基于航迹矢量分级聚类的雷达与电子支援措施抗差关联算法
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摘要
针对同平台雷达与电子支援措施(ESM)存在系统误差、上报目标不完全一致等复杂场景下航迹关联鲁棒性和有效性问题,该文提出一种基于航迹矢量分级聚类的雷达与ESM航迹抗差关联算法。首先推导修正极坐标系(MPC)下目标等价测量方程,基于等价测量的近似展开得到目标状态估计分解方程,利用真实状态对消的方法得到航迹矢量,基于高斯随机矢量的统计特性,采用航迹矢量分级聚类的方法提取同源航迹。最后通过实验仿真验证,所提算法在不同系统误差、目标分布密度、检测概率等环境下具有较好的关联效果和鲁棒性。
To address track-to-track association problem of radar and Electronic Support Measurements(ESM)in the presence of sensor biases and different targets reported by different sensors, an anti-bias track-to-track association algorithm based on track vectors hierarchical clustering is proposed. Firstly, the equivalent measurement is derived in the Modified Polar Coordinates(MPC). Linear relationship between state estimates and real states, sensor biases, measurement errors are established based on the approximate expansion of the equivalent measurement. The track vectors are obtained by the real state cancellation method. The homologous tracks are extracted by the method of track vectors hierarchical clustering, according to the statistical characteristics of Gaussian random vectors. The effectiveness of the proposed algorithm is verified by Monte Carlo simulation experiments in the presence of sensor biases, targets densities and detection probabilities.
To address track-to-track association problem of radar and Electronic Support Measurements(ESM)in the presence of sensor biases and different targets reported by different sensors, an anti-bias track-to-track association algorithm based on track vectors hierarchical clustering is proposed. Firstly, the equivalent measurement is derived in the Modified Polar Coordinates(MPC). Linear relationship between state estimates and real states, sensor biases, measurement errors are established based on the approximate expansion of the equivalent measurement. The track vectors are obtained by the real state cancellation method. The homologous tracks are extracted by the method of track vectors hierarchical clustering, according to the statistical characteristics of Gaussian random vectors. The effectiveness of the proposed algorithm is verified by Monte Carlo simulation experiments in the presence of sensor biases, targets densities and detection probabilities.
引文
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[12]孙仲康,郭福成,冯道旺.单站无源定位技术[M].北京:国防工业出版社,2008:150-160.SUN Zhongkang,GUO Fucheng,and FENG Daowang.Passive Location and Tracking Technology by Single Observer[M].Beijing:National Defense Industry Press,2008:150-160.
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[14]SCALA B F L and FARINA A.Choosing a track association method[J].Information Fusion,2002,3(2):119-122.doi:10.1016/S1566-2535(02)00050-7.
[15]关欣,彭彬彬,衣晓.基于区间重合度的雷达与ESM航迹关联算法[J].雷达科学与技术,2017,15(1):61-67.doi:10.3969/j.issn.1672-2337.2017.01.011.GUAN Xin,PENG Binbin,and YI Xiao.Track association algorithm of radar and ESM based on the interval overlap ratio[J].Radar Science and Technology,2017,15(1):61-67.doi:10.3969/j.issn.1672-2337.2017.01.011.
[16]关欣,彭彬彬,衣晓.修正极坐标系下雷达与ESM航迹对准关联[J].航空学报,2017,38(5):221-232.doi:10.7527/S1000-6893.2016.0287.GUAN Xin,PENG Binbin,and YI Xiao.Track alignmentassociation of radar and ESM in MPC[J].Acta Aeronautics et Astronautics Sinica,2017,38(5):221-232.doi:10.7527/S1000-6893.2016.0287.
[17]KARYPIS G,HAN E H,and KUMAR V.Chameleon:hierarchical clustering using dynamic modeling[J].Computer,1999,32(8):68-75.doi:10.1109/2.781637.
[18]何友,修建娟,张晶炜,等.雷达数据处理及应用[M].北京:电子工业出版社,2009:220-223.HE You,XIU Jianjuan,ZHANG Jingwei,et al.Radar Data Processing with Applications[M].Beijing:Publishing House of Electronics Industry,2009:220-223.
[19]ZHU Hongyan,WANG Wei,and WANG Chen.Robust track-to-track association in the presence of sensor biases and missed detections[J].Information Fusion,2016,27:33-40.doi:10.1016/j.inffus.2015.05.002.
[2]彭彬彬,关欣.基于空间分布信息的雷达与ESM航迹灰色关联算法[J].电光与控制,2017,24(6):34-38.doi:10.3969/j.issn.1671-637X.2017.06.007.PENG Binbin and GUAN Xin.Gray track correlation algorithm of radar and ESM based on spatial distribution information[J].Electronics Optics&Control,2017,24(6):34-38.doi:10.3969/j.issn.1671-637X.2017.06.007.
