校正源存在下抑制部分同步时钟偏差和传感器位置误差的时差定位闭式解  

A closed⁃form solution for TDOA source localization with calibration emitter in presence of partial synchronization clock biases and sensor location uncertainties

作　　者：王鼎 高卫港 聂福全 吴志东 WANG Ding;GAO Weigang;NIE Fuquan;WU Zhidong(Institute of Information System Engineering,PLA Strategic Support Force Information Engineering University,Zhengzhou 450001,China;Weihua Group Co.,Ltd,Changyuan 453400,China;National Digital Switching System Engineering and Technology Research Center,Zhengzhou 450002,China)

机构地区：[1]中国人民解放军战略支援部队信息工程大学信息系统工程学院,郑州450001 [2]卫华集团有限公司,长垣453400 [3]国家数字交换系统工程技术研究中心,郑州450002

出　　处：《航空学报》2023年第16期210-233,共24页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(62171469,62071029);河南省科技攻关项目(192102210092);战略支援部队信息工程大学科研发展基金项目(F4108,F4109)。

摘　　要：同步时钟偏差和传感器位置先验观测误差是影响时差(TDOA)定位精度的重要因素。针对部分同步模型,提出一种协同校正源观测信息的TDOA定位新方法,旨在显著抑制两类模型误差影响。针对TDOA观测模型的强非线性特征,提出一种两阶段(称为阶段A和阶段B)闭式定位方法,可实现对各类参数解耦合估计,并且避免迭代运算。阶段A仅利用校正源观测,基于线性消元思想,利用贝叶斯(Bayesian)估计和加权最小二乘(WLS)估计,分步获得传感器位置和同步时钟偏差闭式解。阶段B则联合目标源观测与阶段A估计结果,推导新的伪线性观测方程,并利用WLS估计和拉格朗日乘子法获得目标源位置闭式解,随后基于Bayesian估计得到更精确的同步时钟偏差和传感器位置联合闭式解。此外,推导了相关克拉美罗界(CRB),并通过数学分析,证明新方法具有渐近统计最优性。仿真实验验证了文中理论分析有效性和新方法优越性。It is known that synchronization clock biases and sensor location uncertainties can significantly degrade the target localization accuracy based on Time Difference of Arrival(TDOA)measurements.To effectively restrain the in⁃fluence of the errors of the two models,this paper proposes a new TDOA target localization method using the calibra⁃tion emitter for the partially synchronous model.Considering the highly nonlinear characteristic of the TDOA measure⁃ment model,a closed-form positioning method based on two stages(Stage-A and Stage-B)is proposed,which can achieve decoupling estimation of unknowns and avoid iterative operation.Specifically,in Stage-A,only TDOA mea⁃surements from the calibration emitter are used.Based on the idea of linear elimination,the closed-form solutions for the sensor position and synchronization clock bias are obtained sequentially by utilizing the linear Bayesian estimator and the Weighted Least Squares(WLS)estimator,respectively.In Stage-B,the TDOA measurements from the tar⁃get are combined with the estimation results obtained in Stage-A,and a set of new pseudo-linear observation equa⁃tions is derived.Afterwards,the closed-form solution for the target location is produced by using the WLS estimator and the Lagrange multiplier method.Finally,a more accurate joint closed-form solution for sensor position and syn⁃chronization clock bias is given based on the linear Bayesian estimator.The relevant Cramér-Rao Bound(CRB)is also derived,and the asymptotic optimality of the proposed estimator is proved by mathematical analysis.Simulation results corroborate the validity of the theoretical development and superiority of the new method.

关 键 词：目标源定位 时差(TDOA) 同步时钟偏差 传感器位置误差 校正源 闭式解 理论性能分析 

分 类 号：V247[航空宇航科学与技术—飞行器设计] TN97[电子电信—信号与信息处理]