CN106959471B - Boat magnetic compensation method based on the non-linear boat total field gradient compensation model of magnetic - Google Patents
Boat magnetic compensation method based on the non-linear boat total field gradient compensation model of magnetic Download PDFInfo
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Abstract
The present invention provides a kind of boat magnetic compensation methods based on the non-linear boat total field gradient compensation model of magnetic, time series weighted modeling is carried out to the output of flux-gate magnetometer, estimate direction cosines, the boat magnetic compensation aspect of model matrix in earth's magnetic field and aircraft, it predicts the aircraft platform magnetic disturbance that optical pumping magnetometer observes and obtains the non-linear total field gradient compensation model of boat magnetic, the non-linear total field gradient compensation model of boat magnetic is solved, boat magnetic compensation result is obtained.The present invention interferes the compensation problem in magnetic field, substantially increases the precision of boat magnetic compensation by establishing non-linear boat magnetic resultant field gradient former caused by the delay between effective solution data channel.
Description
Technical field
The present invention relates to geophysics aeromagnetic survey fields, and mould is compensated more particularly, to based on the total field gradient of non-linear boat magnetic
The boat magnetic compensation method of type.
Background technology
Airborne magnetic prospecting is a kind of important airborne geophysical prospecting means, is widely used in geophysics field.Due to boat
It needs magnetometer being fixed on aircraft when empty magnetic prospecting, the interference magnetic field of aircraft itself can cause sternly the measurement of magnetometer
The influence of weight, therefore effectively interfere magnetic field to compensate caused by aircraft and have great importance.
It is domestic at present that external magnetic compensation equipment is mainly used in aeromagnetic survey field, such as the AADC systems of RMS companies
Row magnetic compensation instrument, the boat magnetic compensation equipment of PICO companies.The backoff algorithm of above-mentioned compensation equipment is calculated based on traditional boat magnetic compensation
Method designs, shown in algorithm flow chart Fig. 1.Its feature of the algorithm is first to collect optical pumped magnetometer and flux-gate magnetometer
Data by a low-pass filter, filter out part and the incoherent noise of aircraft magnetic disturbance, calculated thereafter by least square
Method achievees the purpose that remove aircraft interference magnetic field.
It is found by the applicant that there are following defects for above-mentioned compensation method, boat magnetic compensation algorithm is based on traditional linear boat magnetic compensation
Model assumes in model between data to be that ideal synchronisation does not postpone to exist, however at present used in navigate magnetic compensation exploring equipment
By different module (optical pumping frequency measuring block, fluxgate data acquisition module, navigation positioning module, data storage and compensation
Module etc.) composition, the work clock of each module is asynchronous, and real time data is difficult to stringent synchronization, exists so as to cause Aeromagnetic data
When interaction process compensates, occur because compensating deviation caused by postponing between signal path, it is final to influence the aeromagnetic survey quality of data.
Invention content
(1) technical problems to be solved
The main object of the present invention is to provide a kind of boat magnetic compensation side based on the non-linear boat total field gradient compensation model of magnetic
Method, when carrying out the total field gradient data compensation of boat magnetic, the signal path delay that this method can be effectively between sensor is described,
And deviation magnetic disturbance caused by effectively eliminating synchronous error, ensure the validity of boat magnetic compensation.
(2) technical solution
The present invention provides a kind of boat magnetic compensation methods based on the non-linear boat total field gradient compensation model of magnetic, including:Step
Rapid S1:Time series weighted modeling is carried out to the output of flux-gate magnetometer, obtains the estimated value of flux-gate magnetometer output;Step
Rapid S2:The estimated value exported by the flux-gate magnetometer obtains the direction cosines estimated value of earth's magnetic field and aircraft, and boat magnetic
The estimated value of compensation model eigenmatrix;Step S3:By the estimated value of the boat magnetic compensation aspect of model matrix, optical pumping magnetic is predicted
The aircraft platform magnetic disturbance that power meter observes;Step S4:It is mended by the estimated value of the earth's magnetic field and the direction cosines of aircraft, boat magnetic
It repays the estimated value of aspect of model matrix and aircraft platform magnetic disturbance that optical pumping magnetometer observes, obtains non-linear boat magnetic resultant field
Gradient compensation model;And step S5:The non-linear total field gradient compensation model of boat magnetic is solved, boat magnetic compensation result is obtained.
