CN110333552B - Aeromagnetic compensation method based on Liu estimation - Google Patents

Aeromagnetic compensation method based on Liu estimation Download PDF

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CN110333552B
CN110333552B CN201910636938.5A CN201910636938A CN110333552B CN 110333552 B CN110333552 B CN 110333552B CN 201910636938 A CN201910636938 A CN 201910636938A CN 110333552 B CN110333552 B CN 110333552B
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葛健
王文杰
董浩斌
刘欢
霍治帆
王洪鹏
薛励玥
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China University of Geosciences
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Abstract

The invention provides a Liu estimation-based aeromagnetic compensation method which comprises the steps of obtaining corrected flight data through corrected flight of an airplane, further obtaining an attitude matrix X of the corrected flight through calculation according to the corrected flight data, and then calculating a magnetic interference coefficient β of the corrected flight, further obtaining airplane interference magnetismField HINFThen, the compensated flight data and the attitude matrix A of the compensated flight are obtained through the compensated flight of the airplane, and the magnetic interference data H of the compensated flight are calculated and obtained according to the attitude matrix A of the compensated flight and the magnetic interference coefficient βT(ii) a Finally according to HTAnd HTOTAnd realizing aeromagnetic compensation based on Liu estimation. The invention has the beneficial effects that: according to the technical scheme provided by the invention, the optimal correction factor is selected by adopting a Liu estimation method, so that the problem that the magnetic interference coefficient is seriously deviated from the true value due to unstable solving of the least square inverse matrix caused by the correlation between attitude matrix column vectors in the aeromagnetic compensation model is effectively solved, and the stability of the aeromagnetic compensation model is improved.

Description

Aeromagnetic compensation method based on Liu estimation
Technical Field
The invention relates to the field of aeromagnetic compensation, in particular to an aeromagnetic compensation method based on Liu estimation.
Background
The aeromagnetic survey is an important magnetic prospecting method, has the advantages of safety, economy, high efficiency, reliability and the like, and is widely applied to the geophysical field. Aeromagnetic measurements are made by loading a high-precision magnetometer on an aircraft and measuring the total magnetic field of the area through which the magnetometer passes during flight. Due to the existence of ferromagnetic substances on the airplane, the constant magnetic field, the induced magnetic field and the eddy magnetic field generated in the flying process can interfere with the target magnetic anomaly signal, so that the actual detection capability of the aviation magnetic measurement is limited to a great extent. Therefore, effective magnetic compensation for the interference field of the aircraft itself is of great significance for aeromagnetic prospecting.
The current model of aeromagnetic force compensators is the AADC-II series product of RMS, Canada. The compensation algorithm is based on a traditional small signal model, high-pass filtering is firstly carried out on data of the optical pump magnetometer and the fluxgate magnetometer, and then a magnetic interference coefficient is solved through a least square method so as to realize aeromagnetic compensation. However, in the process of solving the magnetic interference coefficient, due to the ill-conditioned nature of the model equation, that is, the column vector of the attitude matrix has correlation, the magnetic interference coefficient obtained after matrix inversion deviates from the true value seriously, and the aeromagnetic compensation quality is affected. Therefore, a method for reducing the ill-posed characteristic of the magnetic compensation model is needed to be provided, and the aeromagnetic compensation quality is improved.
