王锴松 , 周国华 , 刘月林 , 等 . 地磁模拟法测量舰船感应磁场的数值模拟 [J ] . 兵工学报 , 2022 , 43 ( 3 ): 617 - 625 . DOI: 10.12382/bgxb.2021.0110 http://doi.org/10.12382/bgxb.2021.0110 地磁模拟法测量舰船感应磁场具有测量速度快、实施方便等优点，但感应磁场测量精度受模拟地磁场均匀度所限制，研究其影响规律对推广应用地磁模拟法具有重要意义。从地磁模拟法原理出发，借助COMSOL多物理场有限元仿真平台，设计椭球壳解析算例来验证该仿真平台分析地磁模拟法测量感应磁场的有效性。设计某舰船算例进行数值模拟研究，定量分析了地磁模拟法测量舰船感应磁场的精度受模拟地磁场均匀度影响的变化规律，以及舰桥结构对感应磁场测量精度的影响程度。结果表明：当模拟地磁场均匀度达到91%时，感应磁场测量精度优于90%，若继续增加均匀度，则感应磁场测量精度提升效果变缓，工程效费比降低；舰桥结构对均匀度评估的影响程度为0.2%，对感应磁场测量精度的影响程度为2.7%，且当整体均匀度高于91%后，其影响程度降至2.5%，可忽略该结构对感应磁场测量的影响。研究结论为实际舰船消磁中进一步推广应用地磁模拟法提供了依据,也为地磁模拟线圈的优化设计提供了一定的参考。

WANG K S , ZHOU G H , LIU Y L , et al. Numerical simulation of measuring ship's induced magnetic field by geomagnetic field simulation method [J ] . Acta Armamentarii , 2022 , 43 ( 3 ): 617 - 625 . (in Chinese) DOI: 10.12382/bgxb.2021.0110 http://doi.org/10.12382/bgxb.2021.0110 Geomagnetic field simulation method has the advantages of fast measurement speed and convenient implementation, but the measurement accuracy of induced magnetic field is restricted by the uniformity of simulated geomagnetic field, so it is of great significance to study its influence law for popularizing and applying geomagnetic field simulation method. Based on the principle of geomagnetic field simulation method, with the help of COMSOL Multiphysics, an analytical example of an ellipsoidal shell is designed to verify the effectiveness of the simulation platform in analyzing geomagnetic field simulation method to measure induced magnetic field, and then a ship-type example is designed for numerical simulation. The variation law of the accuracy of measuring ship's induced magnetic field by geomagnetic field simulation method affected by the uniformity of simulated geomagnetic field and the influence of bridge structure on the measurement accuracy of induced magnetic field are quantitatively analyzed. The results show that the measurement accuracy of induced magnetic field is better than 90% when the uniformity of simulated geomagnetic field reaches 91%. If the uniformity continues to increase, the improvement effect of induced magnetic field measurement accuracy will slow down and the cost-effectiveness ratio of engineering will decrease. The influence of bridge structure on uniformity evaluation is 0.2%, and the influence degree of induced magnetic field measurement accuracy is 2.7%. When the overall uniformity is higher than 91%, its influence degree drops to 2.5%, so the influence of this structure on measuring induced magnetic field can be ignored. The research conclusion provides a basis for the further popularization and application of geomagnetic field simulation method in practical ship degaussing, and also provides a certain reference for optimization design of geomagnetic field simulation coils.

郭成豹 , 胡松 , 王文井 , 等 . 利用磁传感器阵列磁场差值的舰船磁场反演建模方法 [J ] . 兵工学报 , 2022 , 43 ( 1 ): 111 - 119 . DOI: 10.3969/j.issn.1000-1093.2022.01.012 http://doi.org/10.3969/j.issn.1000-1093.2022.01.012 为抑制地磁场变化、人工设施磁干扰等磁场环境噪声干扰的影响，提出一种利用磁传感器阵列磁场差值的舰船磁场反演建模方法。对于每个测量时刻分别给出磁传感器阵列中各个磁传感器间磁场差值的计算公式，采用三维舰船磁单极子阵列模型构建利用磁场差值进行舰船磁源反演的线性方程组，基于正则化技术求解得到舰船反演磁源模型。通过典型虚拟舰船磁场进行验证实验。结果表明：该建模方法能够消除相关性磁场环境噪声的干扰影响，实现在磁噪声环境中的舰船磁场高精度反演建模，验证了方法的有效性；使用新方法，不需要设置地磁参考传感器，相应设施的建设成本低、选址容易，为磁噪声环境中舰船磁场测量数据的高精度反演建模提供了新的技术选择。

