基于压缩感知的高精度地磁基准图构建方法

doi:10.13700/j.bh.1001-5965.2019.0313

北京航空航天大学学报 ›› 2020, Vol. 46 ›› Issue (4): 791-797.doi: 10.13700/j.bh.1001-5965.2019.0313

基于压缩感知的高精度地磁基准图构建方法

马啸宇¹, 张金生¹, 郝亮亮¹, 李婷¹, 王少博¹, 李琳²

1. 火箭军工程大学精确制导与仿真实验室, 西安 710025;
2. 火箭军96863部队, 洛阳 471000

收稿日期:2019-06-17 发布日期:2020-04-21
通讯作者: 张金生 E-mail:zjinshengchina@163.com
作者简介:马啸宇,男,硕士研究生。主要研究方向:地磁导航、导航制导与控制;张金生,男,博士,教授,硕士生导师。主要研究方向:导航、制导与控制。
基金资助:
国家自然科学基金（61673017）；中国博士后科学基金（2019M3643）

High-precision geomagnetic reference map construction method based on compressed sensing

MA Xiaoyu¹, ZHANG Jinsheng¹, HAO Liangliang¹, LI Ting¹, WANG Shaobo¹, LI Lin²

1. Pricision Guidance and Simulation Lab, Rocket Force University of Engineering, Xi'an 710025, China;
2. 96863 Troop of Rocket Army, Luoyang 471000, China

Received:2019-06-17 Published:2020-04-21
Supported by:
National Natural Science Foundation of China (61673017); China Postdoctoral Science Foundation (2019M3643)

摘要/Abstract

摘要： 地磁基准图的构建是实现地磁匹配导航的基石。针对实测数据量较小时利用插值法构建的地磁基准图精度不理想的问题，将压缩感知理论应用到地磁信息采集中。结合地磁基准图的结构特点设计了以离散余弦变换作为稀疏基、单位矩阵作为观测矩阵，以压缩采样匹配追踪（CoSaMP）算法作为重构算法的基于压缩感知的高精度地磁基准图构建方法，并与三次样条插值、Kriging插值及PSO-Kriging插值法进行对比。实验结果表明：所提方法具有较高的重构精度和稳定性，与性能最好的PSO-Kriging插值法相比，在6.25%采样率下重构地磁基准图，所提方法使得峰值信噪比（PSNR）由66.97 dB提高至74.67 dB，绝对误差由25.47 nT减小至10.26 nT，均方根误差由28.57 nT减小至11.33 nT。

关键词: 地磁匹配导航, 地磁基准图构建, 插值法, 压缩感知, 信号重构

Abstract: The construction of geomagnetic reference map is the cornerstone of geomagnetic matching navigation.In this paper, the compressed sensing theory is applied to the geomagnetic information acquisition, which aims at solving the problem that the accuracy of the geomagnetic reference map is not satisfactory with the less measured data based on interpolation methods.A high-precision method of geomagnetic reference map construction based on compressed sensing is put forward, taking the structural characteristics of the geomagnetic reference map into consideration. The discrete cosine transform matrix is used as sparse basis, the unit matrix is used as measurement matrix, and the compression sampling matching pursuit (CoSaMP) algorithm is used as the reconstruction method. The experimental results show that the proposedmethod has better reconstruction accuracy and stability compared withthe methods of cubic spline interpolation, Kriging interpolation and PSO-Kriging interpolation. Compared with the PSO-Kriging interpolation method which has the best performance among the three, when geomagnetic reference map is reconstructed at the sampling rate of 6.25%, the proposed method makes the peak signal-to-noise ratio (PSNR) increase from 66.97 dB to 74.67 dB, themeanabsolute error reduce from 25.47 nT to 10.26 nT,and the root mean square error decrease from 28.57 nT to 11.33nT.

Key words: geomagnetic matching navigation, geomagnetic reference map construction, interpolation algorithm, compressed sensing, signal reconstruction

中图分类号:

马啸宇, 张金生, 郝亮亮, 李婷, 王少博, 李琳. 基于压缩感知的高精度地磁基准图构建方法[J]. 北京航空航天大学学报, 2020, 46(4): 791-797.

MA Xiaoyu, ZHANG Jinsheng, HAO Liangliang, LI Ting, WANG Shaobo, LI Lin. High-precision geomagnetic reference map construction method based on compressed sensing[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(4): 791-797.

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基于压缩感知的高精度地磁基准图构建方法

High-precision geomagnetic reference map construction method based on compressed sensing

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