多弹道目标跟踪伴随着速度快、密集程度高以及测量误差大等因素,在跟踪过程中发生航迹中断是一个很普遍的现象。在未知导弹任何先验信息前提下如何将中断前后的航迹片段进行关联,提高航迹的连续性已成为亟待解决的难题。针对该问题提出了一种实时的离散最优关联算法,它利用速度信息对中断前后弹道外推航迹进行粗关联;将对数似然函数作为关联代价函数,采用拍卖算法完成关联代价函数的二维全局最优分配实现细关联并提高了关联概率;对关联上的航迹片段利用"窗口"统计最小误差方法进行优化,提高了整个航迹的连续性。仿真结果表明该算法能够将航迹平均周期提高1倍,在航迹中断期间对比最小二乘方法能够较大幅度地减小跟踪位置和速度的均方根(RMS)误差。
Track breakage is a common issue in a multiple ballistic target tracking scenario with high speeds, high densities and large measurement errors. How to improve the track continuity by associating the break track segments without any prior information is therefore a focus of research efforts. This paper proposes a real-time discrete optimal association algorithm which uses the velocity information to realize coarse association for extrapolation between the break track segments and improves the association probability by calculating the association cost function of trajectory segments using log-likelihood function and by adopting auction algorithm to realize 2D optimal assignment and fine association. Furthermore, the algorithm uses "Window" statistics method to calculate the minimum error in order to optimize the track continuity. Simulation results show that the proposed algorithm doubles the mean track life and yields significant improvements in position and speed root mean square RMS errors during the track breakage.
[1] Wang H, Kirubarajan T, Bar-Shalom Y. Large scale air traffic surveillance using IMM estimators with assignment [J]. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(1): 255-266.
[2] Kirubarajan. T, Bar-Shalom Y, Blair W D, et al. IMMPDAF for radar management and tracking benchmark with ECM [J]. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(4): 1115-1134.
[3] Yeom S W, Kirubarajan T, Bar-Shalom Y. Track segment association, fine-step IMM and initialization with Doppler for improved track performance[J]. IEEE Transactions on Aerospace and Electronic Systems, 2004, 40(1):293-309.
[4] Bar-Shalom Y, Li X R, Kirubarajan T. Estimation with applications to tracking and navigation[M]. New York: Wiley, 2001: 453-477.
[5] Bar-Shalom Y, Blair W D. Multitarget/multisensor tracking: applications and advances[M]. Vol. III. Norwood, MA: Artech House, 2000:267-295.
[6] William J F. Interacting multiple model filter for tactical ballistic missile tracking [J]. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(2): 418-426.
[7] Benavoli A, Chisci L, Farina A. Tracking of a ballistic missile with a-prior information[J]. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(3): 1000-1016.
[8] Harlin W J, Cicci D A. Ballistic missile trajectory prediction using a state transition matrix[J]. Applied Mathematics and Computation, 2007, 188(2):1832-1847.
[9] Rao B, Zhao Y L, Xiao S P, et al. Discrimination of exo-atmospheric active decoys using acceleration information[J]. IET Radar, Sonar and Navigation, 2010, 4(4):626-638.
[10] Li X R, Jilkov V P. Survey of maneuvering target tracking. Part II: motion models of ballistic and space targets[J]. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(1): 96-119.
[11] 俞建国, 刘梅, 武云丽, 等. 基于非对称交互式多模型弹道导弹跟踪[J]. 系统工程与电子技术, 2010, 32(12): 2570-2575. Yu Jianguo, Liu Mei, Wu Yunli, et al. Ballistic missile tracking based on asymmetric interacting multiple models[J]. Journal of Systems Engineering and Electronics, 2010, 32(12): 2570-2575. (in Chinese)
[12] 何友, 修建娟, 张晶炜, 等. 雷达数据处理及应用[M]. 2版. 北京:电子工业出版社, 2009:35-37, 66-74. He You, Xiu Jianjuan, Zhang Jingwei, et al. Radar data process and application[M]. 2nd ed. Beijing: Electronic Industry Press, 2009: 35-37, 66-74. (in Chinese)
[13] 金文彬, 刘永祥, 黎湘, 等. 再入目标质阻比估计算法研究[J]. 国防科技大学学报, 2004, 26(5):46-51. Jin Wenbin, Liu Yongxiang, Li Xiang. et al. Research on estimation of mass-to-drag ratio of reentry objects[J]. Journal of National University of Defense Technology, 2004, 26(5):46-51. (in Chinese)
[14] Naiem A, El-Beltagy M, Rasmy M. A centrally coordinated parallel auction algorithm for large scale assignment problems//The 7th International Conference on Informatics and Systems. 2010: 1-4.
[15] Mercker T, Casbeer D W, Millet P T. An extension of consensus-based auction algorithms for decentralized, time-constrained task assignment//American Control Conference 2010. 2010:6324-6329.
[16] Chen P, Xing L, Xiao M M, et al. Cooperative dynamic weapon-target assignment algorithm of multiple missiles based on networks//Chinese Control and Decision Conference 2009. 2009:126-130.
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