摘要 现有直接定位(Direct Position Determination,DPD)算法主要研究对象是视距目标.针对传统无线电定位技术对超视距目标定位精度低的问题,提出一种辐射源信号波形已知的超视距直接定位(Over-the-Horizon Direct Position Determination,ODPD)方法.该方法基于电离层电子密度参数,依据最大似然(Maximum Likelihood,ML)准则,从信号数据域直接推导出仅关于目标位置的代价函数.其次,本文推导了关于电离层虚高测量误差的定位误差协方差矩阵.实验表明ODPD方法在低信噪比下相比现有算法,能显著提高超视距目标的定位精度,定位性能更接近克拉美罗界(Cramér-Rao Low Bound,CRLB).误差分析显示,电离层虚高误差标准差在20km时,引起的定位误差能控制在10km的范围内.
Abstract:Direct Position Determination (DPD) algorithms usually focus on line-of-sight target.Aiming at the problems that traditional radio positioning technology is suboptimal,especially in the over-the-horizon target localization,this paper proposes an Over-the-horizon Direct Positioning Determination (ODPD) method with known radiation source waveforms.Based on the ionospheric electron density parameter,the cost function just about the target position is directly derived from the signal data domain through the Maximum Likelihood (ML) criterion.Furthermore,this paper deduces the positioning error covariance matrix considering the measurement error of the ionospheric virtual height.Experiments show that compared with the existing algorithms,the ODPD method can significantly improve the positioning accuracy of the over-the-horizon target at low SNR.The ODPD positioning performance is closer to the Cramér-Rao low bound (CRLB).When the standard deviation of the ionospheric virtual high error is 20km,the positioning error caused can be controlled within the range of 10km.
余婉婷, 于宏毅, 杜剑平, 王鼎. 辐射源信号波形已知的超视距目标直接定位方法[J]. 电子学报, 2019, 47(11): 2368-2377.
YU Wan-ting, YU Hong-yi, DU Jian-ping, WANG Ding. A Direct Position Determination Method for Over-the-Horizon Target on Known Radiation Source Waveforms. Acta Electronica Sinica, 2019, 47(11): 2368-2377.
[1] 周益明,刘跃平,蒋春山.基于短波机会照射的超视距隐身目标探测定位技术[J].中国电子科学研究院学报,2014,9(1):45-49. ZHOU Yi-ming,LIU Yue-ping,JIANG Chun-shan.Research on beyond-light-of-sight detection and location technology against stealth targets based on opportunistic illuminator of shortwave[J].Journal of CAEIT,2014,9(1):45-49.(in Chinese)
[2] YANG L,HO K C.An approximately efficient TDOA localization algorithm in closed-form for locating multiple disjoint sources with erroneous sensor positions[J].IEEE Transactions on Signal Processing,2009,57(12):4598-4615.
[3] YANG K,AN J,BU X,et al.Constrained total least-squares location algorithm using time-difference-of-arrival measurements[J].IEEE Transactions on Vehicular Technology,2010,59(3):1558-1562.
[4] 郝本建,李赞,万鹏武,等.基于TDOA与GROA的信号源被动定位偏差消除技术[J].电子学报,2014,42(3):477-484. HAO Ben-jian,LI Zan,WAN Peng-wu,et al.Bias reduction for passive source localization based on TDOA and GROA[J].Acta Electronica Sinica,2014,42(3):477-484.(in Chinese)
[5] 朱国辉,冯大政,聂卫科.传感器位置误差情况下基于多维标度分析的时差定位算法[J].电子学报,2016,44(1):21-26. ZHU Guo-hui,FENG Da-zheng,NIE Wei-ke.Multidimensional scaling based TDOA localization algorithm with sensor location errors[J].Acta Electronica Sinica,2016,44(1):21-26.(in Chinese)
[6] 郝本建,朱建峰,李赞,等.基于TDOAs与FDOAs的多信号源及感知节点联合定位算法[J].电子学报,2015,43(10):1888-1897. HAO Ben-jian,ZHU Jian-feng,LI Zan,et al.Joint multiple disjoint sources and sensors localization based on TDOAs and FDOAs[J].Acta Electronica Sinica,2015,43(10):1888-1897.(in Chinese)
[7] SUN M,HO K C.An asymptotically efficient estimator for TDOA and FDOA positioning of multiple disjoint sources in the presence of sensor location uncertainties[J].IEEE Transactions on Signal Processing,2011,59(7):3434-3440.