Disclosure of Invention
In order to solve the problems, the invention provides a method for aeromagnetic compensation based on Liu estimation; a method for aeromagnetic compensation based on Liu estimation mainly comprises the following steps:
s101: obtaining corrected flight data through corrected flight of the airplane; the correcting flight data includes: first total magnetic field HTOTAnd first three-component magnetic field data; the first total magnetic field is measured by an optical pump sensor of the airplane, and the first three-component magnetic field data is measured by a fluxgate sensor of the airplane;
s102: for the first total magnetic field H in the corrected flight dataTOTRespectively carrying out high-pass filtering on the first three-component magnetic field data to obtain a filtered first total magnetic field H and filtered first three-component magnetic field data;
s103: calculating a direction cosine constant, a direction cosine small quantity and a derivative thereof of each direction of the airplane according to the filtered first three-component magnetic field data to obtain a corrected flying attitude matrix X;
s104: centralizing the attitude matrix X of the corrected flight to obtain a centralized corrected flight attitude matrix
Figure GDA0002578914040000021
And is calculated to obtain
Figure GDA0002578914040000022
All eigenvalues λ ofiAnd the eigenvector matrix Q ═ Q (Q)1,q2,…q16) (ii) a Wherein the content of the first and second substances,1,2 …,16, and λ1≥λ2≥…λ16Respectively correspond to q1,q2,…,q16A feature vector;
s105: according to the characteristic vector matrix Q and the corrected flight attitude matrix
Figure GDA0002578914040000023
And obtaining a fitting coefficient expression by the filtered first total magnetic field H, and solving the fitting coefficient expression by a least square method to obtain a fitting coefficient
Figure GDA0002578914040000024
S106: according to the characteristic value lambdaiAnd fitting coefficient
Figure GDA0002578914040000025
Calculating to obtain an optimal Liu estimation correction factor d for correcting flightopt；
S107: estimating an optimal correction factor d from said LiuoptAnd the attitude matrix X of the corrected flight adopts a Liu estimation expression, and the magnetic interference coefficient β under Liu estimation is obtained through calculation;
s108: obtaining compensated flight data through compensated flight of the airplane; the compensated flight data comprises second three-component magnetic field data; further calculating the direction cosine and the derivative thereof in each direction in the second three-component magnetic field data to obtain a compensated flight attitude matrix A; the second three-component magnetic field data are measured by a fluxgate sensor of the airplane;
s109, calculating magnetic interference data H of the compensated flight according to the magnetic interference coefficient β of the corrected flight and the attitude matrix A of the compensated flightT；
S110: according to the magnetic interference data H of the compensated flightTAnd the first total magnetic field HTOTAnd (3) realizing the aeromagnetic compensation based on Liu estimation by adopting a formula (1):
HC＝HU-HT(1)
in the above formula, the first and second carbon atoms are,HU＝HTOT，HCis the earth magnetic field to be compensated.
Further, in step S103, the expression of the attitude matrix X of the corrected flight is as shown in formula (2):
Figure GDA0002578914040000026
in the above formula, the first and second carbon atoms are,
Figure GDA0002578914040000027
is the direction cosine constant in the ith course; t is the flight time length of the aircraft on the ith course during the corrected flight;
Figure GDA0002578914040000031
is the direction cosine fractional, v, in the ith coursei' is a derivative thereof; fiMeasuring data of the ith channel of the fluxgate sensor in the first three-component magnetic field data; hpf (F)i) Represents a pair FiCarrying out high-pass filtering; i equals 1,2 or 3.
Further, in step S104, the centering formula is shown as formula (3):
Figure GDA0002578914040000032
in the above formula, the first and second carbon atoms are,
Figure GDA0002578914040000033
to represent
Figure GDA0002578914040000034
Column i element of (1);
Figure GDA0002578914040000035
is the average value of the elements in the ith column of the attitude matrix X, i is 1,2, …, 16;
Figure GDA0002578914040000036
each element of the ith column representing X is subtracted by the average value of the ith column, respectively.
Further, in step S105, the fitting coefficient expression is as shown in formula (4):
Figure GDA0002578914040000037
in the above formula, the first and second carbon atoms are,
Figure GDA0002578914040000038
further, in step S106, Liu estimates the optimal correction factor doptThe calculation formula (2) is shown in formula (5):
Figure GDA0002578914040000039
in the above formula, the first and second carbon atoms are,
Figure GDA00025789140400000310
is composed of
Figure GDA00025789140400000311
The variance of (a); lambda [ alpha ]iIs composed of
Figure GDA00025789140400000312
I is 1,2 …,16, and λ1≥λ2≥…λ16Respectively correspond to
Figure GDA00025789140400000313
Is (Q) the eigenvector matrix Q ═ Q1,q2,…q16) Characteristic vector q in (1)1,q2… and q16；
Figure GDA00025789140400000314
For the centered corrected flight attitude matrix,
Figure GDA00025789140400000315
is a transpose thereof.
