CN112308112A - Geomagnetic reference map construction method based on sparse representation and dictionary learning - Google Patents

Geomagnetic reference map construction method based on sparse representation and dictionary learning Download PDF

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CN112308112A
CN112308112A CN202011009480.XA CN202011009480A CN112308112A CN 112308112 A CN112308112 A CN 112308112A CN 202011009480 A CN202011009480 A CN 202011009480A CN 112308112 A CN112308112 A CN 112308112A
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sparse
geomagnetic
dictionary
reference map
construction method
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张金生
马啸宇
王仕成
李婷
卢兆兴
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Rocket Force University of Engineering of PLA
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Abstract

The invention provides a geomagnetic reference map construction method based on sparse representation and dictionary learning, which comprises the following steps of: initializing a sparse dictionary by utilizing moment harmonic analysis; training the sparse dictionary by utilizing a K-SVD algorithm; the method has the advantages that the high-resolution geomagnetic reference map is reconstructed by utilizing the characteristic that the low-resolution geomagnetic reference map and the high-resolution geomagnetic reference map have the same sparse coefficient, the method has higher construction precision on the geomagnetic reference map, has lower requirements on a data set required by training, and has better robustness on noise.

Description

Geomagnetic reference map construction method based on sparse representation and dictionary learning
Technical Field
The invention relates to the technical field of geomagnetic reference, in particular to a geomagnetic reference map construction method based on sparse representation and dictionary learning.
Background
In recent years, the navigation technology in China is rapidly developed, and the inertial navigation technology and the satellite navigation technology are main research directions in the field of navigation guidance. However, in the inertial navigation, the gyroscope drift can be accumulated continuously over time in a long-distance task, and the satellite navigation is easily interfered by various environmental factors. The geomagnetic navigation technology is an important auxiliary navigation means, and due to the fact that a geomagnetic field is stable and has the characteristics of small time change, strong anti-interference capability and the like, the geomagnetic navigation technology gradually receives extensive attention and research.
The geomagnetic matching navigation technology firstly models a geomagnetic field and acquires data to prepare a geomagnetic reference map, then acquires real-time magnetic measurement information of a target area, and finally matches the acquired geomagnetic field information with the reference map, so that the purpose of positioning navigation is realized, and the high-precision geomagnetic reference map is the basis for realizing geomagnetic matching navigation.
At present, there are two main methods for constructing a geomagnetic reference map: firstly, the method is constructed according to the existing geomagnetic field physical model, and secondly, a gridding geomagnetic reference map is constructed according to actually measured geomagnetic field data. The existing world magnetic field model and the international geomagnetic reference magnetic field are analyzed against the main magnetic field model of the earth. In general, the local geomagnetic field can be most reflected by the abnormal field in the earth, and the change of the abnormal field is difficult to reflect by a world geomagnetic field model. Therefore, when the geomagnetic field in the local area is constructed with high precision, a method of interpolation modeling based on measured data is generally used. In recent years, research on a geomagnetic reference map construction method mainly focuses on an interpolation method, and commonly used methods include: bicubic interpolation, Kriging interpolation, Particle Swarm Optimization (PSO) based Kriging interpolation, and the like. Although the existing algorithm has a certain improvement in evaluation indexes such as peak signal-to-noise ratio, root-mean-square error and the like of a reference graph, detailed information among magnetic measurement points is difficult to recover well.
