CN110333552A - A kind of boat magnetic compensation method based on Liu estimation - Google Patents
A kind of boat magnetic compensation method based on Liu estimation Download PDFInfo
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Abstract
The present invention provides a kind of boat magnetic compensation methods based on Liu estimation, comprising: obtains Caliberation Flight data by the Caliberation Flight of aircraft first；And then the attitude matrix X of Caliberation Flight is calculated according to Caliberation Flight data；Then the magnetic disturbance factor beta of Caliberation Flight is calculated, and then obtains aircraft interference magnetic field HINF；The attitude matrix A of compensation flying quality and compensation flight is obtained by the compensation flight of aircraft again, and then according to the attitude matrix A and magnetic disturbance factor beta of compensation flight, the magnetic disturbance data H of compensation flight is calculatedT；Finally according to HTAnd HTOT, realize the boat magnetic compensation estimated based on Liu.The beneficial effects of the present invention are: technical solution proposed by the invention selects optimal modifying factor by using Liu estimation method, the problem of correlation makes the solution of least square method inverse matrix unstable and leads to magnetic disturbance coefficient substantial deviation true value between attitude matrix column vector in boat magnetic compensation model is effectively overcome, the stability of boat magnetic compensation model is improved.
Description
Technical field
The present invention relates to boat magnetic compensation field more particularly to a kind of boat magnetic compensation methods based on Liu estimation.
Background technique
Aeromagnetic detection as a kind of important magnetic prospecting method, have many advantages, such as it is safe, economical, efficient, reliable, on ground
Ball physics is widely used.Aeromagnetic detection is by the way that high-precision magnetometer to be loaded on aircraft, in flight course
In the total magnetic field in the region passed through is measured.Generation due to the presence of ferromagnetic material on aircraft, in flight course
Stationary magnetic field, induced magnetic field and eddy current magnetism target magnetic anomaly regular signal can be interfered, which greatly limits
Aeromagnetic actual detection ability.Therefore, effective magnetic compensation is carried out for aeromagnetic method for the interference field of aircraft itself
Exploration has great importance.
The model of the instrument of aeromagnetics compensation at present is the AADC-II series of products of RMS company, Canada.Its backoff algorithm base
In traditional small-signal model, high-pass filtering first is carried out to the data of optical pumped magnetometer and flux-gate magnetometer, then by most
Small square law seeks magnetic disturbance coefficient, to realize boat magnetic compensation.But during solving magnetic disturbance coefficient, due to the disease of model equation
State property, i.e. attitude matrix column vector have correlation, cause magnetic disturbance coefficient substantial deviation obtained after matrix inversion true
Value influences magnetic compensation quality of navigating.It is, therefore, desirable to provide a kind of method that can reduce magnetic compensation model pathosis, promotes boat magnetic and mends
Repay quality.
Summary of the invention
To solve the above-mentioned problems, the present invention provides a kind of boat magnetic compensation methods based on Liu estimation；One kind is based on
The boat magnetic compensation method of Liu estimation, mainly comprises the steps that
S101: Caliberation Flight data are obtained by the Caliberation Flight of aircraft；The Caliberation Flight data include: first total magnetic
Field HTOTWith the first three-component magnetic field data；Wherein, the first total magnetic field is measured by the optical pumping sensor of aircraft itself, and the one or three
Component magnetic field data are measured by the fluxgate sensor of aircraft itself；
S102: to the first total magnetic field H in the Caliberation Flight dataTOTIt is carried out respectively with the first three-component magnetic field data
High-pass filtering obtains filtered first total magnetic field H and filtered first three-component magnetic field data；
S103: according to the filtered first three-component magnetic field data, the direction cosines for calculating aircraft all directions are normal
Amount, direction cosines are a small amount of and its derivative, obtain the attitude matrix X of Caliberation Flight；
S104: centralization is carried out to the attitude matrix X of the Caliberation Flight, the Caliberation Flight posture square after obtaining centralization
