基于目标指示的两坐标警戒雷达目标高度补偿状态估计
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摘要
为了克服现有目标高度补偿算法存在的模型假设不合理、实际应用效果难以保证等问题,本文以目标恒海拔等速运动为前提,利用协同单元提供的目标指示信息,对两坐标雷达的空间目标跟踪问题重新进行了研究.首先根据不同坐标系间的转换关系,构建了目标高度的准确表达式.然后通过恒等变换和合理的近似,得到了目标高度的估计公式,并利用绝对值不等式和柯西-施瓦茨不等式,推导得到了高度估计公式的误差.最后联合目标高度估计公式和两坐标雷达的缺维量测方程,采用扩展卡尔曼滤波方法,实现了目标空间状态的估计.仿真结果表明:本文算法可有效地对目标高度进行补偿,获得稳定、可靠的目标空间状态估计,从而为两坐标雷达目标空间状态估计问题提供了相对有效完善的解决方法.
There are some shortcomings in the existing target height compensation algorithms,such as unreasonable model assumptions and unstable application effect. To avoid these defects,the problem of tracking the aerial target in 3-D space w ith a 2-D radar w as restudied under the assumption that the target flights at a constant speed and a fixed altitude and the radar can obtain the indication information of the target from other collaborative detect units. First,on the basis of the transformation relation betw een different coordinates,an exact formula of the target height w as deduced. Then utilizing identical transformation and reasonable approximations,an approximate estimation formula of the target height w as derived. And the error in the formula w as calculated using absolute value inequality and Cauchy-Schw arz inequality. At last,combining the original measurement equation of the 2-D radar w ith the target height estimation equation and using extended Kalman filter,the target space state w as estimated. The simulation result show s the proposed algorithm can effectively compensate the target height information and obtain the stable and reliable estimation of the target space state,w hich can be used in the actual projects as the effective and perfect method for the target space state estimate problem of the 2-D radar.
There are some shortcomings in the existing target height compensation algorithms,such as unreasonable model assumptions and unstable application effect. To avoid these defects,the problem of tracking the aerial target in 3-D space w ith a 2-D radar w as restudied under the assumption that the target flights at a constant speed and a fixed altitude and the radar can obtain the indication information of the target from other collaborative detect units. First,on the basis of the transformation relation betw een different coordinates,an exact formula of the target height w as deduced. Then utilizing identical transformation and reasonable approximations,an approximate estimation formula of the target height w as derived. And the error in the formula w as calculated using absolute value inequality and Cauchy-Schw arz inequality. At last,combining the original measurement equation of the 2-D radar w ith the target height estimation equation and using extended Kalman filter,the target space state w as estimated. The simulation result show s the proposed algorithm can effectively compensate the target height information and obtain the stable and reliable estimation of the target space state,w hich can be used in the actual projects as the effective and perfect method for the target space state estimate problem of the 2-D radar.
引文
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[18]罗迎,张群,李松,等.基于分布式组网雷达的弹道目标三维进动特征提取[J].电子学报,2012(06):1079-1085.LUO Ying,ZHANG Qun,LI Song,et al.Three-dimensional precession feature extraction of ballistic targets in distributed radar netw orks[J].Acta Electronica Sinica,2012(06):1079-1085.(in Chinese)
[19]卢策吾,刘小军,方广有.基于感知压缩的探地雷达数据压缩采集[J].电子学报,2011(09):2204-2206.LU Ce-w u,LIU Xiao-jun,FANG Guang-you.Compressive sensing for GPR data acquisition[J].Acta Electronica Sinica,2011(09):2204-2206.(in Chinese)
[20]赵艳丽,王雪松,王国玉,等.多假目标欺骗干扰下组网雷达跟踪技术[J].电子学报,2007(03):454-458.ZHAO Yan-li,WANG Xue-song,WANG Guo-yu,et al.Tracking technique for radar netw ork in the presence of multi-range-false-target deception jamming[J].Acta Electronica Sinica,2007(03):454-458.(in Chinese)
[21]吴伟,吴耀云,王东进.利用信号幅度信息的多基地雷达系统多目标跟踪算法[J].电子学报,2007(06):1193-1198.WU Wei,WU Yao-yun,WANG Dong-jin.M ulti-Target Tracking Algorithm for M ulti-Static Radar Assisted by Signal Amplitude[J].Acta Electronica Sinica,2007(06):1193-1198.(in Chinese)
[2]雷雨,冯新喜,朱灿彬,等.2D雷达情报组网目标高度估计[J].火力与指挥控制,2011(12):157-159.LEI Yu,FENG Xin-xi,Zhu Can-lin.Estimation of aircraft altitude w ith 2D radar intelligence netw orking[J].Fire Control&Command Control,2011(12):157-159.(in Chinese)
[3]王国宏,许建峰,毛士艺,等.2D雷达组网中目标高度估计误差的Cramér-Rao限[J].航空学报,2004(01):66-68.WANG Guo-hong,XU Jian-feng,M AO Shi-yi,et al.On the CRLB of height estimation in a 2-dimensional-radarbased netw ork[J].Acta Aeronautica et Astronautica Sinica,2004(01):66-68.(in Chinese)
[4]赵孔瑞,于长军,权太范,等.高频地波雷达飞行目标高度估计[J].系统工程与电子技术,2012(08):1571-1575.ZHAO Kong-jian,YU Chang-jun,QUAN Tai-fan,et al.Estimation of flight altitude in high frequency surface w ave radar[J].Journal of Systems Engineering and Electronics,2012(08):1571-1575.(in Chinese)
[5]张硕,金永镐,于长军,等.高频地波雷达目标高度估计起始的HPEKF算法[J].哈尔滨工业大学学报,2007(05):725-729.ZHANG Shuo,JIN Yong-gao,YU Chang-jun,et al.HPEKF algorithm of target altitude estimation initializing in HF surface w ave radar[J].Journal of Harbin Institute of Technology,2007(05):725-729.(in Chinese)
[6]游伟,何子述,胡进峰.基于匹配场处理的天波雷达高度估计算法[J].电子与信息学报,2013(02):401-405.YOU Wei,HE Zi-Shu,HU Jin-Feng.Skyw ave radar altitude estimation algorithm based on matched-field Processing[J].Journal of Electronics&Information Technology,2013(02):401-405.(in Chinese)
[7]Rakvongthai Y,Jifeng R,Sivananthan S,et al.Altitude estimation for 3-D tracking w ith tw o 2-D radars[A].Information Fusion,2011 Proceedings of the 14th International Conference on[C].Chicago,USA:IEEE,2011.1-8.
