基于TOA变化率有偏估计的单通道无源定位
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摘要
针对相对径向加速度较小时,已有的到达时间(time of arrival,TOA)二次变化率定位方法精度低的问题,提出基于TOA变化率的高精度定位方法。为了提高TOA变化率估计精度,提出忽略径向加速度进行有偏估计的方法;基于有偏的TOA变化率,首先采用牛顿迭代方法,获得目标位置的粗估计,再根据粗定位值近似计算定位偏差,对粗定位进行偏差修正,得到目标位置的高精度估计。理论分析了利用有偏估计进行定位带来的随机误差和定位偏差,以及偏差修正后的定位精度。仿真分析表明,在观测站速度和加速度较小时,本文提出的TOA变化率定位方法精度优于TOA二次变化率定位方法,提出的偏差修正方法可有效降低有偏估计带来的定位偏差,定位精度优于无偏TOA变化率定位方法。
Existing localization methods using second order changing rate of time of arrival(TOA)can not achieve a high precise estimation when the acceleration of the observing station is small.A new locating method is proposed by estimating the TOA changing rate for each duration slice of the observation.A biased estimator is used to reduce the root mean square error(RMSE)by ignoring the relative acceleration.Firstly,Newton iterative method is adopted to get a rough estimation of the position based on the biased estimation.Secondly,the position bias can be calculated approximately with the coarse estimation.Finally,the location is revised by eliminating the calculated position bias from the rough estimation.The location errors before and after correction are induced consisting of the random and biased portion.The numerical simulations demonstrate that the localization based on TOA changing rate is more precise than the one based on second order changing rate of TOA,and the correction procedure can modify the position estimation efficiently.The location precision is better than that of the conventional unbiased method.
Existing localization methods using second order changing rate of time of arrival(TOA)can not achieve a high precise estimation when the acceleration of the observing station is small.A new locating method is proposed by estimating the TOA changing rate for each duration slice of the observation.A biased estimator is used to reduce the root mean square error(RMSE)by ignoring the relative acceleration.Firstly,Newton iterative method is adopted to get a rough estimation of the position based on the biased estimation.Secondly,the position bias can be calculated approximately with the coarse estimation.Finally,the location is revised by eliminating the calculated position bias from the rough estimation.The location errors before and after correction are induced consisting of the random and biased portion.The numerical simulations demonstrate that the localization based on TOA changing rate is more precise than the one based on second order changing rate of TOA,and the correction procedure can modify the position estimation efficiently.The location precision is better than that of the conventional unbiased method.
引文
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[2]ROMERO L A,MASON J.Geolocation using TOA,FOA,and altitude information at singular geometries[J].IEEE Trans.on Aerospace and Electronic Systems,2015,51(2):1069-1077.
[3]ZHOU L J,ZHU W Q,LUO J Q,et al.Direct positioning maximum likelihood estimator using TDOA and FDOA for coherent short-pulse radar[J].IET Radar,Sonar&Navigation,2017,11(10):1505-1511.
[4]NGUYEN N H,DOGANCAY K.Multistatic pseudolinear target motion analysis using hybrid measurements[J].Signal Processing,2017,130(C):22-36.
[5]ALAN O,PAWAN S,NATASHA D.Single-sensor RF emitter localization based on multipath exploitation[J].IEEE Trans.on Aerospace and Electronic Systems,2015,15(3):1635-1650.
[6]WEBSTER R J.An exact trajectory solution from Doppler shift measurement[J].IEEE Trans.on Aerospace and Electronic System,1982,18(2):249-252.
[7]CHEN Y T,TOWERS J J.Sequential localization of a radiating source by doppler-shifted frequency measurement[J].IEEETrans.on Aerospace and Electronic System,1992,28(4):1084-1089.
[8]SCALES W C,SWANSON R.Air and sea rescue via satellite systems[J].IEEE Spectrum,1984,21:48-52.
[9]陆安南,孔宪正.单星测频无源定位法[J].通信学报,2004,25(9):160-168.LU A N,KONG X Z.Passive localization from frequency measurements by single satellite[J].Journal of China Institute of Communications,2004,25(9):160-168.
[10]ELAD T,BEN Z B,ANTHONY J W.Single receiver emitter geolocation based on signal periodicity with oscillator instability[J].IEEE Trans.on Signal Processing,2014,62(6):1377-1385.
[11]LIU Y,GUO F C,YANG L,et al.Source localization using a moving receiver and noisy TOA measurements[J].Signal Processing,2016,119(C):185-189.
[12]MADADI Z,QUITIN F,TAY W P.Periodic RF transmitter geolocation using a mobile receiver[C]∥Proc.of the IEEE International Conference on Acoustics,Speech and Signal Processing,2015:2584-2588.
[13]QUITIN F,MADADI Z,TAY W P.RF transmitter geolocation based on signal periodicity:concept and implementation[C]∥Proc.of the IEEE International Conference on Communications,2015:4593-4598.
[14]LIANG K,HUANG Z,HE J Z.A passive localization method of single satellite using TOA sequence[C]∥Proc.of the IEEEInternational Conference on Computer and Communications,2016:1795-1798.
[15]ELAD T,ANTHONY J W.Single sensor path design for best emitter localization via convex optimization[J].IEEE Trans.on Wireless Communications,2017,16(2):939-951.
[16]STEFFES C.Novel TDOA-based single sensor localization approach using signal structure information[C]∥Proc.of the12th Workshop on Positioning,Navigation and Communication,2015.
[17]STEFFES C,OISPUU M.Direct single sensor TDOA localization using signal structure information[C]∥Proc.of the 18th International Conference on Information Fusion(FUSION),2015.
[18]STEFFES C,OISPUU M.Direct position determination for TDOA-based single sensor localization[J].Journal of Advances in Information Fusion,2016,2(11):250-261.
[19]孙仲康.基于运动学原理的无源定位技术[J].制导与引信,2001,22(l):40-44.SUN Z K.Passive location technology based on kinematics theory[J].Guidance&Fuze,2001,22(1):40-44.
[20]冯道旺.利用径向加速度信息的单站无源定位技术研究[D].长沙:国防科技大学,2003.FENG D W.Researches on passive localization techniques using radial acceleration by single observer[D].Changsha:National University of Defense Technology,2003.
[21]徐义,郭福成,冯道旺.一种单星仅测TOA无源定位方法[J].宇航学报,2010,31(2):502-508.XU Y,GUO F C,FENG D W.A new satellite passive localization method using TOA measurement only[J].Journal of Astronautics,2010,31(2):502-508.
[22]KOBY T,JOSEPH T.General classes of performance lower bounds for parameter estimation-part I:non-bayesian bounds for unbiased estimators[J].IEEE Trans.on Information Theory,2010,56(10):5045-5063.
[23]KAY S,ELDAR Y C.Rethinking biased estimation[J].IEEESignal Processing Magazine,2008,25(3):133-136.
[24]周龙健,罗景青,孔辉.基于虚拟时差的运动阵列空间无源定位算法[J].电子与信息学报,2017,39(7):1759-1763.ZHOU L J,LUO J Q,KONG H.A passive location algorithm based on the virtual TDOAs of moving array[J].Journal of Electronics&Information Technology,2017,39(7):1759-1763.
[25]KOBY T,JOSEPH T.Achievable MSE lower bounds in nonBayesian biased estimation[C]∥Proc.of the IEEE Workshop on Sensor Array and Multichannel Processing,2010:117-120.
[26]KOBY T,JOSEPH T.Uniformly best biased estimators in non-bayesian parameter estimation[J].IEEE Trans.on Information Theory,2011,57(11):7635-7647.