Battle arrayAnd it is calculatedAll eigenvalue λsiWith eigenvectors matrix Q=(q1, q2... q16)；Wherein, i=1,2 ...,
16, and λ1≥λ2≥…λ16, respectively correspond q1, q2..., q16A feature vector；
S105: according to described eigenvector matrix Q, the Caliberation Flight attitude matrixIt is total with described filtered first
Magnetic field H obtains fitting coefficient expression formula, and is solved by least square method to fitting coefficient expression formula, obtains fitting coefficient
S106: according to the eigenvalue λiAnd fitting coefficientThe Liu that Caliberation Flight is calculated estimates best modifying factor
Sub- dopt；
S107: best modifying factor d is estimated according to the LiuoptWith the attitude matrix X of the Caliberation Flight, using Liu
The magnetic disturbance factor beta under Liu estimation is calculated in estimated expression；
S108: it flies to obtain compensation flying quality by the compensation of aircraft；The compensation flying quality includes the two or three point
Measure magnetic field data；And then the direction cosines and its derivative of all directions in the second three-component magnetic field data are calculated, it is compensated
The attitude matrix A of flight；Wherein, the second three-component magnetic field data is measured by the fluxgate sensor of aircraft itself；
S109: it according to the attitude matrix A of the magnetic disturbance factor beta of Caliberation Flight and compensation flight, is calculated
Compensate the magnetic disturbance data H of flightT；
S110: according to the magnetic disturbance data H of the compensation flightTWith the first total magnetic field HTOT, real using formula (1)
Boat magnetic compensation now based on Liu estimation:
HC=HU-HT (1)
In above formula, HU=HTOT, HCFor earth's magnetic field to be compensated.
Further, in step S103, shown in the expression formula such as formula (2) of the attitude matrix X of Caliberation Flight:
In above formula,It is the direction cosines constant on i-th of course；Fly when T is Caliberation Flight
Flight duration of the machine on i-th of course；A small amount of, the v for the direction cosines on i-th of coursei' led for it
Number；FiFor the measurement data in i-th of channel of fluxgate sensor in the first three-component magnetic field data；hpf(Fi) indicate to FiIt carries out
High-pass filtering；I is equal to 1,2 or 3.
Further, in step S104, shown in centralization formula such as formula (3):
In above formula,It indicatesThe i-th column element；For the average value of the element of the i-th column of attitude matrix X, i=
1,2 ... 16；Indicate that the average value of the i-th column is individually subtracted in each element of the i-th column of X.
Further, in step S105, shown in fitting coefficient expression formula such as formula (4):
In above formula,
Further, in step S106, Liu estimates best modifying factor doptCalculation formula such as formula (5) shown in:
In above formula,ForVariance；λiForCharacteristic value, i=1,2 ..., 16, and λ1≥λ2≥…λ16,
It respectively correspondsEigenvectors matrix Q=(q1, q2... q16) in feature vector q1, q2... and q16；Centered on change
Caliberation Flight attitude matrix afterwards,For its transposition.
Further, in step S107, shown in the calculation formula of magnetic disturbance factor beta such as formula (6):
β=(X ' X+I)-1[X′H+dopt(X′X)-1X′H] (6)
In above formula, I is unit matrix, and β is the row vector with 16 elements.
Further, in step S108, the calculation formula such as formula (7) for compensating the attitude matrix A of flight is shown:
In above formula,For the direction cosines that earth's magnetic field and aircraft reference axis are formed, ri' it is its derivative；
GiIt is the measurement data that aircraft compensates in-flight i-th of channel of fluxgate sensor, i is equal to 1,2 or 3.
Further, in step S109, the magnetic disturbance data H of flight is compensatedTCalculation formula such as formula (8) shown in:
In above formula, βiFor i-th of element of magnetic disturbance factor beta；AiβiIndicate A i-th column each element respectively with βiPhase
Multiply.
Technical solution provided by the invention have the benefit that technical solution proposed by the invention by using
Liu estimation method selects optimal modifying factor, effectively overcomes related between attitude matrix column vector in boat magnetic compensation model
Property make least square method inverse matrix solve it is unstable and the problem of lead to magnetic disturbance coefficient substantial deviation true value, improve boat
The stability of magnetic compensation model realizes aeromagnetic detection in the process to the effective compensation of resultant field, improves the quality of airborne geophysical prospecting.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is a kind of flow chart of the boat magnetic compensation method based on Liu estimation in the embodiment of the present invention.
