domain knowledge with data-driven models, has shown great potential in predictive modeling for complex physical systems, including recent advancements in human-robot interaction. Building on recent advancements in the KAN method, particularly its successful application in human-robot interaction [31], we aim to explore its integration into trajectory initialization tasks.