Further, in step S107, the calculation formula of the magnetic interference coefficient β is as shown in formula (6):
β＝(X′X+I)-1[X′H+dopt(X′X)-1X′H](6)
in the above formula, I is an identity matrix, and β is a row vector having 16 elements.
Further, in step S108, the calculation formula of the attitude matrix a of the compensated flight is as shown in formula (7):
A＝(r1r2r3r1 2r1r2r1r3r2 2r2r3r1'r1r1'r2r1'r3r2'r1r2'r2r2'r3r3'r1r3'r2) (7)
in the above formula, the first and second carbon atoms are,
Figure GDA00025789140400000316
the direction cosine formed by the earth magnetic field and the aircraft coordinate axis, ri' is a derivative thereof; giThe measured data of the ith channel of the fluxgate sensor in the compensated flight of the airplane are shown, and i is equal to 1,2 or 3.
Further, in step S109, the magnetic disturbance data H of the flight is compensatedTThe calculation formula (c) is shown in formula (8):
Figure GDA0002578914040000041
in the above formula, βiIs the i-th element of the magnetic interference coefficient β AiβiEach element in the ith column representing A is βiMultiplication.
The technical scheme provided by the invention has the beneficial effects that: according to the technical scheme provided by the invention, the optimal correction factor is selected by adopting the Liu estimation method, so that the problem that the magnetic interference coefficient is seriously deviated from the true value due to unstable least square inverse matrix solving caused by the correlation between attitude matrix column vectors in an aeromagnetic compensation model is effectively solved, the stability of the aeromagnetic compensation model is improved, the effective compensation of a total field in the aeromagnetic measurement process is realized, and the quality of aeronautical geophysical prospecting is improved.
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The invention will be further described with reference to the accompanying drawings and examples, in which:
fig. 1 is a flowchart of an aeromagnetic compensation method based on Liu estimation according to an embodiment of the present invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
The embodiment of the invention provides an aeromagnetic compensation method based on Liu estimation.
Referring to fig. 1, fig. 1 is a flowchart of an aeromagnetic compensation method based on Liu estimation according to an embodiment of the present invention, which specifically includes the following steps:
s101: obtaining corrected flight data through corrected flight of the airplane; the correcting flight data includes: first total magnetic field HTOTAnd first three-component magnetic field data; the first total magnetic field is measured by an optical pump sensor of the airplane, and the first three-component magnetic field data is measured by a fluxgate sensor of the airplane;
s102: for the first total magnetic field H in the corrected flight dataTOTRespectively carrying out high-pass filtering on the first three-component magnetic field data to obtain a filtered first total magnetic field H and filtered first three-component magnetic field data;
s103: calculating a direction cosine constant, a direction cosine small quantity and a derivative thereof of each direction of the airplane according to the filtered first three-component magnetic field data to obtain a corrected flying attitude matrix X;
s104: centralizing the attitude matrix X of the corrected flight to obtain a centralized corrected flight attitude matrix
Figure GDA0002578914040000042
And is calculated to obtain
Figure GDA0002578914040000043
All eigenvalues λ ofiAnd the eigenvector matrix Q ═ Q (Q)1,q2,…q16) (ii) a Wherein i is 1,2 …,16, and λ1≥λ2≥…λ16Respectively correspond to q1,q2,…,q16A feature vector;
s105: according to the characteristic vector matrix Q and the corrected flight attitude matrix
Figure GDA0002578914040000051
And obtaining a fitting coefficient expression by the filtered first total magnetic field H, and solving the fitting coefficient expression by a least square method to obtain a fitting coefficient
Figure GDA0002578914040000052
S106: according to the characteristic value lambdaiAnd fitting coefficient
Figure GDA0002578914040000053
Calculating to obtain an optimal Liu estimation correction factor d for correcting flightopt；
S107: estimating an optimal correction factor d from said LiuoptAnd the attitude matrix X of the corrected flight adopts a Liu estimation expression, and the magnetic interference coefficient β under Liu estimation is obtained through calculation;
s108: obtaining compensated flight data through compensated flight of the airplane; the compensated flight data comprises second three-component magnetic field data; further calculating the direction cosine and the derivative thereof in each direction in the second three-component magnetic field data to obtain a compensated flight attitude matrix A; the second three-component magnetic field data are measured by a fluxgate sensor of the airplane;
s109, calculating magnetic interference data H of the compensated flight according to the magnetic interference coefficient β of the corrected flight and the attitude matrix A of the compensated flightT；
S110: according to the magnetic interference data H of the compensated flightTAnd the first total magnetic fieldHTOTAnd (3) realizing the aeromagnetic compensation based on Liu estimation by adopting a formula (1):
HC＝HU-HT(1)
in the above formula, HU＝HTOT，HCIs the earth magnetic field to be compensated.