[8]Poullin D,Flecheux M.Passive 3D tracking of low altitude targets using DVB(SFN Broadcasters)[J].Aerospace and Electronic Systems M agazine,IEEE Transactions on,2012,27(11):36-41.
[9]Jing S,She S,Jia-Dong X.3D shape reconstruction from2D ISAR measurements[A].Wavelet Active M edia Technology and Information Processing(ICWAM TIP),2012International Conference on[C].Chengdu,China:IEEE,2012.25-28.
[10]Rosebrock J.Absolute attitude from monostatic radar measurements of rotating objects[J].Geoscience and Remote Sensing,IEEE Transactions on,2011,49(10):3737-3744.
[11]Luo Z,He J.ML Estimation of true height in 2-D radar netw ork[A].Information Fusion,2007 10th International Conference on[C]Quebec,Canada:IEEE,2007.1-7.
[12]de Marina H G,Pereda F J,Giron-Sierra J M,et al.UAV Attitude estimation using unscented Kalman filter and TRIAD[J].Industrial Electronics,IEEE Transactions on,2012,59(11):4465-4474.
[13]Lu K Y,Kiang J F.Stereo-synthetic aperture radar technique w ith bias correction to estimate terrain height[J].Radar,Sonar&Navigation,IET,2013,7(3):313-320.
[14]Dongliang H,Leung H,Bosse E.A pseudo-measurement approach to simultaneous registration and track fusion[J].Aerospace and Electronic Systems,IEEE Transactions on,2012,48(3):2315-2331.
[15]Bae S H,Kim D Y,Yoon J H,et al.Automated multi-target tracking w ith kinematic and non-kinematic information[J].Radar,Sonar&Navigation,IET,2012,6(4):272-281.
[16]Sukhavasi R T,Hassibi B.The kalman-like particle filter:optimal estimation w ith quantized innovations/measurements[J].Signal Processing,IEEE Transactions on,2013,61(1):131-136.
[17]Lubin C,Baiqing H,An L,et al.Transformed unscented kalman filter[J].Automatic Control,IEEE Transactions on,2013,58(1):252-257.
[18]罗迎,张群,李松,等.基于分布式组网雷达的弹道目标三维进动特征提取[J].电子学报,2012(06):1079-1085.LUO Ying,ZHANG Qun,LI Song,et al.Three-dimensional precession feature extraction of ballistic targets in distributed radar netw orks[J].Acta Electronica Sinica,2012(06):1079-1085.(in Chinese)
[19]卢策吾,刘小军,方广有.基于感知压缩的探地雷达数据压缩采集[J].电子学报,2011(09):2204-2206.LU Ce-w u,LIU Xiao-jun,FANG Guang-you.Compressive sensing for GPR data acquisition[J].Acta Electronica Sinica,2011(09):2204-2206.(in Chinese)
[20]赵艳丽,王雪松,王国玉,等.多假目标欺骗干扰下组网雷达跟踪技术[J].电子学报,2007(03):454-458.ZHAO Yan-li,WANG Xue-song,WANG Guo-yu,et al.Tracking technique for radar netw ork in the presence of multi-range-false-target deception jamming[J].Acta Electronica Sinica,2007(03):454-458.(in Chinese)
[21]吴伟,吴耀云,王东进.利用信号幅度信息的多基地雷达系统多目标跟踪算法[J].电子学报,2007(06):1193-1198.WU Wei,WU Yao-yun,WANG Dong-jin.M ulti-Target Tracking Algorithm for M ulti-Static Radar Assisted by Signal Amplitude[J].Acta Electronica Sinica,2007(06):1193-1198.(in Chinese)