Preferably, in the step S1 magnetic flux is obtained using the output of the second optical pumped magnetometer as time reference benchmark
The estimated value of three axis components of door magnetometer output.
Preferably, the estimated value of three axis components of the flux-gate magnetometer output is obtained in a manner of linear prediction.
Preferably, the step S2 is specifically included:The estimated value exported by the flux-gate magnetometer, obtain earth's magnetic field with
Estimated value of the direction cosines of aircraft in time reference benchmark;And joined in the time by the direction cosines of the earth's magnetic field and aircraft
The estimated value for examining benchmark obtains non-linear estimations value of the eigenmatrix in time reference benchmark of boat magnetic compensation model.
Preferably, the step S3 is specifically included:By the eigenmatrix of boat magnetic compensation model in the non-of time reference benchmark
Linear estimate, the aircraft platform magnetic disturbance that prediction optical pumping magnetometer observes.
Preferably, the optical pumping magnetometer includes the first optical pumping magnetometer and the second optical pumping magnetometer.
Preferably, the step S4 is specifically included:The aircraft platform magnetic disturbance that the optical pumping magnetometer is observed substitutes into
Navigate the total field gradient compensation model of magnetic, obtains interference of the aircraft to the total field gradient of magnetic of navigating;And by the boat magnetic compensation aspect of model
The estimated value of the direction cosines of the estimated value of matrix, earth's magnetic field and aircraft substitutes into interference of the aircraft to the total field gradient of magnetic of navigating, and obtains
The non-linear total field gradient compensation model of boat magnetic.
Preferably, the non-linear total field gradient compensation model of boat magnetic is solved by optimal method in the step S5.
Preferably, the optimal method is Levenberg-Marquardt methods.
Preferably, the boat magnetic compensation method for compensate between optical pumped magnetometer and flux-gate magnetometer, optical pumping magnetic force
Delay between instrument and optical pumped magnetometer and between each channel of fluxgate.
(3) advantageous effect
It can be seen from the above technical proposal that the boat magnetic based on the non-linear boat total field gradient compensation model of magnetic of the present invention is mended
Compensation method has following advantageous effect:
By establishing non-linear boat magnetic resultant field gradient former, interfered caused by the delay between effective solution data channel
The compensation problem in magnetic field substantially increases the precision of boat magnetic compensation.
Description of the drawings
Fig. 1 is traditional boat magnetic compensation method flow diagram.
Fig. 2 is each sensor output delay schematic diagram of aeromagnetic survey system.
Fig. 3 is the boat magnetic compensation method flow based on the non-linear boat total field gradient compensation model of magnetic of the embodiment of the present invention
Figure.
Fig. 4 is deviation interference and compensation effect figure caused by delay.
Specific implementation mode
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific embodiment, and reference
Attached drawing, the present invention is described in more detail.
The total field gradient compensation model of magnetic that navigates is based on boat magnetic compensation model and releases, at any optical pumped magnetometer probe positions,
The interference resultant field of aircraft is indicated by following boat magnetic compensation models:
In formula, ciFor the magnetic compensation coefficient of magnetic resultant field, Hd(t) it is the interference resultant field at optical pumped magnetometer probe, HeIt is earth magnetism
Field resultant field modulus value, Ai(t) it is the characteristic element in boat magnetic compensation model, by the expression for the eigenmatrix A (t) that characteristic element forms
Formula is as follows:
A (t)=(cosX (t) cosY (t) ... cosZ (t) (cosZ (t)) ') (2)
In formula, cosX (t), cosY (t), the direction cosines that cosZ (t) is earth's magnetic field and aircraft can be by three axis magnetic fluxs
The measured value of door magnetometer is calculated:
In formula, T (t), L (t) and V (t) are three axis components of flux-gate magnetometer output.
Therefore, aircraft interference magnetic field can be write as following formula to the contribution of resultant field gradiometry observation:
Above formula is the total field gradient compensation model of magnetic that navigates, wherein GH(t) total field gradient that magnetic field is interfered for aircraft, passes through
To two optical pumped magnetometers at baseline both ends moment t measured value Hd1(t) and Hd2(t) Difference Calculation obtains, and d is two light
Pump the baseline length between magnetometer, ci1For the magnetic compensation system at the first optical pumped magnetometer probe in traditional boat magnetic compensation model
Number, ci2For the magnetic compensation coefficient at the second optical pumped magnetometer probe in traditional boat magnetic compensation model, giFor the compensation system of gradient
Number, Ai(t) it is i-th of element of eigenmatrix A (t) shown in formula (2), the penalty coefficient g of the gradient in formula (4)iIt can be by most
Small two multiplication algorithm is solved.
