Dynamic targets directly affect the localization accuracy and mapping quality of light detection and ranging-based simultaneous localization and mapping (LiDAR SLAM), thereby posing potential safety risks to practical applications such as autonomous navigation and spatial planning. However, existing studies generally have limitations such as reliance on heuristic thresholds, requirement for abundant features, complex model structures, and inadequate real-time performance. Therefore, this paper proposes a robust cascaded method for point cloud motion state determination. First, a sliding window containing six frames of point cloud data is constructed. Based on the clustering results of each frame within the window, a dual centroid registration strategy is adopted to establish continuous matching relationships for point cloud clusters belonging to the same target. On this basis, five unit-length relative position change vectors and point cloud density change vectors are constructed respectively. Second, the local outlier factor (LOF) is used to mark as stable static those point cloud clusters whose relative position change vectors cluster near the zero vector. Among the remaining clusters, those whose point cloud density change vectors cluster near the zero vector are marked as stable dynamic. Finally, this study adaptively optimizes the kernel density estimation (KDE) algorithm to acquire the peak distribution of coordinates inside point cloud clusters, and evaluates peak stability within the window to distinguish unstable static or dynamic point cloud clusters caused by occlusion or field of view changes. Furthermore, after each window update, the point cloud clusters already marked as dynamic are no longer subjected to the aforementioned motion state judgment process, thereby greatly reducing the processing time. Experiments show that the correct detection rate of dynamic point clouds in this study reaches 0.928 2, the false detection rate of static point clouds is only 0.043 6, and the single-frame point cloud processing time is 28.15 ms. In actual measurement scenes, its performance is generally superior to that of comparative methods, and it exhibits stronger robustness and applicability.