文章快速检索 高级检索

1. 空军工程大学 防空反导学院, 西安 710051;
2. 信息感知技术协同创新中心, 西安 710077

Micro-Doppler resolution of multi-ballistic targets in midcourse
WANG Yizhe1 , FENG Cunqian1,2 , LI Jingqing1 , MENG Fanjie1
1. Air and Missile Defense College, Air Force Engineering University, Xi'an 710051, China ;
2. Collaborative Innovation Center of Information Sensing and Understanding, Xi'an 710077, China
Received: 2016-01-11; Accepted: 2016-02-29; Published online: 2016-04-01 17:07
Foundation item: National Natural Science Foundation of China (61372166, 61501495); Natural Science Basic Research Plan in Shaanxi Province of China (2014JM8308)
Corresponding author. E-mail:fengcunqian@sina.com
Abstract: To solve the problems of overlapping and difficult separation of micro-Doppler information of multi-ballistic target echo in narrow-band radar, a novel method based on auction algorithm and wavelet analysis is proposed to separate micro-Doppler of multi-ballistic targets. First, based on the sliding scattering model, the time-frequency skeleton is obtained by preprocessing. Then, the path length is defined by variation rules of Doppler and estimated precession period. The shortest paths corresponding to Doppler curves are extracted by auction algorithm. Finally, micro-Doppler resolution of multi-ballistic targets is realized after translational motion compensation by wavelet analysis. Simulation results indicate that the method can solve path selection problems well in intersection region, and is suitable for various forms of micro-motion.
Key words: multi-ballistic targets resolution     ballistic targets     micro-Doppler     auction algorithm     wavelet analysis

1 进动目标多普勒分析

 图 1 弹道进动多目标微动模型 Fig. 1 Ballistic multi-targets precession model

 (1)

 (2)

 (3)

 (4)

2 基于拍卖算法的多目标分离 2.1 进动周期估计

 (5)

 (6)

2.2 多目标分离的最短路径描述

2.3 改进的最短路径拍卖算法

P=[(m1,1),(m2,2),…,(mk,k)]为D中的一条路径，若其中包含的节点各不相同，则称P为初等路，节点(mk,k)为该路径的终点，路径长度L可表示为

 (7)

 (8)

 (9)

 (10)
 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

(m′,k+1)是最终节点之一，P1即为第1条最短路径，转步骤5；否则进行下一轮迭代。

3 基于小波分析的平动补偿

 图 2 多尺度小波分析 Fig. 2 Multi-scale wavelet analysis

 (17)

 (18)

 (19)

 图 3 算法流程图 Fig. 3 Algorithm flowchart
4 仿真分析

 图 4 初始时频图 Fig. 4 Original time-frequency pattern
 图 5 截取的时频骨架 Fig. 5 Selective time-frequency skeleton
 图 6 提取的最短路径 Fig. 6 Extracted shortest paths

 图 7 小波分解得到的平均趋势 Fig. 7 Average trend from wavelet decomposition
 图 8 消趋后平滑结果 Fig. 8 Result after eliminating trend and smoothing
 图 9 文献[5] Viterbi算法提取结果 Fig. 9 Extracted result using Viterbi algorithm inRef. [5]

 (20)

 图 10 不同信噪比条件下本文方法与文献[5] Viterbi算法性能分析 Fig. 10 Performance analysis by proposed method andViterbi algorithm in Ref. [5] under different SNRs
5 结 论

1) 拍卖算法有效地提取出了各多普勒曲线对应的最短路径，该算法对进动周期的估计精度要求不高，因为Tmax仅作为阈值Δ的一个参考参数，路径长度的定义才是影响算法性能的关键；由于构造Δ时认为平动多普勒变化缓慢，忽略了平动的影响，因此本文方法要求粗补偿达到一定精度，使得剩余平动参数的取值在合理的范围内。

2) 利用小波分解的消趋特性，可以在缺乏具体平动模型先验信息的情况下，有效对多普勒曲线的平动分量进行补偿，当小波基函数选定时，分解的层数越高，消趋误差越小，但计算量越大。

3) 若散射点不在整个观测时间段内可见，将会导致提取的骨架出现断裂、不连续，从而得到的最短路径容易出现错误关联，这是由于本文方法依赖于多普勒曲线的连续性变化规律，此时可考虑对数据实现分段提取后再进行融合处理。

4) 本文较好地实现了多目标微多普勒的分离与提取，该方法不仅适用于滑动目标，而且适用于振动、旋转等其他微动形式的弹道目标。如何利用获取的微多普勒信息进行目标分辨与识别，是下一步研究工作的重点。

