一种基于加权多维标度分析的多个非相关源TDOA/FDOA协同定位方法

A TDOA/FDOA cooperative localization method for multiple disjoint sources based on weighted multidimensional scaling analysis

时/频差定位是针对运动辐射源的一类重要无线定位体制,其定位精度受时/频差观测误差和传感器模型(包括位置和速度)先验观测误差的影响较大。为了提高在大观测误差条件下的定位性能,提出一种基于加权多维标度分析的多个非相关源TDOA/FDOA协同定位方法。新方法包含2个计算阶段:阶段a利用2组多维标度分析中的标量积矩阵形成定位关系式,并进而构造加权矩阵以获得多个非相关源以及各传感器位置和速度的估计值;阶段b利用多维标度分析中引入的中间变量构建阶段a估计误差的约束优化模型,由此获得阶段a估计误差的估计值,并利用其更新阶段a的估计结果。通过一阶误差分析证明,所提方法对辐射源与传感器位置和速度的估计精度均能渐近逼近相应的克拉美罗界(CRB)。仿真实验结果验证了所提方法相比于其他时/频差定位方法的优越性。

TDOA/FDOA localization is an important wireless positioning mechanism for moving emitters,and its loca⁃tion accuracy is greatly affected by measurement errors of TDOA/FDOA and prior measurement errors of sensor mod⁃els(including sensor position and velocity).To improve the localization performance under the condition of high-level measurement errors,a TDOA/FDOA cooperative localization method for multiple disjoint sources is proposed based on weighted multidimensional scaling analysis in this paper.The proposed method consists of two calculation stages:Stage-a and Stage-b.Specifically,in Stage-a,two groups of scalar product matrices in multidimensional scaling analysis are employed to form the positioning relationship,which is further used to yield the solutions for the locations of multiple disjoint sources and sensors by constructing a weighting matrix.In Stage-b,a constrained minimization model is established based on the intermediate variables introduced in multidimensional scaling analysis to determine the estimation errors in Stage-a.By solving this optimization problem,the expression for the localization errors in Stage-a are obtained,so as to refine the position and velocity estimates of the multiple disjoint sources as well as the sensors.In addition,the first-order error analysis is employed to prove that the proposed method can asymptotically reach the Cramér-Rao Bound(CRB)accuracy.Simulation results show that the new method outperforms the existing TDOA/FDOA positioning methods.