Existing boat magnetic compensation model does not account for the delay issue of sensor, but optical pumped magnetometer and magnetic flux in practice
It is the presence of delay between door magnetometer, asynchronous between sensing data will lead to occur compensation deviation when magnetic compensation, to
Influence the effect of magnetic compensation.From formula (4) as it can be seen that for the total field gradient compensation model of magnetic that navigates, main data delay is present in Hd1、
Hd2And Ai(t) between, following three classes can be divided into:(1) relative delay between optical pumped magnetometer and flux-gate magnetometer;(2) light
Pump the relative delay between magnetometer and optical pumped magnetometer;(3) relative delay of each interchannel of fluxgate.
The boat magnetic compensation method of the present invention carries out time series weighted modeling to the output of flux-gate magnetometer first, real
Now to the accurate estimation of flux-gate magnetometer output, is then realized on the basis of this and interfere the non-thread of magnetic field on different optical pumped magnetometers
Property modeling, it is final obtain can handle data channel between there is the total field gradient compensation model of non-linear boat magnetic of delay, and using pair
The nonlinear algorithm answered solves the compensation model.
Data flow between each sensor of aeromagnetic survey system can indicate with Fig. 2, wherein Δ tiFor different sensors or not
With the delay of interchannel, Δ t1For the delay between the first optical pumped magnetometer and the second optical pumped magnetometer, Δ t2、Δt3、Δt4Respectively
For the delay between three axis components and the second optical pumped magnetometer of flux-gate magnetometer output.In the case of ideal is no-delay, Δ ti=
0;For actual aeromagnetic survey system, Δ tiIt is not 0.
As shown in figure 3, the boat magnetic compensation method of the embodiment of the present invention, including:
Step S1:Time series weighted modeling is carried out to the output of flux-gate magnetometer, obtains flux-gate magnetometer output
Estimated value.
Step S1 is specifically included:With the output H of the second optical pumped magnetometerd2(t0) it is time reference benchmark, obtain fluxgate
Three axis components of magnetometer outputWithEstimated value.It can be by time reference benchmark t in the present embodiment0
Sample point near moment obtains estimated value with the mode of linear prediction, is shown below:
In formula, fsFor systematic sampling rate, mj, nj, pjFor the weighting coefficient of linear prediction, l is the sample of weighting sequence covering
Point range, j are j-th of component therein.In ideal undelayed aeromagnetic survey system, above-mentioned weighting coefficient meets such as following table
Up to formula.
mj=nj=pj=δ (t-t0) (6)
In actual aeromagnetic survey system, since each sensor uses different clock chip and acquisition channel
Sequencing and circuit at different levels caused by uncontrollable factor, the data between each sensor such as be delayed can not possibly accomplish
It is complete synchronous, therefore mj, njAnd pjIt cannot be indicated with the impulse function in formula (6), but the weighting function sequence that coefficient is undetermined
Row.
Step S2:The estimated value exported by flux-gate magnetometer, obtains the estimated value of the direction cosines of earth's magnetic field and aircraft,
And the estimated value of boat magnetic compensation aspect of model matrix.
Step S2 includes:
First, the three axis component estimated values exported by flux-gate magnetometerWithObtain earth magnetism
With the direction cosines of aircraft in time reference benchmark t0Estimated value.It brings formula (5) into formula (3), obtains earth's magnetic field and fly
The direction cosines of machine are in time reference benchmark t0Estimated value, as shown in following formula (7):
Then, by the direction cosines of earth's magnetic field and aircraft in time reference benchmark t0Estimated value, obtain boat magnetic compensation mould
The eigenmatrix of type is in time reference benchmark t0Non-linear estimations value.It brings formula (7) result into formula (2), can be navigated
The eigenmatrix of magnetic compensation model is in t0The non-linear estimations value at moment, as shown in formula (8):
Step S3:By the estimated value of boat magnetic compensation aspect of model matrix, the aircraft platform that optical pumping magnetometer observes is predicted
Magnetic disturbance.