Specific embodiment
For a clearer understanding of the technical characteristics, objects and effects of the present invention, now control attached drawing is described in detail
A specific embodiment of the invention.
The embodiment provides a kind of boat magnetic compensation methods based on Liu estimation.
Referring to FIG. 1, Fig. 1 is a kind of flow chart of the boat magnetic compensation method based on Liu estimation, tool in the embodiment of the present invention
Body includes the following steps:
S101: Caliberation Flight data are obtained by the Caliberation Flight of aircraft；The Caliberation Flight data include: first total magnetic
Field HTOTWith the first three-component magnetic field data；Wherein, the first total magnetic field is measured by the optical pumping sensor of aircraft itself, and the one or three
Component magnetic field data are measured by the fluxgate sensor of aircraft itself；
S102: to the first total magnetic field H in the Caliberation Flight dataTOTIt is carried out respectively with the first three-component magnetic field data
High-pass filtering obtains filtered first total magnetic field H and filtered first three-component magnetic field data；
S103: according to the filtered first three-component magnetic field data, the direction cosines for calculating aircraft all directions are normal
Amount, direction cosines are a small amount of and its derivative, obtain the attitude matrix X of Caliberation Flight；
S104: centralization is carried out to the attitude matrix X of the Caliberation Flight, the Caliberation Flight posture square after obtaining centralization
Battle arrayAnd it is calculatedAll eigenvalue λsiWith eigenvectors matrix Q=(q1, q2... q16)；Wherein, i=1,2 ...,
16, and λ1≥λ2≥…λ16, respectively correspond q1, q2..., q16A feature vector；
S105: according to described eigenvector matrix Q, the Caliberation Flight attitude matrixIt is total with described filtered first
Magnetic field H obtains fitting coefficient expression formula, and is solved by least square method to fitting coefficient expression formula, obtains fitting coefficient
S106: according to the eigenvalue λiAnd fitting coefficientThe Liu that Caliberation Flight is calculated estimates best modifying factor
Sub- dopt；
S107: best modifying factor d is estimated according to the LiuoptWith the attitude matrix X of the Caliberation Flight, using Liu
The magnetic disturbance factor beta under Liu estimation is calculated in estimated expression；
S108: it flies to obtain compensation flying quality by the compensation of aircraft；The compensation flying quality includes the two or three point
Measure magnetic field data；And then the direction cosines and its derivative of all directions in the second three-component magnetic field data are calculated, it is compensated
The attitude matrix A of flight；Wherein, the second three-component magnetic field data is measured by the fluxgate sensor of aircraft itself；
S109: it according to the attitude matrix A of the magnetic disturbance factor beta of Caliberation Flight and compensation flight, is calculated
Compensate the magnetic disturbance data H of flightT；
S110: according to the magnetic disturbance data H of the compensation flightTWith the first total magnetic field HTOT, real using formula (1)
Boat magnetic compensation now based on Liu estimation:
HC=HU-HT (1)
In above formula, HU=HTOT, HCFor earth's magnetic field to be compensated.
In step S103, shown in the expression formula such as formula (2) of the attitude matrix X of Caliberation Flight:
In above formula,It is the direction cosines constant on i-th of course；
A small amount of, the v for the direction cosines on i-th of coursei' it is its derivative；FiFor fluxgate sensor in the first three-component magnetic field data
The measurement data in i channel；hpf(Fi) indicate to FiCarry out high-pass filtering；I is equal to 1,2 or 3；Aircraft when T is Caliberation Flight
Flight duration on i-th of course.
In step S104, shown in centralization formula such as formula (3):
In above formula,It indicatesThe i-th column element；For the average value of the element of the i-th column of attitude matrix X, i=
1,2 ... 16；Indicate that the average value of the i-th column is individually subtracted in each element of the i-th column of X.
In step S105, shown in fitting coefficient expression formula such as formula (4):
In above formula,
In step S106, Liu estimates best modifying factor doptCalculation formula such as formula (5) shown in:
In above formula,ForVariance；λiForCharacteristic value, i=1,2 ..., 16, and λ1≥λ2≥…λ16,
It respectively correspondsEigenvectors matrix Q=(q1,q2,…q16) in feature vector q1,q2... and q16；Centered on change
Caliberation Flight attitude matrix afterwards,For its transposition.