 [1] DAVID L R. Ballistic missile defense[J]. Journal of Electronic Defense, 2006, 29 (1) : 46 –52. [2] 冯德军, 徐乐涛, 艾小锋. 空间复杂目标群的雷达目标识别技术[J]. 现代防御技术, 2015, 43 (4) : 1 –6. FENG D J, XU L T, AI X F. Radar recognition technique for complex target groups in space[J]. Modern Defence Technology, 2015, 43 (4) : 1 –6. (in Chinese) [3] CHEN V C.Analysis of radar micro-Doppler signature with time-frequency transform[C]//Proceedings of IEEE Workshop on Statistical Signal and Array Processing.Piscataway,NJ:IEEE Press,2000:463-466. [4] 胡晓伟, 童宁宁, 胡国平, 等. 基于微多普勒的弹道多目标分离方法[J]. 系统工程与电子技术, 2015, 37 (8) : 1734 –1740. HU X W, TONG N N, HU G P, et al. Multi-ballistic targets resolution based on micro-Doppler[J]. Systems Engineering and Electronics, 2015, 37 (8) : 1734 –1740. (in Chinese) [5] LI P, WANG D C, WANG L. Separation of micro-Doppler signals based on time frequency filter and Viterbi algorithm[J]. Signal, Image and Video Processing, 2013, 7 (3) : 593 –605. DOI:10.1007/s11760-011-0263-3 [6] 赵盟盟, 张群, 罗迎, 等. 点迹-曲线关联算法的旋转对称群目标分辨[J]. 空军工程大学学报(自然科学版), 2015, 16 (2) : 43 –48. ZHAO M M, ZHANG Q, LUO Y, et al. Distinguishing of rotationally symmetric group targets based on plot-curve association algorithm[J]. Journal of Air Force Engineering University (Natural Science Edition), 2015, 16 (2) : 43 –48. (in Chinese) [7] 李靖卿, 冯存前, 张栋. 基于自适应视野聚类匹配的多目标分离与提取[J]. 系统工程与电子技术, 2015, 37 (9) : 1974 –1979. LI J Q, FENG C Q, ZHANG D. Multi-target separation and extraction based on adaptive vision cluster matching[J]. Systems Engineering and Electronics, 2015, 37 (9) : 1974 –1979. (in Chinese) [8] MA L, LIU J, WANG T, et al. Micro-Doppler character of sliding-type scattering center on rotationally symmetric target[J]. Science China (Information Sciences), 2011, 54 (9) : 1957 –1967. DOI:10.1007/s11432-011-4254-3 [9] 雷腾, 刘进忙, 杨少春, 等. 基于三站一维距离像融合的弹道目标特征提取方法研究[J]. 宇航学报, 2011, 32 (2) : 228 –234. LEI T, LIU J M, YANG S C, et al. Study on feature extraction method of ballistic target based on three-station range profiles[J]. Journal of Astronautics, 2011, 32 (2) : 228 –234. (in Chinese) [10] 贺思三, 赵会宁, 张永顺. 基于延迟共轭相乘的弹道目标平动补偿[J]. 雷达学报, 2014, 3 (5) : 505 –510. HE S S, ZHAO H N, ZHANG Y S. Translational motion compensation for ballistic targets based on delayed conjugated multiplication[J]. Journal of Radars, 2014, 3 (5) : 505 –510. (in Chinese) [11] 胡晓伟, 童宁宁, 董会旭, 等. 弹道中段群目标平动补偿与分离方法[J]. 电子与信息学报, 2015, 37 (2) : 291 –296. HU X W, TONG N N, DONG H X, et al. Translation compensation and resolution of multi-ballistic targets in midcourse[J]. Journal of Electronics & Information Technology, 2015, 37 (2) : 291 –296. (in Chinese) [12] 肖立, 周剑雄, 何峻, 等. 弹道中段目标进动周期估计的改进自相关法[J]. 航空学报, 2010, 31 (4) : 812 –818. XIAO L, ZHOU J X, HE J, et al. Improved autocorrelation method for precession period estimation of ballistic target in midcourse[J]. Acta Aeronautica et Astronautica Sinica, 2010, 31 (4) : 812 –818. (in Chinese) [13] 罗迎, 柏又青, 张群, 等. 弹道目标平动补偿与微多普勒特征提取方法[J]. 电子与信息学报, 2012, 34 (3) : 602 –608. LUO Y, BAI Y Q, ZHANG Q, et al. Translational motion compensation and micro-Doppler feature extraction of ballistic targets[J]. Journal of Electronics & Information Technology, 2012, 34 (3) : 602 –608. (in Chinese) [14] 赵永嘉, 戴树岭. 基于图像骨架和贪婪算法的无人机航路规划[J]. 北京航空航天大学学报, 2010, 36 (4) : 474 –477. ZHAO Y J, DAI S L. Unmanned aircraft vehicle path planning based on image skeleton and greedy algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2010, 36 (4) : 474 –477. (in Chinese) [15] BERTSEKAS D P, CASTANON D A. The auction algorithm for the transportation problem[J]. Annals of Operations Research, 1989, 20 (1) : 67 –96. DOI:10.1007/BF02216923 [16] STEPHANE G M. A theory for multi-resolution signal decomposition:The wavelet representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, 11 (7) : 674 –693. DOI:10.1109/34.192463 [17] 吴志成, 王重阳, 任爱君. 消除信号趋势项时小波基优选方法研究[J]. 北京理工大学学报, 2013, 33 (8) : 811 –814. WU Z C, WANG C Y, REN A J. Optimal selection of wavelet base functions for eliminating signal trend based on wavelet analysis[J]. Transactions of Beijing Institute of Technology, 2013, 33 (8) : 811 –814. (in Chinese)

#### 文章信息

WANG Yizhe, FENG Cunqian, LI Jingqing, MENG Fanjie

Micro-Doppler resolution of multi-ballistic targets in midcourse

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(1): 113-120
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0038