利用外辐射源的TDOA和FDOA目标定位算法
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摘要
针对单站外辐射源条件下的目标定位问题,提出了一种基于最大似然的时差-频差联合定位算法。首先根据时差和频差的观测方程,构建目标位置和速度的最大似然估计模型。然后采用牛顿迭代算法对最大似然估计模型求解,得到目标位置和速度估计。最后,推导了算法的克拉美罗界和理论误差,并证明了二者相等。仿真结果表明,算法定位精度高于两步加权最小二乘算法和约束总体最小二乘算法,在测量误差较高时仍能达到克拉美罗界。通过对系统几何精度因子图的分析,确定目标及外辐射源数量和位置也是影响定位精度的重要因素。
To solve the single-observer passive location estimation using illuminators of opportunity, a jointing TDOA and FDOA location algorithm based on maximum likelihood is proposed. Firstly, according to the TDOA and FDOA measurement equations, the maximum likelihood model is constructed. Then Newton's method is applied to solve the maximum likelihood model to obtain the estimation of the target position and velocity. The initial iteration value is given by a Least Squares(LS)algorithm. The Cramer-Rao Lower Bound(CRLB)and the theoretical error of the proposed algorithm are also derived and they are proved equal. Simulation results show that the proposed algorithm has higher estimation accuracy than the Two-Step Weighting Least Squares(TSWLS)algorithm and the Constrained Total Least Squares(CTLS)algorithm,which makes it possible to achieve the CRLB at moderate noise level before the threshold effect occurs. Moreover, from the Geometric Dilution Of Precision(GDOP)figure, it concludes target position, illuminator number and position are also important factors affecting the localization accuracy.
To solve the single-observer passive location estimation using illuminators of opportunity, a jointing TDOA and FDOA location algorithm based on maximum likelihood is proposed. Firstly, according to the TDOA and FDOA measurement equations, the maximum likelihood model is constructed. Then Newton's method is applied to solve the maximum likelihood model to obtain the estimation of the target position and velocity. The initial iteration value is given by a Least Squares(LS)algorithm. The Cramer-Rao Lower Bound(CRLB)and the theoretical error of the proposed algorithm are also derived and they are proved equal. Simulation results show that the proposed algorithm has higher estimation accuracy than the Two-Step Weighting Least Squares(TSWLS)algorithm and the Constrained Total Least Squares(CTLS)algorithm,which makes it possible to achieve the CRLB at moderate noise level before the threshold effect occurs. Moreover, from the Geometric Dilution Of Precision(GDOP)figure, it concludes target position, illuminator number and position are also important factors affecting the localization accuracy.
引文
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[14]Ho K C,Lu X,Kovavisaruch L.Source localization using TDOA and FDOA measurements in the presence of receiver location errors:analysis and solution[J].IEEE Transactions on Signal Processing,2007,55(2):684-696.
[15]Valaee S,Champagne B,Kabal P.Localization of wideband signals using least-squares and total least-squares approaches[J].IEEE Transactions on Signal Processing,1999,47(5):1213-1222.
[16]孟祥伟.基于约束总体最小二乘方法的到达时差到达频差无源定位算法[J].电子与信息学报,2014,36(5):1075-1081.
[17]He Y,Zhang C,Tang X,et al.Coherent integration loss due to pulses loss and phase modulation in passive bistatic radar[J].Digital Signal Processing,2013,23(4):1265-1276.
[18]He Q,Blum R S.The significant gains from optimally processed multiple signals of opportunity and multiple receive stations in passive radar[J].IEEE Signal Processing Letters,2014,21(2):180-184.
[19]Yu H,Huang G,Gao J.Constrained total least-squares localisation algorithm using time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties[J].IET Radar,Sonar and Navigation,2012,6(9):891-899.
[20]李金洲,郭福成.传感器位置误差条件下仅用到达频率差的无源定位性能分析[J].航空学报,2011,32(8):1497-1505.
[2]Yu Huagang,Huang Gaoming,Gao Jun,et al.Approximate maximum likelihood algorithm for moving source localization using TDOA and FDOA measurements[J].Chinese Journal of Aeronautics,2012,25(4):593-597.
[3]Subedi S,Zhang Y D,Amin M G,et al.Motion parameter estimation of multiple ground moving targets in multistatic passive radar systems[J].EURASIP Journal on Advances in Signal Processing,2014(1):1-14.
[4]Wang H,Wang J,Zhong L.Mismatched filter for analogue TV-based passive bistatic radar[J].IET Radar,Sonar and Navigation,2011,5(5):573-581.
[5]Zhu Jiabing,Tao Liang,Hong Yi.Study on moving target detection to passive radar based on FM broadcast transmitter[J].Journal of Systems Engineering and Electronics,2007,18(3):462-468.
[6]Michael E,Alexander S,Fabienne M.Design and performance evaluation of a mature FM/DAB/DVB-T multiilluminator passive radar system[J].IET Radar,Sonar and Navigation,2014,8(2):114-122.
[7]Sun H,Tan D K P,Lu Y,et al.Applications of passive surveillance radar system using cell phone base station illuminators[J].IEEE Aerospace and Electronic Systems Magazine,2010,25(3):10-18.
[8]Colone F,Falcone P,Bongioanni C,et al.Wi Fi-based passive bistatic radar:data processing schemes and experimental results[J].IEEE Transactions on Aerospace and Electronic Systems,2012,48(2):1061-1079.
[9]宋杰,何友,蔡复青,等.基于非合作雷达辐射源的无源雷达技术综述[J].系统工程与电子技术,2009,31(9):2151-2156.
[10]金家保,吴宁,杨全,等.基于似然方程校正的时差定位算法[J].计算机工程与应用,2013,49(16):213-215.
[11]Yeredor A,Angle A.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.
[12]Li J,Guo F,Le Y,et al.On the use of calibration sensors in source localization using TDOA and FDOA measurements[J].Digital Signal Processing,2014,27:33-43.
[13]Foy W H.Position-location solutions by Taylor-series estimation[J].IEEE Transactions on Aerospace and Electronic Systems,1976(2):187-193.
[14]Ho K C,Lu X,Kovavisaruch L.Source localization using TDOA and FDOA measurements in the presence of receiver location errors:analysis and solution[J].IEEE Transactions on Signal Processing,2007,55(2):684-696.
[15]Valaee S,Champagne B,Kabal P.Localization of wideband signals using least-squares and total least-squares approaches[J].IEEE Transactions on Signal Processing,1999,47(5):1213-1222.
[16]孟祥伟.基于约束总体最小二乘方法的到达时差到达频差无源定位算法[J].电子与信息学报,2014,36(5):1075-1081.
[17]He Y,Zhang C,Tang X,et al.Coherent integration loss due to pulses loss and phase modulation in passive bistatic radar[J].Digital Signal Processing,2013,23(4):1265-1276.
[18]He Q,Blum R S.The significant gains from optimally processed multiple signals of opportunity and multiple receive stations in passive radar[J].IEEE Signal Processing Letters,2014,21(2):180-184.
[19]Yu H,Huang G,Gao J.Constrained total least-squares localisation algorithm using time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties[J].IET Radar,Sonar and Navigation,2012,6(9):891-899.
[20]李金洲,郭福成.传感器位置误差条件下仅用到达频率差的无源定位性能分析[J].航空学报,2011,32(8):1497-1505.