METHOD FOR CALIBRATING THE SENSITIVITY OF MONOAXIAL OR MULTIAXIAL MAGNETIC FIELD SENSORS

Abstract

In a method for calibrating the sensitivity of a monoaxial or multiaxial magnetic field sensor, the magnetic field sensor is exposed consecutively to at least three magnetic fields having different magnetic field vectors which may be freely orientated in space so that they span an oblique coordinate system. The magnetic fields are measured with the magnetic field sensor in order to obtain a sensitivity vector in the oblique coordinate system of the magnetic field vectors for each sensor axis. The sensitivity vectors are transformed into an orthogonal coordinate system via a transformation matrix, and sensitivity and transverse sensitivity of each sensor axis are then calculated on the basis of the transformed sensitivity vectors either directly or following a further transformation. The method enables rapid, precise calibration of all sensitivities of a magnetic field sensor, since it does not require any orthogonal magnetic fields.

Claims

1. Method for calibrating the sensitivity of at least one monoaxial or multiaxial magnetic field sensor, in which the magnetic field sensor (1) is exposed consecutively to at least three magnetic fields (B.sub.1, B.sub.2, B.sub.3) having different magnetic field vectors, which do not lie in a plane relative to a reference system that is connected fixedly to the magnetic field sensor (1) and which span an oblique coordinate system, the magnetic fields (B.sub.1, B.sub.2, B.sub.3) are measured with the magnetic field sensor (1) for each sensor axis (2, 3, 4) of the magnetic field sensor (1), in order to obtain a sensitivity vector in the oblique coordinate system of the magnetic field for each sensor axis (2, 3, 4), a transformation matrix is created, with which a vector in the oblique coordinate system spanned by the magnetic field vectors can be translated into an orthogonal coordinate system, the sensitivity vectors are transformed into the orthogonal coordinate system with the aid of the transformation matrix, and sensitivity and transverse sensitivity of each sensor axis (2, 3, 4) are calculated from the transformed sensitivity vectors either directly or after a further transformation.

2. Method according to claim 1, characterized in that angles between the sensor axes (2, 3, 4) are calculated from the transformed sensitivity vectors.

3. Method according to claim 1 or 2, characterized in that in the event that the angles between the sensor axes (2, 3, 4) differ from 90°, a second transformation matrix is created, with which a vector in a second oblique coordinate system spanned by the transformed sensitivity vectors can be translated into a second orthogonal coordinate system, the transformed sensitivity vectors are transformed into the second orthogonal coordinate system with the aid of the second transformation matrix, and a corrected sensitivity and transverse sensitivity of each sensor axis (2, 3, 4) is calculated from the sensitivity vectors that have been transformed into the second orthogonal coordinate system.

4. Method according to any one of claims 1 to 3, characterized in that the magnetic fields (B.sub.1, B.sub.2, B.sub.3) are generated with a device for generating homogeneous magnetic fields.

5. Method according to any one of claims 1 to 3, characterized in that the magnetic fields (B.sub.1, B.sub.2, B.sub.3) are generated with one or more nested Helmholtz coils.

6. Method according to any one of claims 1 to 5 for calibrating the sensitivity of multiple monoaxial or multiaxial magnetic field sensors, in which the monoaxial or multiaxial magnetic field sensors (1) are exposed together to the at least three magnetic fields (B.sub.1, B.sub.2, B.sub.3), and the magnetic fields (B.sub.1, B.sub.2, B.sub.3) are measured with the magnetic field sensors (1) for each sensor axis (2, 3, 4) of the magnetic field sensors (1).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In the following text, the suggested method will be explained again, in greater detail, with reference to an exemplary embodiment and in conjunction with the FIGURE, wherein

[0014] FIG. 1 shows a schematic representation of an exemplary orientation of three linearly independent magnetic fields and three sensor axes of a triaxial magnetic field sensor in the suggested method.

WAYS TO IMPLEMENT THE INVENTION

[0015] In the following, the suggested method will be explained again for exemplary purposes by means of the calibration of a triaxial magnetic field sensor using three magnetic fields or magnetic field vectors which are orientated freely in space. In the case of three magnetic fields for the calibration, the values for the flux densities of the three magnetic fields B.sub.1, B.sub.2 and B.sub.3 as well as the angles between the magnetic fields or magnetic field vectors w.sub.B1B2, w.sub.B2B3 and w.sub.B3B1 must be known. To this end, FIG. 1 shows an example of an orientation of the three magnetic field vectors.