In step S103, the expression of the attitude matrix X of the corrected flight is shown in formula (2):
Figure GDA0002578914040000054
in the above formula, the first and second carbon atoms are,
Figure GDA0002578914040000055
is the direction cosine constant in the ith course;
Figure GDA0002578914040000056
is the direction cosine fractional, v, in the ith coursei' is a derivative thereof; fiMeasuring data of the ith channel of the fluxgate sensor in the first three-component magnetic field data; hpf (F)i) Represents a pair FiCarrying out high-pass filtering; i equals 1,2 or 3; and T is the flight time of the aircraft on the ith heading in the corrected flight.
In step S104, the centering formula is shown in formula (3):
Figure GDA0002578914040000061
in the above formula, the first and second carbon atoms are,
Figure GDA0002578914040000062
to represent
Figure GDA0002578914040000063
Column i element of (1);
Figure GDA0002578914040000064
is the average value of the elements in the ith column of the attitude matrix X, i is 1,2 … 16;
Figure GDA0002578914040000065
each element of the ith column representing X is subtracted by the average value of the ith column, respectively.
In step S105, the fitting coefficient expression is as shown in formula (4):
Figure GDA0002578914040000066
in the above formula, the first and second carbon atoms are,
Figure GDA0002578914040000067
in step S106, Liu estimates the optimal correction factor doptThe calculation formula (2) is shown in formula (5):
Figure GDA0002578914040000068
in the above formula, the first and second carbon atoms are,
Figure GDA0002578914040000069
is composed of
Figure GDA00025789140400000610
The variance of (a); lambda [ alpha ]iIs composed of
Figure GDA00025789140400000611
I is 1,2 …,16, and λ1≥λ2≥…λ16Respectively correspond to
Figure GDA00025789140400000612
Is (Q) the eigenvector matrix Q ═ Q1,q2,…q16) Characteristic vector q in (1)1,q2… and q16；
Figure GDA00025789140400000613
For the centered corrected flight attitude matrix,
Figure GDA00025789140400000614
is a transpose thereof.
In step S107, the calculation formula of the magnetic interference coefficient β is shown in formula (6):
β＝(X′X+I)-1[X′H+dopt(X′X)-1X′H](6)
in the above formula, I is an identity matrix, β is a row vector with 16 elements, and after the magnetic interference coefficient β is obtained by calculation, the aircraft interference magnetic field H can be obtained by calculation according to the magnetic interference coefficientINF(ii) a Further adopting the airplane to disturb the magnetic field HINFCompensating for the corrected flight of the aircraft and calculating the improvement ratio IR; interference magnetic field HINFIs shown in equation (7):
HINF＝Φβ (7)
in the above formula, the first and second carbon atoms are,
Figure GDA00025789140400000615
to correct the direction cosine matrix of the flight;
Figure GDA00025789140400000616
the direction cosine, u, formed by the earth magnetic field and the axis of the aircraft coordinatei' is a derivative thereof; fiThe method comprises the following steps that measured data of the ith channel of the fluxgate sensor in the corrected flight of the airplane are obtained, wherein i is equal to 1,2 or 3;
the quality of the Liu estimation effect lies in the selection of the correction factor, the theoretically calculated optimal correction factor can best weaken the ill-conditioned property of the model equation, but at the moment, the theoretically optimal correction factor can also be finely adjusted within a certain range according to historical experience by taking the optimal improvement ratio IR as a standard to obtain the actually optimal correction factor, and the calculation formula of the improvement ratio IR is shown as a formula (8):
Figure GDA0002578914040000071
in the above formula, σuH is total field data H before magnetic compensationTOTHigh pass filtered standard deviation, σc＝HTOT-HINFIs a standard after high-pass filtering of the magnetically compensated total field dataAnd (4) poor.
