CN104765013B - Calibrating three-axle magnetic sensor method - Google Patents
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Abstract
The embodiments of the invention provide a kind of calibrating three-axle magnetic sensor method, the problem of stated accuracy for effectively improving magnetic sensor in the prior art has much room for improvement.Calibrating three-axle magnetic sensor method in the embodiment of the present invention, methods described includes：The measurement model of magnetic sensor is obtained, the measurement model includes calibrating parameters；The calibrating parameters determination value is obtained using Maximum-likelihood estimation.The calibrating three-axle magnetic sensor method is ingenious in design, significantly improves the stated accuracy of magnetic sensor, easy to implement, it is easy to popularization and application.
Description
Technical field
The present invention relates to sensor technical field, in particular to a kind of calibrating three-axle magnetic sensor method.
Background technology
In the prior art, Magnetic Sensor also known as magnetometer, magnetometer, are frequently used for posture and determine or scientific measurement field.
Due to the imperfection of external interference and manufacturing process, there is error in magnetic sensor, thus, using magnetic sensor it
Before, it is necessary to calibration is carried out to it.Inventor it has been investigated that, current magnetic sensor is based primarily upon the constant principle of mould and enters rower
It is fixed, be built upon non-optimal --- on suboptimal estimation basis, therefore calibration result is suboptimum, and precision has much room for improvement.
The content of the invention
In view of this, the purpose of the embodiment of the present invention is to provide a kind of calibrating three-axle magnetic sensor method, existing to improve
The problem of stated accuracy for having magnetic sensor in technology has much room for improvement.
To achieve these goals, the technical scheme that the embodiment of the present invention is used is as follows：
The embodiments of the invention provide a kind of calibrating three-axle magnetic sensor method, methods described includes：
The measurement model of magnetic sensor is obtained, the measurement model includes calibrating parameters；
The calibrating parameters determination value is obtained using the Maximum-likelihood estimation of the quadratic function based on the calibrating parameters.
Wherein, the measurement model is：
K=1,2 ... N, wherein, N is the data sampling point that the magnetic sensor is obtained
Number；For magnetic field vector of the magnetic sensor under coordinate system,T is upper triangular matrix；H is magnetic biasing
Put vector, ekFor independent identically distributed white Gaussian noise.
Wherein, the T is upper triangular matrix, and the Maximum-likelihood estimation is：
Wherein, U (3) is upper triangular matrix T's
Set；λkFor constraintsLagrange coefficient；θ is calibrating parameters,
Wherein, if in the Maximum-likelihood estimation, it is thus necessary to determine that calibrating parameters be x,Wherein, vec (T) represents that T gets up according to the sequential concatenation of row, picked
Except the vector obtained after lower triangle element, the Maximum-likelihood estimation of the acquisition calibrating parameters obtains the demarcation ginseng
Number determination value, including：
According to constraintsObtain constraint equation：
Wherein,For Kronecker product；A is three dimensional symmetry square
Battle array；Vec (A) is that A gets up by the sequential concatenation of row, the vector obtained after lower triangle element is rejected；Subscript T representing matrixs or
The transposition of vector；
Row corresponding with triangle element under A in Y are incorporated into row corresponding with triangle element on A；
If YTY characteristic vector is ze, characteristic vector zeWith minimal eigenvalue, have
Corresponding A, b and c are extracted from z, there is h(0)=-A-1B/2, T(0)=(chol (A))-1, wherein, chol () is
The Qiao Laisiji of matrix is decomposed；Initial Lagrange coefficientInitial magnetic field vector
Iterative calculation is until meet the condition of convergence：
I=0,1 ..., wherein, J is Jacobian matrix derivative vector, and H is extra large gloomy square
Battle array.
Wherein, the Jacobian matrix derivative vector J and Hessian matrix H is：
Wherein,
In the embodiment of the present invention, abandon what magnetic sensor in the prior art was demarcated on the basis of suboptimal estimation
Mode, innovatively obtains calibrating parameters determination value based on " optimal " Maximum-likelihood estimation, with suboptimal estimation of the prior art
Scheme is compared, and significantly improves stated accuracy.
Further, in the embodiment of the present invention, calibrating parameters determination value is obtained according to " optimal " Maximum-likelihood estimation, used
The optimization object function that this mode is obtained is the quadratic function of parameter to be calibrated, compared with biquadratic function of the prior art,
With broader convergence threshold.
In the embodiment of the present invention calibrating three-axle magnetic sensor method design it is simple, easy to implement, demarcation can be significantly improved
Precision, with broader convergence threshold, the scope of application is wider, is particularly suitable for use in posture and encourages not sufficient enough situation, meets reality
Demand, with prominent substantive distinguishing features and marked improvement, is adapted to large-scale promotion application.