In step S107, shown in the calculation formula of magnetic disturbance factor beta such as formula (6):
β=(X ' X+I)-1[X′H+dopt(X′X)-1X′H] (6)
In above formula, I is unit matrix, and β is the row vector with 16 elements；And magnetic disturbance coefficient is being calculated
After β, aircraft interference magnetic field H can be calculated according to magnetic disturbance coefficientINF；And then magnetic field H is interfered using the aircraftINFTo aircraft
Caliberation Flight compensate, and calculate improvement ratio IR；Interfere magnetic field HINFCalculation formula such as formula (7) shown in:
HINF=Φ β (7)
In above formula,
For the direction cosine matrix of Caliberation Flight；For the direction cosines that earth's magnetic field and aircraft reference axis are formed,
ui' it is its derivative；FiIt is the measurement data in i-th of channel of fluxgate sensor in aircraft Caliberation Flight, i is equal to 1,2 or 3；
The quality of Liu estimation effect is the selection of modifying factor, and theoretically calculating resulting best modifying factor can be most
Weaken the pathosis of model equation well, but at this time can also be most preferably to improve than IR as standard, according to historical experience, certain
Theoretical best modifying factor is finely adjusted in range, obtains actual best modifying factor, improves the calculation formula than IR
As shown in formula (8):
In above formula, σu=H is resultant field data H before magnetic compensationTOTStandard deviation after high-pass filtering, σc=HTOT-HINF, it is magnetic
Standard deviation after compensation after resultant field high-pass filtering data.
In step S108, the calculation formula such as formula (9) for compensating the attitude matrix A of flight is shown:
In above formula,For the direction cosines that earth's magnetic field and aircraft reference axis are formed, ri' it is its derivative；
GiIt is the measurement data that aircraft compensates in-flight i-th of channel of fluxgate sensor, i is equal to 1,2 or 3.
In step S109, the magnetic disturbance data H of flight is compensatedTCalculation formula such as formula (10) shown in:
In above formula, βiFor i-th of element of magnetic disturbance factor beta；AiβiIndicate A i-th column each element respectively with βiPhase
Multiply.
The beneficial effects of the present invention are: technical solution proposed by the invention selects most preferably by using Liu estimation method
Modifying factor, effectively overcome in boat magnetic compensation model that correlation makes least square method against square between attitude matrix column vector
Battle array solve it is unstable and the problem of lead to magnetic disturbance coefficient substantial deviation true value, improve the stability of boat magnetic compensation model,
Aeromagnetic detection is realized in the process to the effective compensation of resultant field, improves the quality of airborne geophysical prospecting.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (8)
1. a kind of boat magnetic compensation method based on Liu estimation, it is characterised in that: the following steps are included:
S101: Caliberation Flight data are obtained by the Caliberation Flight of aircraft；The Caliberation Flight data include: the first total magnetic field
HTOTWith the first three-component magnetic field data；Wherein, the first total magnetic field is measured by the optical pumping sensor of aircraft itself, and the one or three point
Amount magnetic field data is measured by the fluxgate sensor of aircraft itself；
S102: to the first total magnetic field H in the Caliberation Flight dataTOTHigh pass is carried out respectively with the first three-component magnetic field data
Filtering, obtains filtered first total magnetic field H and filtered first three-component magnetic field data；
S103: according to the filtered first three-component magnetic field data, direction cosines constant, the side of aircraft all directions are calculated
To cosine is a small amount of and its derivative, the attitude matrix X of Caliberation Flight is obtained；
S104: centralization is carried out to the attitude matrix X of the Caliberation Flight, the Caliberation Flight attitude matrix after obtaining centralization
And it is calculatedAll eigenvalue λsiWith eigenvectors matrix Q=(q1,q2,…q16)；Wherein, i=1,2 ..., 16, and
λ1≥λ2≥…λ16, respectively correspond q1, q2..., q16A feature vector；
S105: according to described eigenvector matrix Q, the Caliberation Flight attitude matrixWith the filtered first total magnetic field H
Fitting coefficient expression formula is obtained, and fitting coefficient expression formula is solved by least square method, obtains fitting coefficient
S106: according to the eigenvalue λiAnd fitting coefficientThe Liu that Caliberation Flight is calculated estimates best modifying factor dopt；
S107: best modifying factor d is estimated according to the LiuoptWith the attitude matrix X of the Caliberation Flight, estimated using Liu
The magnetic disturbance factor beta under Liu estimation is calculated in expression formula；
S108: it flies to obtain compensation flying quality by the compensation of aircraft；The compensation flying quality includes the second three-component magnetic
Field data；And then the direction cosines and its derivative of all directions in the second three-component magnetic field data are calculated, obtain compensation flight
Attitude matrix A；Wherein, the second three-component magnetic field data is measured by the fluxgate sensor of aircraft itself；
S109: according to the attitude matrix A of the magnetic disturbance factor beta of Caliberation Flight and compensation flight, compensation is calculated
The magnetic disturbance data H of flightT；
S110: according to the magnetic disturbance data H of the compensation flightTWith the first total magnetic field HTOT, realized and be based on using formula (1)
The boat magnetic compensation of Liu estimation:
HC=HU-HT (1)
In above formula, HU=HTOT, HCFor earth's magnetic field to be compensated.