In step S108, the calculation formula of the attitude matrix a of compensated flight is shown in formula (9):
A＝(r1r2r3r1 2r1r2r1r3r2 2r2r3r1'r1r1'r2r1'r3r2'r1r2'r2r2'r3r3'r1r3'r2) (9)
in the above formula, the first and second carbon atoms are,
Figure GDA0002578914040000072
the direction cosine formed by the earth magnetic field and the aircraft coordinate axis, ri' is a derivative thereof; giThe measured data of the ith channel of the fluxgate sensor in the compensated flight of the airplane are shown, and i is equal to 1,2 or 3.
In step S109, the magnetic disturbance data H of the flight is compensatedTIs shown in equation (10):
Figure GDA0002578914040000073
in the above formula, βiIs the i-th element of the magnetic interference coefficient β AiβiEach element in the ith column representing A is βiMultiplication.
The invention has the beneficial effects that: according to the technical scheme provided by the invention, the optimal correction factor is selected by adopting the Liu estimation method, so that the problem that the magnetic interference coefficient is seriously deviated from the true value due to unstable least square inverse matrix solving caused by the correlation between attitude matrix column vectors in an aeromagnetic compensation model is effectively solved, the stability of the aeromagnetic compensation model is improved, the effective compensation of a total field in the aeromagnetic measurement process is realized, and the quality of aeronautical geophysical prospecting is improved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (8)

1. A method for aeromagnetic compensation based on Liu estimation is characterized in that: the method comprises the following steps:
s101: obtaining corrected flight data through corrected flight of the airplane; the correcting flight data includes: first total magnetic field HTOTAnd first three-component magnetic field data; the first total magnetic field is measured by an optical pump sensor of the airplane, and the first three-component magnetic field data is measured by a fluxgate sensor of the airplane;
s102: for the first total magnetic field H in the corrected flight dataTOTRespectively carrying out high-pass filtering on the first three-component magnetic field data to obtain a filtered first total magnetic field H and filtered first three-component magnetic field data;
s103: calculating a direction cosine constant, a direction cosine small quantity and a derivative thereof of each direction of the airplane according to the filtered first three-component magnetic field data to obtain a corrected flying attitude matrix X;
s104: centralizing the attitude matrix X of the corrected flight to obtain a centralized corrected flight attitude matrix
Figure FDA0002578914030000011
And is calculated to obtain
Figure FDA0002578914030000012
All eigenvalues λ ofiAnd the eigenvector matrix Q ═ Q (Q)1，q2，…q16) (ii) a Wherein i is 1,2, …,16, and λ1≥λ2≥…λ16Respectively correspond to q1，q2，…，q16A feature vector;
s105: according to the characteristic vector matrix Q and the corrected flight attitude matrix
Figure FDA0002578914030000013
And obtaining a fitting coefficient expression by the filtered first total magnetic field H, and solving the fitting coefficient expression by a least square method to obtain a fitting coefficient
Figure FDA0002578914030000014
S106: according to the characteristic value lambdaiAnd fitting coefficient
Figure FDA0002578914030000015
Calculating to obtain an optimal Liu estimation correction factor d for correcting flightopt；
S107: estimating an optimal correction factor d from said LiuoptAnd the attitude matrix X of the corrected flight adopts a Liu estimation expression, and the magnetic interference coefficient β under Liu estimation is obtained through calculation;
s108: obtaining compensated flight data through compensated flight of the airplane; the compensated flight data comprises second three-component magnetic field data; further calculating the direction cosine and the derivative thereof in each direction in the second three-component magnetic field data to obtain a compensated flight attitude matrix A; the second three-component magnetic field data are measured by a fluxgate sensor of the airplane;
s109, calculating magnetic interference data H of the compensated flight according to the magnetic interference coefficient β of the corrected flight and the attitude matrix A of the compensated flightT；
S110: according to the magnetic interference data H of the compensated flightTAnd the first total magnetic field HTOTAnd (3) realizing the aeromagnetic compensation based on Liu estimation by adopting a formula (1):
HC＝HU-HT(1)
in the above formula, HU＝HTOT，HCIs the earth magnetic field to be compensated.