[3]QI Lin,DONG Kai,LIU Yu,et al.Anti-bias track-to-track association algorithm based on distance detection[J].IETRadar,Sonar&Navigation,2017,11(2):269-276.doi:10.1049/iet-rsn.2016.0139.
[4]李保珠,董云龙,李秀友,等.基于t分布混合模型的抗差关联算法[J].电子与信息学报,2017,39(7):1774-1778.doi:10.11999/JEIT161084.LI Baozhu,DONG Yunlong,LI Xiuyou,et al.Anti-bias track association algorithm based on t-distribution mixture model[J].Journal of Electronics&Information Technology,2017,39(7):1774-1778.doi:10.11999/JEIT161084.
[5]TRUNK G V and WILSON J D.Association of DF bearing measurements with radar tracks[J].IEEE Transactions on Aerospace and Electronic Systems,1987,23(4):438-447.doi:10.1109/TAES.1987.310877.
[6]WANG Guohong,HE You,GAO Zhiyong,et al.Improved association of ESM measurements with radar tracks[C].IETRadar Systems,Edinburgh,UK,1997:648-652.doi:10.1049/cp:19971755.
[7]WANG Guohong,MAO Shiyi,HE You,et al.Triplethreshold radar-to-ESM correlation algorithm when each radar track is specified by different number of measurements[J].IEE Proceedings-Radar,Sonar and Navigation,2000,147(4):177-181.doi:10.1049/ip-rsn:20000094.
[8]CHEN Huimin and BAR-SHALOM Y.Track association and fusion with heterogeneous local trackers[C].IEEEConference on Decision and Control,New Orleans,USA,2007:2675-2680.doi:10.1109/CDC.2007.4434638.
[9]WANG Guohong,ZHANG Xiangyu,and TAN Shuncheng.Effect of biased estimation on radar-to-ESM track association[J].Journal of System Engineering and Electronic Techniques,2012,23(2):188-194.doi:10.1109/JSEE.2012.00024.
[10]BENAMEUR K.Radar ESM track-to-track association[R].Ottawa:Defence Research Establishment Ottawa,2001.
[11]ZHOU Y F,LI W,and LEUNG H.Maximum likelihood based ESM/radar track association algorithm in a new modified polar coordinate[R].Ottawa:Defence Research and Development Canada,2004.
[12]孙仲康,郭福成,冯道旺.单站无源定位技术[M].北京:国防工业出版社,2008:150-160.SUN Zhongkang,GUO Fucheng,and FENG Daowang.Passive Location and Tracking Technology by Single Observer[M].Beijing:National Defense Industry Press,2008:150-160.
[13]OFFER C R.Performance of bearing-only ESM-radar tracking association[C].IET Data Fusion and Target Tracking Conference,London,UK,2012:1-6.doi:10.1049/cp.2012.0409.
[14]SCALA B F L and FARINA A.Choosing a track association method[J].Information Fusion,2002,3(2):119-122.doi:10.1016/S1566-2535(02)00050-7.
[15]关欣,彭彬彬,衣晓.基于区间重合度的雷达与ESM航迹关联算法[J].雷达科学与技术,2017,15(1):61-67.doi:10.3969/j.issn.1672-2337.2017.01.011.GUAN Xin,PENG Binbin,and YI Xiao.Track association algorithm of radar and ESM based on the interval overlap ratio[J].Radar Science and Technology,2017,15(1):61-67.doi:10.3969/j.issn.1672-2337.2017.01.011.
[16]关欣,彭彬彬,衣晓.修正极坐标系下雷达与ESM航迹对准关联[J].航空学报,2017,38(5):221-232.doi:10.7527/S1000-6893.2016.0287.GUAN Xin,PENG Binbin,and YI Xiao.Track alignmentassociation of radar and ESM in MPC[J].Acta Aeronautics et Astronautics Sinica,2017,38(5):221-232.doi:10.7527/S1000-6893.2016.0287.
[17]KARYPIS G,HAN E H,and KUMAR V.Chameleon:hierarchical clustering using dynamic modeling[J].Computer,1999,32(8):68-75.doi:10.1109/2.781637.
[18]何友,修建娟,张晶炜,等.雷达数据处理及应用[M].北京:电子工业出版社,2009:220-223.HE You,XIU Jianjuan,ZHANG Jingwei,et al.Radar Data Processing with Applications[M].Beijing:Publishing House of Electronics Industry,2009:220-223.
[19]ZHU Hongyan,WANG Wei,and WANG Chen.Robust track-to-track association in the presence of sensor biases and missed detections[J].Information Fusion,2016,27:33-40.doi:10.1016/j.inffus.2015.05.002.
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