基于目标高斯分布的定位系统节点最优部署方法

doi:10.12305/j.issn.1001-506X.2021.07.08

系统工程与电子技术 ›› 2021, Vol. 43 ›› Issue (7): 1791-1796.doi: 10.12305/j.issn.1001-506X.2021.07.08

基于目标高斯分布的定位系统节点最优部署方法

周荣艳^1,², 陈建峰^1,*, 李晓强¹, 谭伟杰³

1. 西北工业大学航海学院, 陕西西安 710072
2. 南阳理工学院, 河南南阳 473004
3. 贵州大学公共大数据国家重点实验室, 贵州贵阳 550025

收稿日期:2020-04-08 出版日期:2021-06-30 发布日期:2021-07-08
通讯作者: 陈建峰
作者简介:周荣艳(19855—)，女，博士研究生，主要研究方向为阵列信号处理、无线传感网|陈建峰(1972—)，男，教授，博士研究生导师，博士，主要研究方向为阵列信号处理、水声工程|李晓强(1978—)，男，博士研究生，主要研究方向为阵列信号处理、目标方位估计|谭伟杰(1981—)，男，讲师，博士，主要研究方向为稀疏信号处理、通信信号处理及信息安全
基金资助:
国家自然科学基金(61501374);河南省高校重点科研(18B510013)

Optimal deployment method of sensors in localization system based on targets with Gaussian distribution

Rongyan ZHOU^1,², Jianfeng CHEN^1,*, Xiaoqiang LI¹, Weijie TAN³

1. School of Marine Science and Technology, Northwest Polytechnic University, Xi'an 710072, China
2. Nanyang Institute of Technology, Nanyang 473004, China
3. State Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China

Received:2020-04-08 Online:2021-06-30 Published:2021-07-08
Contact: Jianfeng CHEN

摘要/Abstract

摘要：

针对三维空间定位系统中目标位置服从高斯先验分布假设条件下节点最优部署问题, 分析了纯方位目标定位算法中估计误差的费希尔信息矩阵, 推导出基于目标先验分布的克拉美罗界(Cramer-Rao bound, CRB)。为了解决目标位置在任意高斯分布时, 协方差矩阵为非对角阵的问题, 提出了基于三维坐标旋转的最大后验概率估计方法, 将协方差矩阵转化为对角阵以实现最小化CRB的迹, 从而得到定位系统中节点的最优部署。最后, 通过梯度下降算法对节点最优部署问题的理论推导进行仿真, 验证了该部署方法的有效性，同时仿真结果中不同节点部署方法的对比也表明了该方法可有效降低定位误差。

关键词: 参数估计, 克拉美罗界, 最大后验估计, 节点最优部署

Abstract:

The optimal deployment of sensors problem is considered when the target location obeys Gaussian prior distribution in three-dimensional space positioning system. The Fisher information matrix of the estimation error in bearings-only localization algorithm is analyzed and Cramer-Rao bound (CRB) based on the target prior distribution is derived. Then, the maximum posterior probability estimation method based on three-dimensional coordinate rotation is discussed to convert a non-diagonal covariance matrix into a diagonal matrix, which aims to minimize the trace of the CRB, and the optimal sensor deployment is obtained. Finally, the gradient-descent algorithm is adopted to simulate effectiveness of the method is verified. Simulation results also show that the method can effectively reduce the localization error compared with the different sensor deployment.

Key words: parameter estimation, Craomer-Rao bound (CRB), the maximum posterior probability (MAP), optimal sensor deployment

中图分类号:

TN92

周荣艳, 陈建峰, 李晓强, 谭伟杰. 基于目标高斯分布的定位系统节点最优部署方法[J]. 系统工程与电子技术, 2021, 43(7): 1791-1796.

Rongyan ZHOU, Jianfeng CHEN, Xiaoqiang LI, Weijie TAN. Optimal deployment method of sensors in localization system based on targets with Gaussian distribution[J]. Systems Engineering and Electronics, 2021, 43(7): 1791-1796.

图/表 4

参考文献 26

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方法	tr(CRB)
方法	实验1	实验2
方法1	65.65	64.31
方法2	18.72	20.35
方法3	6.65	6.79

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基于目标高斯分布的定位系统节点最优部署方法

Optimal deployment method of sensors in localization system based on targets with Gaussian distribution

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