[8] YEREDOR A,ANGEL E.Joint TDOA and FDOA estimation:A conditional bound and its use for optimally weighted localization[J].IEEE Transactions on Signal Processing,2011,59(4):1612-1623.
[9] WEISS A J.Direct position determination of narrowband radio frequency transmitters[J].IEEE Signal Processing Letters,2004,11(5):513-516.
[10] WEISS A J.Direct geolocation of wideband emitters based on delay and Doppler[J].IEEE Transactions on Signal Processing,2011,59(6):2513-5520.
[11] AMAR A,WEISS A J.Localization of narrowband radio emitters based on Doppler frequency shifts[J].IEEE Transactions on Signal Processing,2008,56(11):5500-5508.
[12] 王鼎,张刚.一种基于窄带信号多普勒频率测量的运动目标直接定位方法[J].电子学报,2017,45(3):591-598. WANGDing,ZHANG Gang.A direct localization method for moving narrowband source based on Doppler frequency shifts[J].Acta Electronica Sinica,2017,45(3):591-598.(in Chinese)
[13] AMAR A,WEISS A J.Direct position determination in the presence of model errors-known waveforms[J].Digital Signal Processing,2006,16(1):52-83.
[14] 王鼎,吴志东,尹洁昕.信号波形已知条件下多目标直接定位性能分析及其改进算法[J].电子学报,2017,45(12):2881-2889. WANG Ding,WU Zhi-dong,YIN Jie-wei.Aperformance analysis and improved algorithm for multi-source direct localization with known signal waveforms[J].Acta Electronica Sinica,2017,45(12):2881-2889.(in Chinese)
[15] 马贤同,罗景青,孟祥豪.多目标位置信息场直接定位法[J].信息与控制,2015,44(6):673-677. MA Xian-tong,LUO Jing-qing,MENG Xiang-hao.Position information field direct position determination for multiple target[J].Information and Control,2015,44(6):673-677.(in Chinese)
[16] BAR-SHALOM O,WEISS A J.Direct position determination of OFDM signals[A].IEEE 8th Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2007)[C].USA:IEEE,2007.1-5.
[17] REUVEN A M,WEISS A J.Direct position determination of cyclostationary signals[J].Signal Processing,2009,89(12):2448-2464.
[18] 王鼎,张刚,沈彩耀,等.一种针对恒模信号的运动单站直接定位算法[J].航空学报,2016,37(5):1622-1633. WANG Ding,ZHANG Gang,SHEN Cai-yao,et al.A direct position determination algorithm for constant modulus signals with single moving observer[J].Acta Aeronautica et Astronautica Sinica,2016,37(5):1622-1633.(in Chinese)
[19] 王云龙,吴瑛.联合时延与多普勒频率的直接定位改进算法[J].西安交通大学学报,2015,49(4):123-129. WANG Yun-long,WU Ying.An improved direct position determination algorithm with combined time delay and doppler[J].Journal of Xi'an Jiaotong University,2015,49(4):123-129.(in Chinese)
[20] 柳文,焦培南,王世凯,等.电离层短波三维射线追踪及其应用研究[J].电波科学学报,2008,23(1):41-48. LIU Wen,JIAO Pei-nan,WANG Shi-kai,et al.Short wave ray tracing in the ionosphere and its application[J].Chinese Journal of Radio Science,2008,23(1):41-48.(in Chinese)
[21] 虞超,沈国柱,顾斌,等.电磁波在电离层的传播特性研究[J].南京信息工程大学学报(自然科学版),2013,5(4):379-384. YU Chao,SHEN Guozhu,GU Bin,et al.Study on propagation characteristics of electromagnetic waves in ionosphere[J].Journal of Nanjing University of Information Technology (Natural Science Edition),2013,5(4):379-384.(in Chinese)
[22] BILITZA D,RAWER K,BOSSY L,et al.International reference ionosphere[J].Planetary and Space Science,1990,40(4):544.
[23] DU J,WANG D,YU W,et al.Direct position determination of unknown signals in the presence of multipath propagation[J].Sensors,2018,18(3):892.
[24] WYMEERSCH H,MARANO S,GIFFORD W M,et al.A machine learning approach to ranging error mitigation for UWB localization[J].IEEE Transactions on Communications,2012,60(6):1719-1728.