Step S3 is specifically included:
The t obtained with formula (8)0The eigenmatrix estimated value at moment, the aircraft that the second optical pumping magnetometer of prediction observes are flat
Platform magnetic disturbance, as shown in formula (9):
In formula,For i-th of element in formula (8), c 'i2For magnetic disturbance at the second optical pumping magnetometer probe
Penalty coefficient.
The t obtained with formula (8)0The eigenmatrix estimated value at moment, the aircraft that the first optical pumping magnetometer of prediction observes are flat
Platform magnetic disturbance, as shown in formula (10):
Wherein c 'i1For the penalty coefficient of magnetic disturbance at the first optical pumping magnetometer probe.
Step S4:It is special by the estimated value and boat magnetic compensation model of the obtained earth's magnetic fields step S2 and the direction cosines of aircraft
It levies the estimated value of matrix, the aircraft platform magnetic disturbance that the optical pumping magnetometer that step S3 is obtained observes, it is total to obtain non-linear boat magnetic
Field gradient compensation model.
Step S4 includes:
First, aircraft platform magnetic disturbance optical pumping magnetometer observed substitutes into the boat total field gradient compensation model of magnetic, obtains
Interference of the aircraft to the total field gradient of magnetic of navigating.It brings formula (9) and formula (10) into formula (4), aircraft can be obtained to boat magnetic resultant field ladder
The interference of degree, is shown below:
Then, by the estimated value generation of the direction cosines of the estimated value for the magnetic compensation aspect of model matrix that navigates, earth's magnetic field and aircraft
Enter interference of the aircraft to the total field gradient of magnetic of navigating, obtains the non-linear total field gradient compensation model of boat magnetic.
Specifically, it brings formula (8) into formula (11), there is following formula:
It brings formula (7) into formula (12) again, obtains following formula:
It takesAs the sphere of action of weighting sequence, by formula (7) byIt is expanded toAnd bring formula (11) into again, while assuming space resultant field in Δ t1In time
It is held essentially constant, then last abbreviation obtains following formula:
Shown in the non-linear total field gradient compensation model of boat magnetic such as formula (14), wherein containing (3 (l+fs·Δt1)+18) and it is a not
Know coefficient.By solving the unknowm coefficient, you can the aircraft magnetic disturbance of compensation existence time synchronous error.
Step S5:The non-linear total field gradient compensation model of boat magnetic is solved, boat magnetic compensation result is obtained.
The non-linear total field gradient compensation model of boat magnetic is non-linear form, the minimum two in the magnetic compensation that can not be navigated by tradition
Multiply method solution, herein proposes and solve the problem with Levenberg-Marquardt (L-M) method.
During navigating magnetic compensation, optical pumped magnetometer measurement can be obtained by formula (4) and obtain aircraft interference magnetic field in t0Moment
Total field gradient be GH(t0), the mean square error of the remnant field after compensation can be expressed as following formula:
Since the non-linear total field gradient compensation model of boat magnetic is nonlinear function, can be solved by the method for optimization,
It is the adduction of all sample point remnant fields to enable object function, is shown below:
L-M algorithms are suitble to solve Nonlinear Optimization Problem, while can solve Jacobian matrixes during optimizing
Irreversible situation.After bringing formula (14) into formula (15), then willAnalytic expression bring formula (16) into, can obtain final
Object function expression formula such as formula (17) shown in:
In order to obtain minimum remnant field, need to minimize object function, i.e., corresponding optimization problem such as following formula (18)
It is shown.
min(h) (18)
The problem is solved using L-M algorithms.It enables
Wherein, x is by (3 (l+fs·Δt1)+18) coefficient vector of a unknown number to be solved composition, enable F (x)=(F1
(x) F2(x) … Fn(x))T, can be calculated shown in corresponding Jacobian matrixes such as following formula (20).
The optimal solution of the above problem is obtained by way of iteration, the update of kth time is shown in shown in formula (21).
In formula, Jk=J (xk), Fk=F (xk).Wherein vector x is made of four parts, respectively aircraft magnetic disturbance compensation system
G ' and three group of interchannel delay Coefficient m of number, n, p.It can be abbreviated as (g ' m n p)T, wherein g ' is g 'iThe column vector of composition, m
For miThe column vector of composition, n niThe column vector of composition, p piThe column vector of composition.