Disclosure of Invention
In this summary, concepts in a simplified form are introduced that are further described in the detailed description section. This summary of the invention is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter.
In order to at least partially solve the technical problem, the invention provides a geomagnetic reference map construction method based on sparse representation and dictionary learning, which comprises the following steps: s1: initializing a sparse dictionary;
modeling the geomagnetic field of the target area, gridding the reference graph according to the modeling, and measuring the data magnetically according to BR＝B0-BCDecomposition is carried out.
Further, B isR＝B0-BCSaid B isRExpressed as the value of the residual magnetic field of the earth magnetism, B0Expressed as measured geomagnetic field data, BCExpressed as the theoretical value calculated for the international geomagnetic reference field.
Further, by said BR＝B0-BCAnd acquiring the residual magnetic field value of the target area.
Further, the modeling of the residual magnetic field value of the target region is analyzed by a moment resonance analysis, and the specific process is as follows:
in a space without a magnetic field source, the target magnetic potential can be obtained by laplace's equation:
Figure BDA0002697097720000021
can be written as:
Figure BDA0002697097720000022
wherein the content of the first and second substances,
n＝q-m+1,
v＝2π/Lx,
w＝2π/Ly,
Figure BDA0002697097720000031
Pmn(x,y)＝Dmn cos(mvx)cos(nwy)+
Emn cos(mvx)sin(nwy)+
Fmn sin(mvx)cos(nwy)+
Gmnsin (mvx) sin (nwy), x, y, z are three-dimensional coordinates of the magnetic measurement position, V (x, y, z) is the maximum truncation order, LxAnd LyThe length and width of the target rectangular area.
Taking the center of gravity of the rectangular area as the origin of the harmonic moment coordinate system, the coordinate range is as follows:
Figure BDA0002697097720000032
the geomagnetic three-component at this time can be expressed as:
Figure BDA0002697097720000033
wherein the content of the first and second substances,
Qmn(x,y)＝mv(Dmn sin(mvx)cos(nwy)+
Emn sin(mvx)sin(nwy)-
Fmn cos(mvx)cos(nwy)-
Gmn cos(mvx)sin(nwy))
Rmn(x,y)＝nw(Dmn cos(mvx)sin(nwy)-
Emn cos(mvx)cos(nwy)+
Fmn sin(mvx)sin(nwy)-
Gmn sin(mvx)cos(nwy))
Smn(x,y)＝-uPmn(x,y)
the total field strength can thus be expressed as:
Figure BDA0002697097720000034
by the method, a geomagnetic residual field model can be established and accurate gridding data can be acquired;
the sparse dictionary used by the invention is composed of 512 characteristic column vectors, wherein one half of the sparse dictionary is formed by randomly extracting geomagnetic residual field gridding data, the other half of the sparse dictionary is formed by randomly extracting international geomagnetic reference field data, and a finally generated matrix is used as an initial dictionary for dictionary training.
S2: training the sparse dictionary;
learning a low-resolution and high-resolution sparse dictionary by adopting a K-SVD method;
frobenius norm is adopted to measure the deviation between the original image and the image after sparse decomposition, and the jth division in the sparse matrix is kept0Extracting the jth column from all columns except the column without changing0The post column problem can be written as:
Figure BDA0002697097720000041
the above-mentioned
Figure BDA0002697097720000042
Figure BDA0002697097720000043
Represents the jth row of the sparse coefficient X.
By constantly updating djAnd
Figure BDA0002697097720000044
to minimize residual errors, the ultimate goal being to make
Figure BDA0002697097720000045
Is similar to
Figure BDA0002697097720000046
It can therefore be solved by singular value decomposition, however this approach would be vectoring
Figure BDA0002697097720000047
Becoming dense, the number of non-zero terms in X is increased.
Thus defining a matrix
Figure BDA0002697097720000048
Is used for extracting
Figure BDA0002697097720000049
The non-zero term in (a) is,
Figure BDA00026970977200000410
number of lines
Figure BDA00026970977200000411
Length of (2) row number
Figure BDA00026970977200000412
The number of the middle fee zero items. Note the book
Figure BDA00026970977200000413
Namely, it is
Figure BDA00026970977200000414
Only contain
Figure BDA00026970977200000415
