Determine the location of a target has gained considerable interest over the past few years. The Received Signal Strength(RSS) measurements and Differential RSS(DRSS) measurements can be converted to distance or dista...Determine the location of a target has gained considerable interest over the past few years. The Received Signal Strength(RSS) measurements and Differential RSS(DRSS) measurements can be converted to distance or distance ratio estimates for constructing a set of linear equations. Based on these linear equations, a constrained weighted least Squares(CWLS) algorithm for target localization is derived. In addition, an iterative technique based on Newton's method is utilized to give a solution. The covariance and bias of the CWLS algorithm is derived using perturbation analysis. Simulation shows that the proposed estimator achieves better performance than existing algorithms with reasonable complexity.展开更多
针对现有的两步加权最小二乘(Two-stage Weighted Least Squares,TSWLS)和约束加权最小二乘(Constrained Weighted Least Squares,CWLS)在TDOA/AOA混合定位中可能产生测量矩阵奇异的情况,提出了一种改进的CWLS算法来消除奇异矩阵求逆运...针对现有的两步加权最小二乘(Two-stage Weighted Least Squares,TSWLS)和约束加权最小二乘(Constrained Weighted Least Squares,CWLS)在TDOA/AOA混合定位中可能产生测量矩阵奇异的情况,提出了一种改进的CWLS算法来消除奇异矩阵求逆运算.其主要思想是在约束条件下,用含有移动台位置坐标的价值函数对移动台坐标和附加变量分别取偏微分,分离出引入的附加变量,使移动台位置坐标与附加变量分别位于线性方程的两边,求解关于附加变量的一元二次方程,因此避免了对奇异矩阵求逆的运算.在零均值的高斯白噪声环境下,且移动台位于或接近监测基站阵列中心时,通过MATLAB仿真验证了改进的CWLS算法比TSWLS和CWLS算法均能取得更高的定位精度,可以达到克拉美-罗下界(CramérRao Lower Bound,CRLB).展开更多
针对无源定位问题中可进行伪线性处理的观测方程,提出一种基于约束加权最小二乘的无源定位闭式解算的理论框架。首先,在不限定定位观测量情况下,建立基于约束加权最小二乘的定位模型,推导其无约束最优化形式;然后,只需通过广义特征值分...针对无源定位问题中可进行伪线性处理的观测方程,提出一种基于约束加权最小二乘的无源定位闭式解算的理论框架。首先,在不限定定位观测量情况下,建立基于约束加权最小二乘的定位模型,推导其无约束最优化形式;然后,只需通过广义特征值分解即可实现辐射源状态估计并给出其解析表达式,并在此基础上证明了该闭式解的全局最优性和减小定位偏差的特性;最后,将该理论框架应用于到达角(angle of arrival,AOA)/到达时间差(time difference of arrival,TDOA)联合定位场景,验证了其有效性。仿真结果表明,所提算法定位精度能够逼近克拉美-罗下限(Cramer-Rao low bound,CRLB),定位偏差明显小于加权最小二乘算法,尤其在连续定位时间较短,噪声强度较大等情况下,验证了所提理论框架的优越性。展开更多
电力系统状态估计常用加权最小二乘(W LS)法处理,这种方法中量测权值的悬殊和大量的注入量测会导致信息矩阵出现病态问题,降低算法的收敛性。综合带约束的正规方程(NE/C)法和海克特(H ach te l)法数值稳定性好的优点,把量测量合理分类...电力系统状态估计常用加权最小二乘(W LS)法处理,这种方法中量测权值的悬殊和大量的注入量测会导致信息矩阵出现病态问题,降低算法的收敛性。综合带约束的正规方程(NE/C)法和海克特(H ach te l)法数值稳定性好的优点,把量测量合理分类构建信息矩阵,并采用分块稀疏矩阵技术,形成了一种计算速度快、数值稳定性好的状态估计新算法。理论和算例分析验证了该算法的有效性。展开更多
Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWL...Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.展开更多
文摘Determine the location of a target has gained considerable interest over the past few years. The Received Signal Strength(RSS) measurements and Differential RSS(DRSS) measurements can be converted to distance or distance ratio estimates for constructing a set of linear equations. Based on these linear equations, a constrained weighted least Squares(CWLS) algorithm for target localization is derived. In addition, an iterative technique based on Newton's method is utilized to give a solution. The covariance and bias of the CWLS algorithm is derived using perturbation analysis. Simulation shows that the proposed estimator achieves better performance than existing algorithms with reasonable complexity.
文摘针对现有的两步加权最小二乘(Two-stage Weighted Least Squares,TSWLS)和约束加权最小二乘(Constrained Weighted Least Squares,CWLS)在TDOA/AOA混合定位中可能产生测量矩阵奇异的情况,提出了一种改进的CWLS算法来消除奇异矩阵求逆运算.其主要思想是在约束条件下,用含有移动台位置坐标的价值函数对移动台坐标和附加变量分别取偏微分,分离出引入的附加变量,使移动台位置坐标与附加变量分别位于线性方程的两边,求解关于附加变量的一元二次方程,因此避免了对奇异矩阵求逆的运算.在零均值的高斯白噪声环境下,且移动台位于或接近监测基站阵列中心时,通过MATLAB仿真验证了改进的CWLS算法比TSWLS和CWLS算法均能取得更高的定位精度,可以达到克拉美-罗下界(CramérRao Lower Bound,CRLB).
文摘针对无源定位问题中可进行伪线性处理的观测方程,提出一种基于约束加权最小二乘的无源定位闭式解算的理论框架。首先,在不限定定位观测量情况下,建立基于约束加权最小二乘的定位模型,推导其无约束最优化形式;然后,只需通过广义特征值分解即可实现辐射源状态估计并给出其解析表达式,并在此基础上证明了该闭式解的全局最优性和减小定位偏差的特性;最后,将该理论框架应用于到达角(angle of arrival,AOA)/到达时间差(time difference of arrival,TDOA)联合定位场景,验证了其有效性。仿真结果表明,所提算法定位精度能够逼近克拉美-罗下限(Cramer-Rao low bound,CRLB),定位偏差明显小于加权最小二乘算法,尤其在连续定位时间较短,噪声强度较大等情况下,验证了所提理论框架的优越性。
文摘电力系统状态估计常用加权最小二乘(W LS)法处理,这种方法中量测权值的悬殊和大量的注入量测会导致信息矩阵出现病态问题,降低算法的收敛性。综合带约束的正规方程(NE/C)法和海克特(H ach te l)法数值稳定性好的优点,把量测量合理分类构建信息矩阵,并采用分块稀疏矩阵技术,形成了一种计算速度快、数值稳定性好的状态估计新算法。理论和算例分析验证了该算法的有效性。
基金supported by the National Natural Science Foundation of China(61201282)the Science and Technology on Communication Information Security Control Laboratory Foundation(9140C130304120C13064)
文摘Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.
