面向不确定性传感器位置的一致TOA定位  

Consistent TOA Localization with Sensor Position Uncertainties

作　　者：曾广扬 赵洪旭 牟必强 吴均峰 ZENG Guangyang;ZHAO Hongxu;MU Biqiang;WU Junfeng(School of Data Science,Chinese University of Hong Kong,Shenzhen,Shenzhen,Guangdong 518172,China;State Key Laboratory of Industrial Control Technology,Zhejiang University,Hangzhou,Zhejiang 310027,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]香港中文大学(深圳)数据科学学院,广东深圳518172 [2]浙江大学工业控制技术全国重点实验室,浙江杭州310027 [3]中国科学院数学与系统科学研究院,北京100190

出　　处：《信号处理》2024年第10期1791-1801,共11页Journal of Signal Processing

基　　金：国家自然科学基金(62273288,62203375);深圳市科技计划项目(JCYJ20220818103000001)。

摘　　要：目标定位是指利用传感信息估计目标在特定坐标系中的空间位置。基于到达时间(Time of Arrival,TOA)或等价的,基于距离的定位方法凭借其高精度特点得到了广泛研究。现有TOA定位方法一般假设传感器位置是精确的,只考虑距离测量噪声。而考虑了传感器位置不确定性的文献通常缺少统计学优化与分析,无法得到一致性估计。本文同时考虑距离测量噪声和传感器部署不确定性,将目标位置与传感器坐标均当成未知变量构建最大似然问题。本文首先给出关于观测噪声和传感器空间分布的假设,以保证一致性估计器的存在性。有趣的是,本文分析了最大似然估计性质,证明了其不一定具有一致性。本文进一步变换原始观测方程,构建可最优求解的优化问题。特别地,针对距离测量噪声方差已知情况,构建了含二次目标函数和一个二次等式约束的广义信赖域问题,并给出了其最优解求解算法;针对距离测量噪声方差未知情况,构建了普通线性最小二乘问题,实现目标位置和距离测量噪声方差的同时估计。本文针对两种情况分别提出了相应的偏差消除方法,实现了一致估计,即随着观测数量增加,估计值收敛至真实目标位置。一致性特性使所提算法在大样本观测场景可实现超高精度定位。此外,推导了高斯-牛顿迭代算法,可在观测样本和传感器位置不确定性较小时提高算法定位精度。仿真结果验证了所得理论结果的正确性和所提算法在大样本观测下的优越性。Target localization refers to estimating the spatial position of a target in a specific coordinate system using sensing information.It has widespread applications,ranging from advertisement recommendations,global navigation systems,and disaster rescue to battlefield monitoring.Time of arrival(TOA)-based or equivalent range-based localization methods have been widely studied due to their high-precision characteristics.The localization principle is to find the intersection of the circles(for a 2D case)or spheres(for a 3D case)induced from range measurements.However,due to the existence of measurement noises,these circles and spheres generally do not intersect at one point,and thus,optimization-based methods are required to estimate the target position.Existing TOA localization methods typically assume precise sensor positions and only consider range measurement noises,whereas previous studies that have taken sensor position uncertainties into account often lack statistical optimization and analysis,making it difficult to obtain consistent estimates.In this study,we considered both range measurement noises and sensor position uncertainties,and constructed a maximum likelihood problem by treating both the target position and sensor coordinates as unknown variables.The maximum likelihood problem turned out to be a weighted nonlinear least-squares problem.This paper first presented the assumptions on measurement noises and sensor spatial distribution;that is,measurement noises are independent and identically distributed Gaussian noises,and sensor positions have an asymptotic distribution whose probability measure does not concentrate on a line(for a 2D case)or a plane(for a 3D case).Based on these assumptions,the asymptotic identifiability of the target position is guaranteed.Of note,the maximum likelihood estimate is not necessarily consistent,which is quite different from the typical case without sensor position uncertainties.The original measurement equation was further transformed by squaring both sides to construc

关 键 词：到达时间 目标定位 大样本分析 一致估计器 

分 类 号：TN911.7[电子电信—通信与信息系统]