GUO C B , HU S , WANG W J , et al. Ship magnetic field inversion modeling method utilizing the magnetic field difference between magnetic sensors [J ] . Acta Armamentarii , 2022 , 43 ( 1 ): 111 - 119 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2022.01.012 http://doi.org/10.3969/j.issn.1000-1093.2022.01.012 A method of ship magnetic field inversion modeling utilizing the magnetic field difference of magnetic sensor array is proposed to suppress the influence of environmental noise in magnetic fields， such as geomagnetic field variation and magnetic interference of artificial facility，etc. The formulas for calculating the magnetic field difference between the magnetic sensors in the magnetic sensor array are given for each measurement time. The linear equations for inversing the magnetic source from a ship are constructed by using the three-dimensional ship magnetic monopole array model. Finally，the inversed values of the magnetic source model of ship is obtained by using the regularization technique. The magnetic fields of a typical virtual ship are used to verify the validity of the proposed method. The results show that the proposed method can remove the interference effects of coherent magnetic field noise， and achieve high-precision inversion modeling of the magnetic field of a ship in the magnetically noisy environment. The validity of the proposed method is verified. If the proposed method is used for high precision inversion modeling of ship's magnetic field measurement data in magnetically noisy environment， the geomagnetic reference sensors are not required， and the corresponding facilities are low cost and easy to locate.

HOTT M , HARLAKIN A , HOEHER P A . Hybrid communication and localization underwater network nodes based on magnetic induction and visible light for AUV support [C ] // Proceedings of 2020 International Conference on Information and Communication Technology Convergence.Jeju, Korea:IEEE , 2020 : 66 - 68 .

HUANG Y , WAN B W , WU L H . Theoretical investigation on the linear location algorithm of the magnetic gradient tensor ranging by use of cuboid triaxial magnetometer array [J ] . IEEE Transactions on Magnetics , 2021 , 57 ( 11 ): 1 - 11 .

AMIR L , ELAD F , ROGER A , et al. Multiclass permanent magnets superstructure for indoor localization using artificial intelligence [J ] . IEEE Transactions on Magnetics , 2021 : 1 - 1 .

PASKU V , ANGELIS A D , ANGELIS G D , et al. Magnetic field-based positioning systems [J ] . IEEE Communications Surveys & Tutorials , 2017 , 19 ( 3 ): 2013 - 2017 .

CALLMER J , SKOGLUND M , GUSTAFSSON F . Silent localization of underwater sensors using magnetometers [J ] . Eurasip Journal on Advances in Signal Processing , 2010 , 2010 ( 1 ): 709318 . DOI: 10.1155/2010/709318 http://doi.org/10.1155/2010/709318 https://asp-eurasipjournals.springeropen.com/articles/10.1155/2010/709318 https://asp-eurasipjournals.springeropen.com/articles/10.1155/2010/709318

张朝阳 , 肖昌汉 . 海底布放磁传感器的磁定位方法的模拟实验研究 [J ] . 上海交通大学学报 , 2011 , 45 ( 6 ): 826 - 830 .

ZHANG C Y , XIAO C H . Simulation experiment research for magnetic localization method for magnetometer sensor at seabed [J ] . Journal of Shanghai Jiao Tong University , 2011 , 45 ( 6 ): 826 - 830 . (in Chinese)

杨明明 , 刘大明 , 连丽婷 , 等 . 用海面磁偶极子源定位海底矢量磁传感器 [J ] . 探测与控制学报 , 2011 , 33 ( 5 ): 41 - 45 .

YANG M M , LIU D M , LIAN L T , et al. Underwater vector-magnetometer located by using magnetic dipole sources in the offing [J ] . Journal of Detection & Control , 2011 , 33 ( 5 ): 41 - 45 . (in Chinese)

孙晔 , 肖昌汉 , 周国华 . 磁主动式海底磁传感器定位方法及其解析公式 [J ] . 海洋测绘 , 2012 , 32 ( 4 ): 25 - 32 .