2. The method of claim 1, wherein the method comprises the following steps: in step S103, the expression of the attitude matrix X of the corrected flight is shown in formula (2):
Figure FDA0002578914030000021
in the above formula, the first and second carbon atoms are,
Figure FDA0002578914030000022
is the direction cosine constant in the ith course; t is the flight time length of the aircraft on the ith course during the corrected flight;
Figure FDA0002578914030000023
is the direction cosine fractional, v, in the ith coursei' is a derivative thereof; fiMeasuring data of the ith channel of the fluxgate sensor in the first three-component magnetic field data; hpf (F)i) Represents a pair FiCarrying out high-pass filtering; i equals 1,2 or 3.
3. The method of claim 2, wherein the method comprises: in step S104, the centering formula is shown in formula (3):
Figure FDA0002578914030000024
in the above formula, the first and second carbon atoms are,
Figure FDA0002578914030000025
to represent
Figure FDA00025789140300000217
Column i element of (1);
Figure FDA0002578914030000026
is the average value of the elements in the ith column of the attitude matrix X, i is 1,2, …, 16;
Figure FDA0002578914030000027
each element of the ith column representing X is subtracted by the average value of the ith column, respectively.
4. The method of claim 3, wherein the method comprises the following steps: in step S105, the fitting coefficient expression is as shown in formula (4):
Figure FDA0002578914030000028
in the above formula, the first and second carbon atoms are,
Figure FDA0002578914030000029
5. the method of claim 4, wherein the method comprises the following steps: in step S106, Liu estimates the optimal correction factor doptThe calculation formula (2) is shown in formula (5):
Figure FDA00025789140300000210
in the above formula, the first and second carbon atoms are,
Figure FDA00025789140300000211
is composed of
Figure FDA00025789140300000212
The variance of (a); lambda [ alpha ]iIs composed of
Figure FDA00025789140300000213
I is 1,2 …,16, and λ1≥λ2≥…λ16Respectively correspond to
Figure FDA00025789140300000214
Is (Q) the eigenvector matrix Q ═ Q1，q2，…q16) Characteristic vector q in (1)1，q2… and q16；
Figure FDA00025789140300000215
For the centered corrected flight attitude matrix,
Figure FDA00025789140300000216
is a transpose thereof.
6. The method of claim 5, wherein the method comprises: step (ii) of
In S107, the calculation formula of the magnetic interference coefficient β is shown in formula (6):
β＝(X′X+I)-1[X′H+dopt(X′X)-1X′H](6)
in the above formula, I is an identity matrix, and β is a row vector having 16 elements.
7. The method of claim 1, wherein the method comprises the following steps: in step S108, the calculation formula of the attitude matrix a of compensated flight is shown in formula (7):
A＝(r1r2r3r1 2r1r2r1r3r2 2r2r3r1′r1r1′r2r1′r3r′2r1r2′r2r2′r3r′3r1r3′r2) (7)
in the above formula, the first and second carbon atoms are,
Figure FDA0002578914030000031
the direction cosine formed by the earth magnetic field and the aircraft coordinate axis, ri' is a derivative thereof; giThe measured data of the ith channel of the fluxgate sensor in the compensated flight of the airplane are shown, and i is equal to 1,2 or 3.
8. The method of claim 6, wherein the method comprises a method for aeromagnetic compensation based on Liu estimationCharacterized in that: in step S109, the magnetic disturbance data H of the flight is compensatedTThe calculation formula (c) is shown in formula (8):
Figure FDA0002578914030000032
in the above formula, βiIs the i-th element of the magnetic interference coefficient β AiβiEach element in the ith column representing A is βiMultiplication.
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