Embodiment
Below in conjunction with the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described,
Obviously, described embodiment is only a part of embodiment of the invention, rather than whole embodiments.This hair presented below
The detailed description of bright embodiment is not intended to limit the scope of claimed invention, but is merely representative of the choosing of the present invention
Determine embodiment.Based on embodiments of the invention, those skilled in the art are obtained on the premise of creative work is not made
Every other embodiment, belong to the scope of protection of the invention.
Embodiment
Magnetic Sensor is easily disturbed by external magnetic field, and magnetic disturbance can be divided into Hard Magnetic interference and soft magnetism disturbs two kinds, firmly
The mechanism of action of magnetic disturbance and soft magnetism interference is different.Wherein, the interference of permanent magnet or electric current belongs to Hard Magnetic interference, and Hard Magnetic is done
Disturbing can make Magnetic Sensor produce additivity biased error；Soft magnetism interference is produced because of ferromagnetic material by the excitation of background magnetic field, anti-mistake
The distortion of background magnetic field can be caused.In addition, because of the imperfection of manufacturing process, magnetic sensor also exist scale because
Number, sensitive axes cross-couplings and biasing equal error, therefore, before using magnetic sensor, it is necessary to carried out to above error
Calibration.
Inventor it has been investigated that, current magnetic sensor is based primarily upon the constant principle of mould and demarcated, the constant original of mould
Reason refers to：Under the background magnetic field of uniformity, the amplitude size of magnetic sensor output quantity is unrelated with its posture.Based on mould
The measurement model of magnetic sensor is converted to an approximate Maximum-likelihood estimation by constant principle, existing scaling method, is led to
Nonlinear optimization numerical solution is crossed, the parameter to be estimated in Magnetic Sensor measurement model is calculated.Therefore, existing scaling method
It is built upon on suboptimal estimation basis, and its optimization object function is the biquadratic function of parameter to be estimated.Inventor passes through
Research finds that scaling method of the prior art has problems with：
Due to existing demarcation mode be built upon it is non-optimal --- on suboptimal estimation basis, therefore calibration result is
Suboptimum, precision has much room for improvement；
Existing scaling method has the optimization object function of four times, there is multiple Min-max points.Although existing demarcation side
Method does not need external equipment to provide specific posture input, however, to ensure that numerical algorithm converges to true value, it is necessary to which magnetic is sensed
Device is encouraged by sufficient posture, that is to say, that in data acquisition, and the posture of Magnetic Sensor will undergo abundant posture
Change, otherwise may cause the diverging of calibration algorithm.
Based on this, the embodiments of the invention provide a kind of high accuracy, the calibrating three-axle magnetic sensor method of wide convergence domain, institute
The method of stating includes：
The measurement model of magnetic sensor is obtained, the measurement model includes calibrating parameters；
Wherein, the measurement model of preferably magnetic sensor is：
Wherein, N is the data sampling point number that the magnetic sensor is obtained；Exist for the magnetic sensor
Body coordinate system, can be denoted as the magnetic field vector under b systems, without loss of generality (Without loss of generality, WLOG or
WOLOG or w.l.o.g.), it is assumed thatIn order to ensure the uniqueness of calibrating parameters, preferably T is upper triangular matrix, for example：
T is upper 3 × 3 upper triangular matrix；H is magnetic bias vector, ekFor independent same distribution white Gaussian noise, variance matrix can be σ2I3。
The calibrating parameters determination value is obtained using the Maximum-likelihood estimation of the quadratic function based on the calibrating parameters.
The purpose of demarcation is to determine the calibrating parameters in model above, if T is upper triangular matrix, and problem of calibrating can be of equal value
It is written as optimal Maximum-likelihood estimation：
Wherein, U (3) is 3 × 3 upper triangular matrix T set；λkFor constraintsLagrange coefficient；θ is
Calibrating parameters,
As can be seen that in the embodiment of the present invention, the object function of optimal Maximum-likelihood estimation is the secondary letter of calibrating parameters
Number.
Available for the numerical algorithm more than one for solving above Maximum-likelihood estimation, with the height of iteration in the embodiment of the present invention
This-Newton method exemplified by come annotate solve calibrating parameters the step of, the present invention implement in can be adopted method for solving include but
It is not limited to which.
It is preferred that in Maximum-likelihood estimation described above, it would be desirable to it is determined that calibrating parameters be uniformly denoted as x,Wherein, vec (T) represents to play T according to the sequential concatenation of row
Come, reject the vector obtained after lower triangle element, the Maximum-likelihood estimation of the acquisition calibrating parameters obtains the mark
Determine parameter determination value, including：
Determine iteration initial value x0
According to constraintsObtain following constraint equation：
Wherein,For Kronecker product Kronecker；A is
Three dimensional symmetry matrix；Vec (A) is that A gets up according to the sequential concatenation of row, the vector obtained after lower triangle element is rejected；On
Mark the transposition of T representing matrixs or vector；
Row corresponding with triangle element under A in Y are incorporated into row corresponding with triangle element on A；
If YTThe Y characteristic vector with minimal eigenvalue is ze, have：
According to defined above, corresponding A, b and c are extracted from z, there is h(0)=-A-1B/2, T(0)=(chol (A))-1,
Wherein, chol () decomposes for the Qiao Laisiji Cholesky of matrix；Initial Lagrange coefficientInitial magnetic field to
Amount
Iterative calculation is until meet the condition of convergence：
I=0,1 ..., wherein, J is Jacobian matrix Jacobian derivatives vector, H
For extra large gloomy Hessian matrixes.