SUN Y , XIAO C H , ZHOU G H . An active method and its analytical formulas of magnetic sensor positioning using the magnetic source [J ] . Hydrographic Surveying & Charting , 2012 , 32 ( 4 ): 25 - 32 . (in Chinese)

周国华 , 张树 , 赵文春 , 等 . 低速运动条件下的磁传感器定位方法 [J ] . 船电技术 , 2016 , 36 ( 9 ): 1 - 5 .

ZHOU G H , ZHANG S , ZHAO W C , et al. Magnetic sensor positioning method under low speed movement condition [J ] . Marine Electric & Electronic Engineering , 2016 , 36 ( 9 ): 1 - 5 . (in Chinese)

BIAN S Z , HEVESI P , CHRISTENSEN L , et al. Induced magnetic field-based indoor positioning system for underwater environments [J ] . Sensors , 2021 , 21 ( 6 ): 2218 . DOI: 10.3390/s21062218 http://doi.org/10.3390/s21062218 https://www.mdpi.com/1424-8220/21/6/2218 https://www.mdpi.com/1424-8220/21/6/2218 Autonomous underwater vehicles (AUV) are seen as an emerging technology for maritime exploration but are still restricted by the availability of short range, accurate positioning methods necessary, e.g., when docking remote assets. Typical techniques used for high-accuracy positioning in indoor use case scenarios, such as systems using ultra-wide band radio signals (UWB), cannot be applied for underwater positioning because of the quick absorption of the positioning medium caused by the water. Acoustic and optic solutions for underwater positioning also face known problems, such as the multi-path effects, high propagation delay (acoustics), and environmental dependency. This paper presents an oscillating magnetic field-based indoor and underwater positioning system. Unlike those radio wave-based positioning modalities, the magnetic approach generates a bubble-formed magnetic field that will not be deformed by the environmental variation because of the very similar permeability of water and air. The proposed system achieves an underwater positioning mean accuracy of 13.3 cm in 2D and 19.0 cm in 3D with the multi-lateration positioning method and concludes the potential of the magnetic field-based positioning technique for underwater applications. A similar accuracy was also achieved for various indoor environments that were used to test the influence of cluttered environment and of cross environment. The low cost and power consumption system is scalable for extensive coverage area and could plug-and-play without pre-calibration.

NAUREEN A , ZHANG N , FURBER S , et al. A gps-less localization and mobility modelling (LMM) system for wildlife tracking [J ] . IEEE Access , 2020 , 8 : 102709 - 102732 . DOI: 10.1109/Access.6287639 http://doi.org/10.1109/Access.6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

ZHOU Y , XIAO C H , ZHOU G H . Multi-objectivization-based localization of underwater sensors using magnetometers [J ] . IEEE Sensors Journal , 2014 , 14 ( 4 ): 1099 - 1106 . DOI: 10.1109/JSEN.2013.2287915 http://doi.org/10.1109/JSEN.2013.2287915 http://ieeexplore.ieee.org/document/6651756/ http://ieeexplore.ieee.org/document/6651756/

张新明 , 王霞 , 涂强 , 等 . 融合榜样学习和反向学习的粒子群优化算法 [J ] . 河南师范大学学报(自然科学版) , 2017 , 45 ( 6 ): 91 - 99 .

ZHANG X M , WANG X , TU Q , et al. Particle swarm optimization algorithm based on combing example learning and opposition learning [J ] . Journal of Henan Normal University (Natural Science Edition) , 2017 , 45 ( 6 ): 91 - 99 . (in Chinese)

YE W X , FENG W Y , FAN S H . A novel multi-swarm particle swarm optimization with dynamic learning strategy [J ] . Applied Soft Computing , 2017 , 61 : 832 - 843 . DOI: 10.1016/j.asoc.2017.08.051 http://doi.org/10.1016/j.asoc.2017.08.051 https://linkinghub.elsevier.com/retrieve/pii/S1568494617305331 https://linkinghub.elsevier.com/retrieve/pii/S1568494617305331

WU J S , CHEN E H . A novel hybrid particle swarm optimization for feature selection and kernel optimization in support vector regression [C ] // Proceedings of 2010 International Conference on Computational Intelligence and Security.Nanning, China:IEEE , 2010 : 189 - 194 .