无线传感器网络中基于TDOA/FDOA的增强半正定松弛定位算法研究
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摘要
在无线传感器网络定位问题中,考虑了基于到达时间差TDOA(Time-Difference-of-Arrival)和到达频率差FDOA(Frequency-Difference-of-Arrival)的移动未知目标定位问题,TDOA/FDOA联合定位可以有效利用传感器的位置和速度信息,提高了定位精度。提出了一种增强半正定松弛方法,以进一步改善现有的半正定松弛SDR(Semidefinite Relaxation)方法的定位性能。通过利用现有半正定规划问题中优化变量之间的内在联系并将这些联系转化为凸约束,有效提高了现有半正定松弛方法的紧度,从而使被估计的未知目标的位置和速度精度达到了克拉美-罗下界CRLB(Cramer-Rao Lower Bound)。仿真结果表明,该方法的性能在大噪声时优于现有方法。
We address the moving source localization problem by using both time-difference-of arrival( TDOA) and frequency-difference-of-arrival( FDOA) measurements in wireless sensor network. Joint TDOA/FDOA localization can effectively use the sensors position and velocity information to improve the localization accuracy. We propose an enhanced semidefinite relaxation( SDR) method to further improve the localization performance of the existing SDR method. By exploiting the intrinsic relations between the optimization variables in the existing semidefinite programing( SDP) problem and converting them into convex constraints,we effectively improve the tightness of the SDR method,so that the accuracy of the estimated source position and velocity can reach the Cramer-Rao lower bound( CRLB). Simulation results show that the performance of the proposed method outperforms the existing methods when the noise is large.
We address the moving source localization problem by using both time-difference-of arrival( TDOA) and frequency-difference-of-arrival( FDOA) measurements in wireless sensor network. Joint TDOA/FDOA localization can effectively use the sensors position and velocity information to improve the localization accuracy. We propose an enhanced semidefinite relaxation( SDR) method to further improve the localization performance of the existing SDR method. By exploiting the intrinsic relations between the optimization variables in the existing semidefinite programing( SDP) problem and converting them into convex constraints,we effectively improve the tightness of the SDR method,so that the accuracy of the estimated source position and velocity can reach the Cramer-Rao lower bound( CRLB). Simulation results show that the performance of the proposed method outperforms the existing methods when the noise is large.
引文
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[12]Wang Gang,Li Youming,Nirwan Ansari.A Semidefinite Relaxation Method for Source Localization Using TDOA and FDOAMeasurements[J].IEEE Transaction on Vehicular Technology,2013,62(2):853-862.
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[14]Wang G,Cai S,Li Y,et al.A Bias-Reduced Nonlinear WLSMethod for TDOA/FDOA-Based Source Localization[J].IEEETransactions on Vehicular Technology,2016,65(10):8603-8615.
[15]Qu Xiaomei,Xie Lihua,Tan Wenrong.Iterative Constrained Weighted Least Squares Source Localization Using TDOA and FDOAMeasurements[J].IEEE Transactions on Signal Processing,2017,65(15):3990-4003.
[16]Grant M,Boyd S.CVX:MATLAB Software for Disciplined Convex Programming[M].
[2]Sakarindr P,Ansari N.Security Services in Group Communications over Wireless Infrastructure,Mobile Ad Hoc,and Wireless Sensor Networks[J].IEEE Wireless Communications,2007,14(5):8-20.
[3]姜志鹏,陈正宇,刘影,等.TOA定位算法非线性优化问题研究[J].传感技术学报,2015,28(11):1716-1719.
[4]Zou Y,Liu H,Xie W,et al.Semidefinite Programming Methods for Alleviating Sensor Position Error in TDOA Localization[J].IEEEAccess,2017,5:23111-23120.
[5]Zhang Y,Xing S,Zhu Y,et al.RSS-Based Localization in WSNs Using Gaussian Mixture Model via Semidefinite Relaxation[J].IEEE Communications Letters,2017,21(6):1329-1332.
[6]骆吉安,谭智文,郭云飞.声纳阵列网络基于移动信标到达角的渐进最优节点自定位算法[J].传感技术学报,2016,29(3):403-410.
[7]Wang Y,Wu Y.An Efficient Semidefinite Relaxation Algorithm for Moving Source Localization Using TDOA and FDOA Measurements[J].IEEE Communications Letters,2017,21(1):80-83.
[8]Torrieri D J.Statistical Theory of Passive Location Systems[J].IEEE Transactions on Aerospace and Electronic Systems,1984,20(2):183-197.
[9]Chan Y T,Ho K C.A Simple and Efficient Estimator for Hyperbolic Location[J].IEEE Transactions on Signal Processing,1994,42(8):1905-1915.
[10]Ho K C,Lu X,Kovavisaruch L.An Accurate Algebraic Solution for Moving Source Location Using TDOA and FDOA Measurements[J].IEEE Transactions on Signal Processing,2004,52(9):2453-2463.
[11]Ho K C,Xu W.Source Localization Using TDOA and FDOAMeasurements in the Presence of Receiver Location Errors:Analysis and Solution[J].IEEE Transactions on Signal Processing,2007,55(2):684-696.
[12]Wang Gang,Li Youming,Nirwan Ansari.A Semidefinite Relaxation Method for Source Localization Using TDOA and FDOAMeasurements[J].IEEE Transaction on Vehicular Technology,2013,62(2):853-862.
[13]Ho K C.Bias Reduction for an Explicit Solution of Source Localization Using TDOA[J].IEEE Transactions on Signal Processing,2012,60(5):2101-2114.
[14]Wang G,Cai S,Li Y,et al.A Bias-Reduced Nonlinear WLSMethod for TDOA/FDOA-Based Source Localization[J].IEEETransactions on Vehicular Technology,2016,65(10):8603-8615.
[15]Qu Xiaomei,Xie Lihua,Tan Wenrong.Iterative Constrained Weighted Least Squares Source Localization Using TDOA and FDOAMeasurements[J].IEEE Transactions on Signal Processing,2017,65(15):3990-4003.
[16]Grant M,Boyd S.CVX:MATLAB Software for Disciplined Convex Programming[M].