Journal of Geodesy and Geoinformation Science ›› 2021, Vol. 4 ›› Issue (4): 7483.doi: 10.11947/j.JGGS.2021.0406
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Li LIU^{1}(),Qingfeng XU^{2}(),Hui GU^{1},Lei ZHOU^{1},Zhenfu LIU^{1},Lili CAO^{1}
Received:
20200120
Accepted:
20200516
Online:
20211220
Published:
20211230
Contact:
Qingfeng XU
Email:liuli_sast@163.com;xuqfster@126.com
About author:
Li LIU (1978—), female, senior engineer, engaged in develop satellite T.T.&C. and payload electronics.Email: Supported by:
Li LIU,Qingfeng XU,Hui GU,Lei ZHOU,Zhenfu LIU,Lili CAO. Aeromagnetic Compensation Algorithm Based on LevenbergMarquard Neural Network[J]. Journal of Geodesy and Geoinformation Science, 2021, 4(4): 7483.
Tab.1
The input features of subnetworks"
Subnetwork  Function  Features  Input layer dimension  Hidden layer dimension 

Z_{1}  H_{sq}  t  3  1 
Z_{2}  H_{loc}  φ×θ ^{*}  6  3 
Z_{3}  H_{perm}  cosα, cosβ, cosγ  9  4 
Z_{4}  H_{ind}  cosα^{2}, cosαcosβ, cosαcosγ, cosβ^{2},cosβcosγ  15  7 
Z_{5}  H_{eddy}  cosαcosα', cosαcosβ', cosαcosγ', cosβcosα', cosβcosβ', cosβcosγ', cosγcosα', cosγcosβ'  24  12 
Z_{6}  H_{g}  dφ,dθ  6  3 
Tab.2
LM algorithm flow"
Input training set, and set MSE goal, minimum gradient, regularization coefficient μ, etc.  

Initialize network connection weights and thresholds.  
Iterate  ① Compute the output error E_{r} of all inputs with the current weights and biases. 
② Compute the sum of the square differences S_{se} corresponding to all inputs.  
③ Compute the jacobian matrix:H=J(se)^{T}×J(se).^{*}  
④ Compute the gradient:g=J(se)^{T}×E_{r}.  
⑤ Compute the adjustment value of the gradient:Δg=(H+Iμ)^{1}g. ^{**}.  
⑥ Recompute S_{se} with g+Δg:if S_{se} goes down then decreases μ and goes to step ①, and if S_{se} goes up then increases μ and goes to step ⑤.  
↑No  Whether the stop condition MSE goal, minimum gradient, or maximum epochs is reached. 
Yes→  Stop training, and output the weights, biases and training parameters. 
Tab.6
Standard deviation of compensationnT"
Experiment code  Standard Deviation of Raw data  Standard Deviation of LS compensation  Standard Deviation of networks Z_{3}—Z_{5} compensation  Standard Deviation of all networks compensation 

UAV2  17.8126  1.1256  0.9324  0.5004 
UAV3  41.1538  0.7028  0.4856  0.4855 
SCSS1  191.8949  23.0391  0.7030  0.6018 
SCSS2  118.0897  45.7260  5.6801  1.0443 
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