Is a non-zero term of (1). The above equation problem can be written as:
Figure BDA00026970977200000416
solving by singular value decomposition, fixing
Figure BDA00026970977200000417
Updating
Figure BDA00026970977200000418
Namely, it is
Figure BDA00026970977200000419
Fixing
Figure BDA0002697097720000051
Updating
Figure BDA0002697097720000052
Namely, it is
Figure BDA0002697097720000053
The target requirements can be met after alternating iteration for a plurality of times.
Compared with the prior art, the invention has the technical effects that: initializing a sparse dictionary by utilizing moment-harmonic analysis and training the sparse dictionary by utilizing a K-SVD algorithm; the method has the advantages that the high-resolution geomagnetic reference map is reconstructed by utilizing the characteristic that the low-resolution geomagnetic reference map and the high-resolution geomagnetic reference map have the same sparse coefficient, the method has higher construction precision on the geomagnetic reference map, has lower requirements on a data set required by training, and has better robustness on noise; compared with the PSO-kring interpolation method, the peak signal-to-noise ratio (SPNR) is improved to 27.12dB from 26.33dB under the quadruple amplification factor; the Structural Similarity (SSIM) is improved from 0.511 to 0.536; root Mean Square Error (RMSE) was reduced from 18.65nT to 15.12 nT.
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In order that the advantages of the invention will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings.
Fig. 1 is a schematic structural diagram of an embodiment of a geomagnetic reference map construction method based on sparse representation and dictionary learning.
Detailed Description
Preferred embodiments of the invention are described below. It should be understood by those skilled in the art that these embodiments are only for explaining the technical principle of the invention, and do not limit the scope of the invention.
The invention provides a geomagnetic reference map construction method based on sparse representation and dictionary learning, which comprises the following steps of:
s1: initializing a sparse dictionary;
modeling the geomagnetic field of the target area, gridding the reference graph according to the modeling, and measuring the data magnetically according to BR＝B0-BCDecomposition is carried out.
Specifically, the BR＝B0-BCIn (A), BRExpressed as the value of the residual magnetic field of the earth magnetism, B0Expressed as measured geomagnetic field data, BCExpressed as the theoretical value calculated for the international geomagnetic reference field.
Specifically, by said BR＝B0-BCAnd acquiring the residual magnetic field value of the target area.
Specifically, the modeling of the residual magnetic field value of the target region is analyzed by a moment-resonance analysis, and the specific process is as follows:
in a space without a magnetic field source, the target magnetic potential can be obtained by laplace's equation:
Figure BDA0002697097720000061
can be written as:
Figure BDA0002697097720000062
wherein the content of the first and second substances,
n＝q-m+1,
v＝2π/Lx,
w＝2π/Ly,
Figure BDA0002697097720000063
Pmn(x,y)＝Dmncos(mvx)cos(nwy)+
Emncos(mvx)sin(nwy)+
Fmnsin(mvx)cos(nwy)+
Gmnsin (mvx) sin (nwy), x, y, z are three-dimensional coordinates of the magnetic measurement position, V (x, y, z) is the maximum truncation order, LxAnd LyThe length and width of the target rectangular area.
Taking the center of gravity of the rectangular area as the origin of the harmonic moment coordinate system, the coordinate range is as follows:
Figure BDA0002697097720000064
the geomagnetic three-component at this time can be expressed as:
Figure BDA0002697097720000071
wherein the content of the first and second substances,
Qmn(x,y)＝mv(Dmn sin(mvx)cos(nwy)+
Emn sin(mvx)sin(nwy)-
Fmncos(mvx)cos(nwy)-
Gmncos(mvx)sin(nwy))
Rmn(x,y)＝nw(Dmncos(mvx)sin(nwy)-
Emn cos(mvx)cos(nwy)+
Fmn sin(mvx)sin(nwy)-
Gmnsin(mvx)cos(nwy))
Smn(x,y)＝-uPmn(x,y)
the total field strength can thus be expressed as:
Figure BDA0002697097720000072
by the method, a geomagnetic residual field model can be established and accurate gridding data can be acquired; the sparse dictionary used by the invention is composed of 512 characteristic column vectors, wherein one half of the sparse dictionary is formed by randomly extracting geomagnetic residual field gridding data, the other half of the sparse dictionary is formed by randomly extracting international geomagnetic reference field data, and a finally generated matrix is used as an initial dictionary for dictionary training.
