基于磁势梯度与高斯过程的空间磁场构建方法  

An Ambient Magnetic Field Construction Method Based on the Gradient of the Magnetic Potential and Gaussian Processes

作　　者：吴志东 唐涛 王鼎 WU Zhi-dong;TANG Tao;WANG Ding(Institute of Information System Engineering,PLA Strategic Support Force Information Engineering University,Zhengzhou,Henan 450001,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,河南郑州450001

出　　处：《电子学报》2020年第12期2304-2312,共9页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61201381,No.61401513);河南省科技攻关计划项目(No.192102210117,No.192102210092);中国博士后科学基金面上项目(No.2016M592989)。

摘　　要：构建准确的空间磁场是实现地磁室内定位的基础,针对传统构建模型未考虑磁场分布规律,导致其构建磁场精度差的问题,本文提出了基于磁势梯度与高斯过程的磁场构建方法.首先,将磁势梯度和磁场的关系中引入高斯过程,并用平方指数核函数的空间梯度与地球磁场分布的方差和作为高斯过程核函数;然后,将带有约束的超参数优化问题转换为无约束优化问题,并利用Rprop算法优化超参数;最后,通过仿真分析了新方法相比于传统方法的优势,讨论了超参数对构建精度的影响,并且使用三轴矢量磁传感器,分别在小区域较强磁场异常环境、开阔区域强磁场异常环境和弱磁场异常环境中开展磁场构建实验,结果证明提出的方法能够用于真实环境下空间磁场的准确构建.Modeling the spatial magnetic field precisely is the basis for the geomagnetism-based indoor localization and tracking system.Traditional magnetic constructing schemes ignore the distribution of magnetic field,which causes low accuracy of the constructing magnetic field.To deal with this problem,this paper presents a magnetic field modeling method based on the gradient of the magnetic potential and Gaussian processes.Firstly,the relationship between the gradient of the magnetic potential and magnetic field is introduced into the Gaussian processes.Furthermore,the sum of the squared exponential kernel spatial gradient and geomagnetic offset field distribution variance is used as the kernel function of the Gaussian processes.By transforming the constrained hyperparameters optimization problem into an unconstrained optimization problem,we employ the Rprop algorithm to estimate the hyperparameters.Finally,simulations are implemented to analyze the advantage of proposed method over traditional methods,and the impact of the hyperparameters on magnetic discernibility is also discussed.In addition,we carry out magnetic field constructing tests using a triaxial vector magnetic sensor in different environments,including small area relatively strong magnetic field distorted environment,strong magnetic field distorted environment,and open area weak magnetic field distorted environment,to validate the performance of the proposed method in different real environments.The results of the experiments prove that the proposed scheme works well in practical applications.

关 键 词：地磁室内定位 磁场构建 高斯过程 磁势梯度 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]