Jacobian matrix Jacobian derivatives vector J and Hai Sen Hessian matrix Hs are specially：
Wherein,
In above-mentioned, according to actual conditions, the condition of convergence can flexibly be set as that maximum iteration, or target function value are
It is no to have stablized.
Calibrating three-axle magnetic sensor method in the embodiment of the present invention, sets up on " optimal " Maximum-likelihood estimation basis
On, optimization object function is the quadratic function of parameter to be calibrated, than the biography in the prior art based on approximate Maximum-likelihood estimation
Scaling method of uniting has higher precision and broader convergence domain, is particularly suitable for use in posture and encourages not sufficient enough situation.
The foregoing is only a specific embodiment of the invention, but protection scope of the present invention is not limited thereto, any
Those familiar with the art the invention discloses technical scope in, change or replacement can be readily occurred in, should all be contained
Cover within protection scope of the present invention.Therefore, protection scope of the present invention described should be defined by scope of the claims.
Claims (2)
1. a kind of calibrating three-axle magnetic sensor method, it is characterised in that methods described includes：
The measurement model of magnetic sensor is obtained, the measurement model includes calibrating parameters；
The calibrating parameters determination value is obtained using the Maximum-likelihood estimation of the quadratic function based on the calibrating parameters；
The measurement model is：
K=1,2 ... N, wherein, N is the data sampling point number that the magnetic sensor is obtained；For magnetic field vector of the magnetic sensor under coordinate system,T is upper triangular matrix；H be magnetic bias to
Amount, ekFor independent identically distributed white Gaussian noise；
The T is upper triangular matrix, and the Maximum-likelihood estimation is：
Wherein, U (3) is upper triangular matrix T set；
λkFor constraintsLagrange coefficient, k=1~N；θ is calibrating parameters,
If in the Maximum-likelihood estimation, it is thus necessary to determine that calibrating parameters be x,
Wherein, vec (T) is represented to get up T according to the sequential concatenation of row, is rejected the vector obtained after lower triangle element, the acquisition
The Maximum-likelihood estimation of the calibrating parameters, obtains the calibrating parameters determination value, including：
According to constraintsObtain constraint equation：
Wherein,For Kronecker product；A is three dimensional symmetry matrix；
Vec (A) is that A gets up by the sequential concatenation of row, the vector obtained after lower triangle element is rejected；Subscript T representing matrixs or to
The transposition of amount；
Row corresponding with triangle element under A in Y are incorporated into row corresponding with triangle element on A；
If YTY characteristic vector is ze, characteristic vector zeWith minimal eigenvalue, have
Corresponding A, b and c are extracted from z, there is h(0)=-A-1B/2, T(0)=(chol (A))-1, wherein, chol () is matrix
Qiao Laisiji decompose；Initial Lagrange coefficientInitial magnetic field vector
Iterative calculation is until meet the condition of convergence：
I=0,1 ..., wherein, J is Jacobian matrix derivative vector, and H is Hessian matrix.
2. calibrating three-axle magnetic sensor method according to claim 1, it is characterised in that the Jacobian matrix derivative to
Measuring the J and Hessian matrix H is：
Wherein,
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| CN107037235B (en) * | 2016-11-28 | 2023-08-01 | 东南大学 | Soft measurement method and measurement device for brake slip quantity |
| CN108919156B (en) * | 2018-06-27 | 2020-09-08 | 中国人民解放军海军航空大学 | Off-line correction method of three-axis magnetometer based on noise compensation |
| CN110174123B (en) * | 2019-05-08 | 2021-03-23 | 苏州大学 | Real-time calibration method for magnetic sensor |
| CN110824570B (en) * | 2019-10-28 | 2021-07-27 | 杭州电子科技大学 | Body magnetism correction method of three-axis magnetic sensor |
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| EP2459959A1 (en) * | 2009-07-28 | 2012-06-06 | Canon Kabushiki Kaisha | Position and orientation calibration method and apparatus |
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| JP2012002695A (en) * | 2010-06-17 | 2012-01-05 | Fujikura Ltd | Error factor determination method and device thereof, error compensation method, triaxial magnetic sensor, sensor module, and program for determining error factor |
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| EP2459959A1 (en) * | 2009-07-28 | 2012-06-06 | Canon Kabushiki Kaisha | Position and orientation calibration method and apparatus |
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