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Real-time, point-by-point localization of magnetic targets such as ferrous unexploded ordnance can be achieved by the cube magnetic gradiometer system designed by the Naval Surface Warfare Center. The localization method uses the Frobenius norm of the magnetic gradient tensor to calculate the location of the magnetic target. This method assumes that the potential field of the Frobenius norm of the magnetic gradient tensor is a prefect sphere. But the Frobenius norm of the magnetic gradient tensor has an asphericity parameter, and its potential field is an ellipsoid, which can cause asphericity error. Since the current localization method can be affected seriously by the asphericity error, an improved method is proposed in this paper to eliminate the asphericity error. The improved method is based on a new invariant, which does not contain asphericity parameter. The new invariant can be obtained by the combination of the Frobenius norm and eigenvalues of the magnetic gradient tensor. In detail the procedure is as follows: first, the magnetic gradient tensor of the center point of the regular hexahedron's six planes can be measured by the cube magnetic gradiometer system, then these eigenvalues can be calculated and combined according to a certain relationship to eliminate the asphericity parameter, then the new invariants of the six planes can be obtained, and the spatial gradient of the new invariant can be calculated from the six new invariants, then the localization of the magnetic target can be calculated from the spatial gradient of the new invariant. This improved method can overcome the asphericity error effectively, and it can be used for real-time, point-by-point localization and detection of unexploded ordnance. Simulation experiments show that the localization error of the improved method is much smaller than that of the original method, the average relative error can be reduced by 10.9%. The improved method can be deployed on the highly maneuverable platform. The platform motion will not be constrained, and the improved method will be made more effectively in detection and localization of the magnetic targets. Thus the improved method can be widely applied in naval mines localization, mineral exploration, ferrous resources exploration, moving magnetic target tracking, and other fields.
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Keywords:
- magnetic gradient tensor /
- invariant /
- asphericity error /
- localization
[1] Nara T, Suzuki S, Ando S 2006 IEEE Transactions on Magnetics 42 3291
[2] Yu Z T, L J W, Fan L H, Zhang B T 2014 Systems Engineering and Electronics 36 1250 (in Chinese) [于振涛, 吕俊伟, 樊利恒, 张本涛 2014 系统工程与电子技术 36 1250]
[3] Young J A, Clark D A 2010 International Conference on Electromagnetics in Advanced Applicatioons Sydney, Australia, September 20-24, 2010 p701
[4] Yu Z T, L J W, Bi B, Zhou J 2014 Acta Phys. Sin. 63 110702(in Chinese) [于振涛, 吕俊伟, 毕波, 周静 2014 物理学报 63 110702]
[5] Wang L Q, Wang W M 2014 Chin. Phys. B 23 028703
[6] Wiegert R, Lee K H, Oeschger J 2008 IEEE Oceans 2008 Conference Proceedings Quebec City, Canada, September 15-18, 2008 p1
[7] Huang K Z, Xue M Z, Lu M W 2003 Tensor Analysis(Beijing: Tsinghua University Press) p55 (in Chinese) [黄克智, 薛明德, 陆明万 张量分析 2003 张量分析(北京: 清华大学出版社) 第55页]
[8] Wilson H 1985 Canada Technical Memorandum 8513
[9] Clark D A 2012 22th International Geophysical Conference and ExhibitionBrisbane, Australia, February 26-29, 2012 p1
[10] Wiegert R, Oeschger J 2006 IEEE Oceans 2006 Conference Proceedings Boston, Massachusetts, September 18-21, 2006 p1
[11] Wiegert R 2009 Proc. SPIE 7303Florida, USA, May 04, 2009 p1
[12] Chen J F, Zhang Q, Pan M C, Weng F B, Chen D X, Pang H F 2012 Chin. J. Sens. Actuators 25 1088 (in Chinese) [陈谨飞, 张琦, 潘孟春, 翁飞兵, 陈棣湘, 庞鸿锋 2012 传感技术学报 25 1088]
[13] Sui Y Y, Li G, Wang S L 2012 IEEE Transactions on Magnetics 48 4701
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[1] Nara T, Suzuki S, Ando S 2006 IEEE Transactions on Magnetics 42 3291
[2] Yu Z T, L J W, Fan L H, Zhang B T 2014 Systems Engineering and Electronics 36 1250 (in Chinese) [于振涛, 吕俊伟, 樊利恒, 张本涛 2014 系统工程与电子技术 36 1250]
[3] Young J A, Clark D A 2010 International Conference on Electromagnetics in Advanced Applicatioons Sydney, Australia, September 20-24, 2010 p701
[4] Yu Z T, L J W, Bi B, Zhou J 2014 Acta Phys. Sin. 63 110702(in Chinese) [于振涛, 吕俊伟, 毕波, 周静 2014 物理学报 63 110702]
[5] Wang L Q, Wang W M 2014 Chin. Phys. B 23 028703
[6] Wiegert R, Lee K H, Oeschger J 2008 IEEE Oceans 2008 Conference Proceedings Quebec City, Canada, September 15-18, 2008 p1
[7] Huang K Z, Xue M Z, Lu M W 2003 Tensor Analysis(Beijing: Tsinghua University Press) p55 (in Chinese) [黄克智, 薛明德, 陆明万 张量分析 2003 张量分析(北京: 清华大学出版社) 第55页]
[8] Wilson H 1985 Canada Technical Memorandum 8513
[9] Clark D A 2012 22th International Geophysical Conference and ExhibitionBrisbane, Australia, February 26-29, 2012 p1
[10] Wiegert R, Oeschger J 2006 IEEE Oceans 2006 Conference Proceedings Boston, Massachusetts, September 18-21, 2006 p1
[11] Wiegert R 2009 Proc. SPIE 7303Florida, USA, May 04, 2009 p1
[12] Chen J F, Zhang Q, Pan M C, Weng F B, Chen D X, Pang H F 2012 Chin. J. Sens. Actuators 25 1088 (in Chinese) [陈谨飞, 张琦, 潘孟春, 翁飞兵, 陈棣湘, 庞鸿锋 2012 传感技术学报 25 1088]
[13] Sui Y Y, Li G, Wang S L 2012 IEEE Transactions on Magnetics 48 4701
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