S2: training the sparse dictionary;
learning a low-resolution and high-resolution sparse dictionary by adopting a K-SVD method;
frobenius norm is adopted to measure the deviation between the original image and the image after sparse decomposition, and the jth division in the sparse matrix is kept0Extracting the jth column from all columns except the column without changing0The post column problem can be written as:
Figure BDA0002697097720000073
the above-mentioned
Figure BDA0002697097720000081
Figure BDA0002697097720000082
Represents the jth row of the sparse coefficient X.
By constantly updating djAnd
Figure BDA0002697097720000083
to minimize residual errors, the ultimate goal being to make
Figure BDA0002697097720000084
Is similar to
Figure BDA0002697097720000085
It can therefore be solved by singular value decomposition, however this approach would be vectoring
Figure BDA0002697097720000086
Becoming dense, the number of non-zero terms in X is increased.
Thus defining a matrix
Figure BDA0002697097720000087
Is used for extracting
Figure BDA0002697097720000088
The non-zero term in (a) is,
Figure BDA0002697097720000089
number of lines
Figure BDA00026970977200000810
Length of (2) row number
Figure BDA00026970977200000811
The number of the middle fee zero items. Note the book
Figure BDA00026970977200000812
Namely, it is
Figure BDA00026970977200000813
Only contain
Figure BDA00026970977200000814
Is a non-zero term of (1). The above equation problem can be written as:
Figure BDA00026970977200000815
solving by singular value decomposition, fixing
Figure BDA00026970977200000816
Updating
Figure BDA00026970977200000817
Namely, it is
Figure BDA00026970977200000818
Fixing
Figure BDA00026970977200000819
Updating
Figure BDA00026970977200000820
Namely, it is
Figure BDA00026970977200000821
The target requirements can be met after alternating iteration for a plurality of times.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. A geomagnetic reference map construction method based on sparse representation and dictionary learning is characterized by comprising the following steps:
s1: initializing a sparse dictionary;
s2: and training the sparse dictionary.
2. The sparse representation and dictionary learning-based geomagnetic reference map construction method according to claim 1, wherein the sparse dictionary initialization process is as follows: modeling the geomagnetic field of the target area, gridding the reference graph according to the modeling, and measuring the data magnetically according to BR＝B0-BCDecomposition is carried out.
3. The sparse representation and dictionary learning-based geomagnetic reference map construction method according to claim 2, wherein B isR＝B0-BCSaid B isRExpressed as the value of the residual magnetic field of the earth magnetism, B0Expressed as measured geomagnetic field data, BCExpressed as the theoretical value calculated for the international geomagnetic reference field.
4. The sparse representation and dictionary learning-based geomagnetic reference map construction method according to claim 2, wherein the B isR＝B0-BCAnd acquiring the residual magnetic field value of the target area.
5. The sparse representation and dictionary learning-based geomagnetic reference map construction method according to claim 4, wherein the modeling of the residual magnetic field values of the target region is analyzed by a moment-harmonic analysis.
6. The sparse representation and dictionary learning-based geomagnetic reference map construction method according to claim 1, wherein the sparse dictionary training is performed by learning a low-resolution and high-resolution sparse dictionary by using a K-SVD method.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112967357A (en) * 2021-02-19 2021-06-15 中国人民解放军国防科技大学 Frequency spectrum map construction method based on convolutional neural network

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112967357A (en) * 2021-02-19 2021-06-15 中国人民解放军国防科技大学 Frequency spectrum map construction method based on convolutional neural network
CN112967357B (en) * 2021-02-19 2023-05-23 中国人民解放军国防科技大学 Spectrum map construction method based on convolutional neural network

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