基于CWLS时差频差无源定位闭式解算方法
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摘要
针对时差频差无源定位场景,提出一种基于约束加权最小二乘的无源定位闭式解算方法。在两步加权最小二乘算法基础上,建立了基于约束加权最小二乘的无源定位模型,推导其无约束最优化形式并给出目标状态估计的解析解。推导了目标状态估计均方误差的表达式,通过理论分析证明所提算法在保持两步加权最小二乘算法定位精度基础上,具有偏差减小特性。仿真结果表明,所提算法定位精度能够逼近CRLB,定位偏差明显小于两步加权最小二乘算法,验证了理论分析的有效性和所提算法的优越性。
For TDOA and FDOA passive localization,a novel theoretical analysis is developed to position the source with a closed-form solution based on the Constrained Weighted Least Squares(CWLS).Firstly,a localization model based on the CWLS is constructed based on classical Two Step Weighted Least Squares(TS-WLS)then the unconstrained optimization equations and algebraic solution is derived.Furthermore,the Mean square Error(MSE)of estimations is got,and which is utilized to prove that this solution keeps the same localization accuracy as TS-WLS solution and owns a characteristic of reducing location bias. Simulation results indicate that this proposed algorithm can achieve the CRLB performance and is far better than the TS-WLS algorithm as for the estimation bias. Simulations corroborate the effectiveness of the theoretical analysis and the advantages of proposed method.
For TDOA and FDOA passive localization,a novel theoretical analysis is developed to position the source with a closed-form solution based on the Constrained Weighted Least Squares(CWLS).Firstly,a localization model based on the CWLS is constructed based on classical Two Step Weighted Least Squares(TS-WLS)then the unconstrained optimization equations and algebraic solution is derived.Furthermore,the Mean square Error(MSE)of estimations is got,and which is utilized to prove that this solution keeps the same localization accuracy as TS-WLS solution and owns a characteristic of reducing location bias. Simulation results indicate that this proposed algorithm can achieve the CRLB performance and is far better than the TS-WLS algorithm as for the estimation bias. Simulations corroborate the effectiveness of the theoretical analysis and the advantages of proposed method.
引文
[1]郭福成,樊昀,周一宇,等.空间电子侦察定位原理[M].北京:国防工业出版社,2012.
[2]徐征.机载多平台无源定位跟踪算法研究[D].烟台:海军航空工程学院,2014.
[3]LI J Z,GUO F C,JIANG W L.Source localization and calibration using TDOA and FDOA measurements in the presence of sensor location uncertainty[J].Science China Information Sciences,2014,57:042315:1-042315:12.
[4]SMITH J,ABEL J.Closed-form least-squares source location estimation from range-difference measurements[J].IEEETransactions on Acoustics,Speech and Signal Processing,1987,35(12):1661-1669.
[5]HO K C,LU X N,KOVAVISARUCH L.Source localization using TDOA and FDOA measurements in the presence of receiver location error:analysis and solution[J].IEEETransactions on Signal Processing,2007,50(2):684-696.
[6]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].IEEETrans-actions on Signal Processing,2011,59(7):3434-3440.
[7]王鼎,李长胜,张瑞杰,等.基于无源定位观测方程的一类伪线性加权最小二乘定位闭式解及其理论性能分析[J].中国科学:信息科学,2015,45(9):1197-1217.
[8]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.
[9]冯奇,曲长文,李廷军.基于约束加权最小二乘的无源定位闭式解算方法[J].系统工程与电子技术,2017,39(2):263-268.
[10]张贤达.矩阵分析与应用[M].北京:清华大学出版社,2004:528-546.
[11]HO K C,CHAN Y T.Geometric-polar tracking from bearings-only and Doppler bearing measurements[J].IEEE Transactions on Signal Processing,2008,56(11):5540-5554.
[12]HO K C.Bias reduction for an explicit solution of source localization using TDOA[J].IEEE Transactions on Signal Processing,2012,60(5):2101-2113.
[2]徐征.机载多平台无源定位跟踪算法研究[D].烟台:海军航空工程学院,2014.
[3]LI J Z,GUO F C,JIANG W L.Source localization and calibration using TDOA and FDOA measurements in the presence of sensor location uncertainty[J].Science China Information Sciences,2014,57:042315:1-042315:12.
[4]SMITH J,ABEL J.Closed-form least-squares source location estimation from range-difference measurements[J].IEEETransactions on Acoustics,Speech and Signal Processing,1987,35(12):1661-1669.
[5]HO K C,LU X N,KOVAVISARUCH L.Source localization using TDOA and FDOA measurements in the presence of receiver location error:analysis and solution[J].IEEETransactions on Signal Processing,2007,50(2):684-696.
[6]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].IEEETrans-actions on Signal Processing,2011,59(7):3434-3440.
[7]王鼎,李长胜,张瑞杰,等.基于无源定位观测方程的一类伪线性加权最小二乘定位闭式解及其理论性能分析[J].中国科学:信息科学,2015,45(9):1197-1217.
[8]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.
[9]冯奇,曲长文,李廷军.基于约束加权最小二乘的无源定位闭式解算方法[J].系统工程与电子技术,2017,39(2):263-268.
[10]张贤达.矩阵分析与应用[M].北京:清华大学出版社,2004:528-546.
[11]HO K C,CHAN Y T.Geometric-polar tracking from bearings-only and Doppler bearing measurements[J].IEEE Transactions on Signal Processing,2008,56(11):5540-5554.
[12]HO K C.Bias reduction for an explicit solution of source localization using TDOA[J].IEEE Transactions on Signal Processing,2012,60(5):2101-2113.