2. a kind of boat magnetic compensation method based on Liu estimation as described in claim 1, it is characterised in that: in step S103, school
Shown in the expression formula of the attitude matrix X just to fly such as formula (2):
In above formula,It is the direction cosines constant on i-th of course；Aircraft exists when T is Caliberation Flight
Flight duration on i-th of course；A small amount of, the v for the direction cosines on i-th of coursei' it is its derivative；
FiFor the measurement data in i-th of channel of fluxgate sensor in the first three-component magnetic field data；hpf(Fi) indicate to FiIt carries out high
Pass filter；I is equal to 1,2 or 3.
3. a kind of boat magnetic compensation method based on Liu estimation as claimed in claim 2, it is characterised in that: in step S104, in
Shown in heart formula such as formula (3):
In above formula,It indicatesThe i-th column element；For attitude matrix X i-th column element average value, i=1,2 ...
16；Indicate that the average value of the i-th column is individually subtracted in each element of the i-th column of X.
4. a kind of boat magnetic compensation method based on Liu estimation as claimed in claim 3, it is characterised in that: in step S105, intend
It closes shown in coefficient expressions such as formula (4):
In above formula,
5. a kind of boat magnetic compensation method based on Liu estimation as claimed in claim 4, it is characterised in that: in step S106,
Liu estimates best modifying factor doptCalculation formula such as formula (5) shown in:
In above formula,ForVariance；λiForCharacteristic value, i=1,2 ..., 16, and λ1≥λ2≥…λ16, right respectively
Ying ZheEigenvectors matrix Q=(q1, q2... q16) in feature vector q1, q2... and q16；Centered on change after school
Positive flight attitude matrix,For its transposition.
6. a kind of boat magnetic compensation method based on Liu estimation as claimed in claim 5, it is characterised in that: in step S107, magnetic
Shown in the calculation formula of interference coefficient β such as formula (6):
β=(X ' X+I)-1[X′H+dopt(X′X)-1X′H] (6)
In above formula, I is unit matrix, and β is the row vector with 16 elements.
7. a kind of boat magnetic compensation method based on Liu estimation as described in claim 1, it is characterised in that: in step S108, mend
Shown in the calculation formula such as formula (7) for repaying the attitude matrix A of flight:
In above formula,For the direction cosines that earth's magnetic field and aircraft reference axis are formed, ri' it is its derivative；
GiIt is the measurement data that aircraft compensates in-flight i-th of channel of fluxgate sensor, i is equal to 1,2 or 3.
8. a kind of boat magnetic compensation method based on Liu estimation as claimed in claim 6, it is characterised in that: in step S109, mend
Repay the magnetic disturbance data H of flightTCalculation formula such as formula (8) shown in:
In above formula, βiFor i-th of element of magnetic disturbance factor beta；AiβiIndicate A i-th column each element respectively with βiIt is multiplied.
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| CN112965014A (en) * | 2021-03-04 | 2021-06-15 | 哈尔滨工业大学 | Compensation method and device for magnetic interference caused by change of mechanical structure of airplane |
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