In order to enable result is most fast to converge in optimal solution, does pretreatment first with least-squares algorithm and obtain 18
Penalty coefficient as the parts parameter g ' in x initial values, and arbitrarily sets remaining parameter, and interative computation to object function is received
It holds back.It is the penalty coefficient in the non-linear boat total field gradient compensation model of magnetic to iterate to calculate obtained vector x.
The carried non-linear total field gradient compensation model of boat magnetic above is verified below by numerical simulation.In emulation
The magnetic compensation coefficient of boat magnetic resultant field gradient system given first, as shown in table 1.Using normalized gradient computational methods, baseline
Length is 1m.
1 magnetic compensation coefficient of table
g1 | g2 | g3 | g4 | g5 | g6 |
58.5 | 10.2 | 4 | 0.0011 | -0.00014 | 0.00013 |
g7 | g8 | g9 | g10 | g11 | g12 |
0.00026 | 0.000047 | 0.00039 | 0.02 | -0.00034 | -0.000022 |
g13 | g14 | g15 | g16 | g17 | g18 |
0.00023 | 0.019 | -0.00014 | -0.000019 | -0.0002 | 0.002 |
For true aeromagnetic survey system, there are following three kinds delays, 1. optical pumped magnetometers and flux-gate magnetometer number
According to a relative delay;2. relative delay between optical pumped magnetometer and optical pumped magnetometer data;3. each interchannel number of flux-gate magnetometer
According to relative delay.The influence that will illustrate all kinds of delays by emulating below, it is normal using boat magnetic compensation in data quality accessment
Signal estimation method:The standard deviation of signal and the peak-to-peak value of signal carry out the compensation effect of gauge signal.
It is 10 sample intervals that delay is taken in emulation, and Fig. 4 is the front and back aberration curve of compensation, and wherein solid line is linear model
Least square method compensation after as a result, in corresponding diagram the left side the longitudinal axis;Dotted line is the non-linear total field gradient compensation model LM of boat magnetic
As a result, the longitudinal axis on the right in corresponding diagram after compensation.Caused by Fig. 4 (a) postpones between optical pumped magnetometer and flux-gate magnetometer
Deviation is interfered and compensation;Deviation interference and compensation caused by delay between Fig. 4 b optical pumped magnetometers and optical pumped magnetometer;Fig. 4 c magnetic
Deviation interference and compensation caused by open gate magnetometer x channel delays.Table 2 is the statistical result of deviation.It is visible each from Fig. 4 and table 2
The asynchronous of sensor signal can be such that compensation result generates between larger deviation, especially optical pumped magnetometer and flux-gate magnetometer
It is asynchronous, the interference of the deviation of generation is nonsynchronous 10 times or so between optical pumped magnetometer.
Influence of 2 signal delay of table to compensation
As seen from Table 2, the peak-to-peak value of the deviation interference between optical pumped magnetometer and flux-gate magnetometer is from 0.2557nT/m
It is reduced to 0.0025nT/m, standard deviation is reduced to 1.576 × 10 from 0.0153nT/m-4nT/m;Optical pumped magnetometer and optical pumping magnetic force
The peak-to-peak value of deviation interference between instrument is reduced to 0.0025nT/m from 0.025nT/m, and standard deviation is reduced to from 0.0016nT/m
1.577×10-4nT/m;The peak-to-peak value of the deviation interference in the channels flux-gate magnetometer x is reduced to 0.0022nT/ from 0.0752nT/m
M, standard deviation are reduced to 1.576 × 10 from 0.0059nT/m-4nT/m.Situation devious after being compensated compared to conventional method, text
Middle the carried total field gradient compensation model of non-linear boat magnetic, has preferably compensation result after iterative calculation by L-M algorithms
Promotion, effectively inhibit delay caused by deviation interference.
In the present invention, step S1 can complete to model using the time series of different length;The optical pumping magnetic force used
Instrument quantity does not have to the total field gradient of single magnetic for being confined to two compositions, and multiple optical pumped magnetometers probe can be used to form more gradients
It measures, can equally obtain corresponding nonlinear compensation model.
So far, attached drawing is had been combined the embodiment of the present invention is described in detail.According to above description, art technology
Personnel should have clear understanding to the boat magnetic compensation method based on the non-linear boat total field gradient compensation model of magnetic of the present invention.
