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Correlation filter (CF)-based methods have demonstrated exceptional performance in visual object tracking for unmanned aerial vehicle (UAV) applications, but suffer from the undesirable boundary effect. To solve this issue, spatially regularized correlation filters (SRDCF) proposes the spatial regularization to penalize filter coefficients, thereby significantly improving the tracking performance. However, the temporal information hidden in the response maps is not considered in SRDCF, which limits the discriminative power and the robustness for accurate tracking. This work proposes a novel approach with dynamic consistency pursued correlation filters, i.e., the CPCF tracker. Specifically, through a correlation operation between adjacent response maps, a practical consistency map is generated to represent the consistency level across frames. By minimizing the difference between the practical and the scheduled ideal consistency map, the consistency level is constrained to maintain temporal smoothness, and rich temporal information contained in response maps is introduced. Besides, a dynamic constraint strategy is proposed to further improve the adaptability of the proposed tracker in complex situations. Comprehensive experiments are conducted on three challenging UAV benchmarks, i.e., UAV123@10FPS, UAVDT, and DTB70. Based on the experimental results, the proposed tracker favorably surpasses the other 25 state-of-the-art trackers with real-time running speed ($\sim$43FPS) on a single CPU.