## 1 Introduction  
Multi-target tracking is widely used in surveillance, autonomous driving, and military applications. Given the escalating complexity of the global security landscape, the significance of this technology within the military domain has become increasingly pronounced, particularly in military early warning, battlefield situational awareness, and target reconnaissance. Multi-target tracking is an essential technology in modern military operations, significantly improving operational efficiency, precision, and real-time strategic decision-making [1]. Recent sensor and image processing advancements introduced novel algorithms for tracking maneuvering targets. For instance, [PERSON] et al. [2] proposed a novel method to enhance the accuracy and efficiency of maneuvering target tracking by analyzing and processing sensor data in intricate environments. Similarly, [PERSON] et al. [3] introduced a concave optimization-based initialization method for multi-target tracking, leveraging optimization algorithms to improve target identification and classification during the early stages. [PERSON] et al. [4] developed a multi-frame tracking pre-detection algorithm tailored to scenarios characterized by high dynamic variations and low signal-to-noise ratios, thereby addressing the complexities of maneuver target tracking. Additionally, [PERSON] et al. [5] devised a multi-model estimator for tracking sharply maneuvering ground targets, enhancing tracking accuracy through the integration of multiple motion models to adapt to rapid changes in target motion. Current methods work well in certain cases but struggle to generalize across environments and target types. The trajectory initialization process, as a crucial aspect of target tracking [6], serves as a digital representation of a natural physical phenomenon. It is essential for describing, analyzing, and solving problems related to tracking maneuvering targets. The method converts sensor data into a digital format, enabling dynamic target analysis. Trajectory initialization not only plays a key role in efficient target tracking and monitoring but also significantly impacts various aspects of tracking, such as accuracy, prediction capability, and responsiveness to complex airspace situations. Therefore, the efficiency and accuracy of trajectory initialization are vital for real-time data processing, flight tracking [7], and long-term target motion prediction and analysis. Researching effective and stable trajectory initialization methods is crucial for target detection and tracking, especially in scenarios with solid clutter. Efficient initialization of trajectory parameters is essential for ensuring stable and accurate tracking systems. Enhancing the universality, accuracy, and response speed of trajectory initialization algorithms directly influences the stability and practicality of tracking systems. Trajectory initialization methods are categorized as batch or sequential processing [8]. Sequential processing techniques, such as the intuitive method, logic-based method, and modified logic method, are suitable for clutter-free scenes. On the other hand, batch processing techniques, like the Hough transform, suit high-clutter scenarios. Various trajectory initialization algorithms have been proposed in the literature. [PERSON] [9] introduced a method based on kinematics to determine if measured data belongs to the same target. [PERSON] et al. [10] enhanced the trajectory initialization algorithm by incorporating constraints in the correlation domain to eliminate V-shaped measurement point traces. [PERSON] et al. [11] improved the traditional correlation wave gate structure with angular constraints using a modified Hough transform for batch processing. [PERSON] et al. [12] developed a trajectory initialization algorithm that combines the Hough transform and the 3/4 logic method. [PERSON], [PERSON] et al.