It should be noted that in attached drawing or specification text, the realization method for not being painted or describing is affiliated technology
Form known to a person of ordinary skill in the art, is not described in detail in field.In addition, above-mentioned definition to each element and not only limiting
The various modes mentioned in embodiment, those of ordinary skill in the art simply can be changed or replaced to it, such as:
(1) direction term mentioned in embodiment, such as "upper", "lower", "front", "rear", "left", "right" etc. are only ginsengs
The direction of attached drawing is examined, is not used for limiting the scope of the invention;
(2) above-described embodiment can be based on the considerations of design and reliability, and the collocation that is mixed with each other uses or and other embodiment
Mix and match uses, i.e., the technical characteristic in different embodiments can freely form more embodiments.
The purpose of the present invention, technical solution and advantageous effect is described in detail in particular embodiments described above,
It should be understood that the above is only a specific embodiment of the present invention, it is not intended to restrict the invention, it is all in the present invention
Spirit and principle within, any modification, equivalent substitution, improvement and etc. done, should be included in protection scope of the present invention it
It is interior.
Claims (8)
1. a kind of boat magnetic compensation method based on the non-linear boat total field gradient compensation model of magnetic, which is characterized in that including:
Step S1:Time series weighted modeling is carried out to the output of flux-gate magnetometer, obtains estimating for flux-gate magnetometer output
Evaluation;
Step S2:The estimated value exported by the flux-gate magnetometer obtains the direction cosines estimated value of earth's magnetic field and aircraft, with
And the estimated value of boat magnetic compensation aspect of model matrix;
Step S3:By the estimated value of the boat magnetic compensation aspect of model matrix, the aircraft platform that prediction optical pumped magnetometer observes
Magnetic disturbance;
Step S4:By the estimated value of the earth's magnetic field and the direction cosines of aircraft, the estimated value for the magnetic compensation aspect of model matrix that navigates
And the aircraft platform magnetic disturbance that optical pumped magnetometer observes, obtain the non-linear total field gradient compensation model of boat magnetic;And
Step S5:The non-linear total field gradient compensation model of boat magnetic is solved, boat magnetic compensation result is obtained;
Wherein, the optical pumped magnetometer includes the first optical pumped magnetometer and the second optical pumped magnetometer, with the second optical pumping in step S1
The output of magnetometer is time reference benchmark, obtains the estimated value of three axis components of the flux-gate magnetometer output.
2. boat magnetic compensation method as described in claim 1, which is characterized in that obtain the fluxgate in a manner of linear prediction
The estimated value of three axis components of magnetometer output.
3. boat magnetic compensation method as described in claim 1, which is characterized in that the step S2 is specifically included:
The estimated value exported by the flux-gate magnetometer obtains the direction cosines of earth's magnetic field and aircraft in time reference benchmark
Estimated value;And
By the direction cosines of the earth's magnetic field and aircraft in the estimated value of time reference benchmark, the feature of boat magnetic compensation model is obtained
Non-linear estimations value of the matrix in time reference benchmark.
4. boat magnetic compensation method as described in claim 1, which is characterized in that the step S3 is specifically included:By boat magnetic compensation
The eigenmatrix of model predicts that the aircraft platform magnetic that optical pumped magnetometer observes is dry in the non-linear estimations value of time reference benchmark
It disturbs.
5. boat magnetic compensation method as described in claim 1, which is characterized in that the step S4 is specifically included:
The aircraft platform magnetic disturbance that the optical pumped magnetometer is observed substitutes into the boat total field gradient compensation model of magnetic, obtains aircraft pair
The interference for the total field gradient of magnetic of navigating;And
The estimated value of the direction cosines of the estimated value of the boat magnetic compensation aspect of model matrix, earth's magnetic field and aircraft is substituted into aircraft
Interference to the total field gradient of magnetic of navigating, obtains the non-linear total field gradient compensation model of boat magnetic.
6. boat magnetic compensation method as described in claim 1, which is characterized in that solved by optimal method in the step S5
The non-linear total field gradient compensation model of boat magnetic.
7. boat magnetic compensation method as claimed in claim 6, which is characterized in that the optimal method is Levenberg-
Marquardt methods.
8. boat magnetic compensation method as described in any one of claim 1 to 7, which is characterized in that the boat magnetic compensation method is used for
It compensates between optical pumped magnetometer and flux-gate magnetometer, between optical pumped magnetometer and optical pumped magnetometer and fluxgate is each logical
Delay between road.
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