To enhance the detection performance of infrared targets for low-altitude, slow-moving, and small (LSS) UAVs under complex background interference, a spatio-temporal correlation-based detection method is proposed. This approach addresses both single-frame static object detection and dynamic trajectory prediction. First, for static detection in single frames, improvements are made to the YOLOv8 algorithm to mitigate the loss of fine-grained information typically caused by downsampling. This is achieved by introducing a no-stride convolutional layer and a P2 detection head, thereby enhancing the capability to detect small targets. Second, for dynamic trajectory prediction, a Kalman filter is employed to estimate and track the UAV's motion trajectory. By integrating this prediction module with the single-frame detector, the system can maintain target localization even when detection confidence drops. Based on confidence evaluation, the system adaptively switches to the trajectory prediction mode to ensure continuous tracking. Temporal correlation is further reinforced by aligning target information across consecutive frames and enabling inter-frame information interaction, effectively establishing spatio-temporal associations. Experimental results show that the improved YOLOv8-P2-SPD model achieves an average precision (mAP@0.5) of 86.8% for single-frame detection. Under challenging backgrounds such as clouds, mountains, and urban structures, the proposed spatio-temporal correlation method improves detection accuracy by 12.1% and recall by 12.2% compared to single-frame detection alone. This approach effectively addresses the limitations of conventional deep learning models in detecting LSS targets under complex background interference and is well-suited for real-world deployment in such scenarios.