[0016] The location and strength of the magnetic fields can also be expressed in vector notation:

{right arrow over (B.sub.1)}=B.sub.1.Math.{right arrow over (g.sub.1)},{right arrow over (B.sub.2)}=B.sub.2.Math.{right arrow over (g.sub.2)},{right arrow over (B.sub.3)}=B.sub.3.Math.{right arrow over (g.sub.3)}

[0017] In this context, {right arrow over (g.sub.1)}, {right arrow over (g.sub.2)} and {right arrow over (g.sub.3)} represent the “base vectors” of a coordinate system of the magnetic fields, which correspond to the directions of the magnetic fields.

[0018] The field vectors may be freely orientated in space, although the angles between the fields must be known. Therefore, the following applies:

[00001]$\cos \left(w_{B^1{B}^2}\right)=\frac{\stackrel{.fwdarw.}{B_1}.Math.\stackrel{.fwdarw.}{B_2}}{.Math.\stackrel{.fwdarw.}{B_1}.Math..Math..Math.\stackrel{.fwdarw.}{B_2}.Math.};\cos \left(w_{B^2{B}^3}\right)=\frac{\stackrel{.fwdarw.}{B_2}.Math.\stackrel{.fwdarw.}{B_3}}{.Math.\stackrel{.fwdarw.}{B_2}.Math..Math..Math.\stackrel{.fwdarw.}{B_3}.Math.};\cos \left(w_{B^3{B}^1}\right)=\frac{\stackrel{.fwdarw.}{B_3}.Math.\stackrel{.fwdarw.}{B_1}}{.Math.\stackrel{.fwdarw.}{B_3}.Math..Math..Math.\stackrel{.fwdarw.}{B_1}.Math.}$

[0019] The quantity of the vectors {right arrow over (g.sub.1)}, {right arrow over (g.sub.2)} and {right arrow over (g.sub.3)} may also be interpreted as basis ĝ of the oblique coordinate system which is spanned by the three magnetic fields. Expressed in a Cartesian (orthogonal) coordinate system ê with base vectors {right arrow over (e.sub.1)}, {right arrow over (e.sub.2)} and {right arrow over (e.sub.3)}, the location of the oblique coordinate system can be defined relative to the Cartesian system as follows: {right arrow over (g.sub.1)} is parallel to {right arrow over (e.sub.1)}, {right arrow over (g.sub.2)} is in the plane of {right arrow over (e.sub.1)} and {right arrow over (e.sub.2)}, {right arrow over (g.sub.3)} is situated anywhere in space:

[00002]$\stackrel{.fwdarw.}{g_1}=\left(\begin{array}{c}{x}_1\\ 0\\ 0\end{array}\right),\stackrel{.fwdarw.}{g_2}=\left(\begin{array}{c}{x}_2\\ y_2\\ 0\end{array}\right),\stackrel{.fwdarw.}{g_3}=\left(\begin{array}{c}{x}_3\\ y_3\\ z_3\end{array}\right)$

[0020] With a fixed length of base vectors |{right arrow over (g.sub.1)}|=|{right arrow over (g.sub.2)}|=|{right arrow over (g.sub.3)}|=1, the equations for the angles between the magnetic field vectors may also be written as follows:

cos(w.sub.B.sub.1.sub.B.sub.2)={right arrow over (g.sub.1)}.Math.{right arrow over (g.sub.2)}, cos(w.sub.B.sub.2.sub.B.sub.3)={right arrow over (g.sub.2)}.Math.{right arrow over (g.sub.3)}, cos(w.sub.B.sub.3.sub.B.sub.1)={right arrow over (g.sub.3)}.Math.{right arrow over (g.sub.1)}

[0021] After these three equations are resolved according to the components of the base vectors, they can be expressed as follows:

[00003]$\stackrel{.fwdarw.}{g_1}=\left(\begin{array}{c}1\\ 0\\ 0\end{array}\right);\stackrel{.fwdarw.}{g_2}=\left(\begin{array}{c}\cos \left(w_{B^1{B}^2}\right)\\ \sin \left(w_{B^1{B}^2}\right)\\ 0\end{array}\right);$$\stackrel{.fwdarw.}{g_3}=\left(\begin{array}{c}\cos \left(w_{B^3{B}^1}\right)\\ \frac{\cos \left(w_{B^2{B}^3}\right)}{\sin \left(w_{B^1{B}^2}\right)}-\cot \left(w_{B^1{B}^2}\right).Math.\cos \left(w_{B^3{B}^1}\right)\\ \sqrt{{\sin }^2\left(w_{B^3{B}^1}\right)-{\left(\frac{\cos \left(w_{B^2{B}^3}\right)}{\sin \left(w_{B^1{B}^2}\right)}-\cot \left(w_{B^1{B}^2}\right).Math.\cos \left(w_{B^3{B}^1}\right)\right)}^2}\end{array}\right)$

[0022] In order to effect a change of basis between an orthogonal coordinate system and the oblique coordinate system of the magnetic fields, the following transformation matrix T.sub.ê.sup.ĝ may be formed from the base vectors for transformation from ê to ĝ:

[00004]${\underset{\_}{T}}_{\hat{e}}^{\hat{g}}={\left(\stackrel{.fwdarw.}{g_1}\stackrel{.fwdarw.}{g_2}\stackrel{.fwdarw.}{g_3}\right)}^T=\left(\begin{array}{ccc}1& 0& 0\\ \cos \left(w_{B^1{B}^2}\right)& \sin \left(w_{B^1{B}^2}\right)& 0\\ \cos \left(w_{B^3{B}^1}\right)& \frac{\cos \left(w_{B^2{B}^3}\right)}{\sin \left(w_{B^1{B}^2}\right)}-\cot \left(w_{B^1{B}^2}\right).Math.\cos \left(w_{B^3{B}^1}\right)& \sqrt{{\sin }^2\left(w_{B^3{B}^1}\right)-{\left(\frac{\cos \left(w_{B^2{B}^3}\right)}{\sin \left(w_{B^1{B}^2}\right)}-\cot \left(w_{B^1{B}^2}\right).Math.\cos \left(w_{B^3{B}^1}\right)\right)}^2}\end{array}\right)$

[0023] This transformation is applied to vectors of basis ê: ĝ=T.sub.ê.sup.ĝ.Math.ê

[0024] For the inverse transformation from the oblique to the Cartesian system, the inverse of the matrix must be applied to the basis ĝ: ê=T.sub.ê.sup.ĝ.sup.−1.Math.ĝ=T.sub.ĝ.sup.ê.Math.ĝ

[0025] The inverse of the matrix can be calculated by several different methods. One possible representation of the inverse is shown below:

[00005]${\underset{\_}{T}}_{\hat{e}}^{\hat{g}}={\underset{\_}{T}}_{\hat{e}}^{{\hat{g}}^{-1}}=\left(\begin{array}{ccc}1& 0& 0\\ -\cot \left(w_{B^1{B}^2}\right)& \frac{1}{\sin \left(w_{B^1{B}^2}\right)}& 0\\ \frac{\cot \left(w_{B^1{B}^2}\right).Math.F_Z-\cos \left(w_{B^3{B}^1}\right)}{F_N}& \frac{-1}{\sin \left(w_{B^1{B}^2}\right)}.Math.\frac{F_Z}{F_N}& \frac{1}{F_N}\end{array}\right)$$\mathrm{with}{F}_Z=\frac{\cos \left(w_{B^2{B}^3}\right)}{\sin \left(w_{B^1{B}^2}\right)}-\cot \left(w_{B^1{B}^2}\right).Math.\cos \left(w_{B^3{B}^1}\right)\mathrm{and}{F}_N=\sqrt{{\sin }^2\left(w_{B^3{B}^1}\right)-F_Z^2}$

[0026] With T.sub.ĝ.sup.ê it is now possible to transform vectors from the base system of the magnetic fields which is freely orientated in space into a Cartesian coordinate system. In Cartesian coordinates, it is a simple matter to carry out analytical calculations of sensitivities.

[0027] In order to carry out the calibration, in the suggested method the measurement focus of one or more monoaxial or multiaxial measuring magnetic field sensors, in the present example of a triaxial magnetic field sensor, is brought to a specific place where the spatial position or alignment of the magnetic field vectors and the strength of the magnetic fields are known. In this situation the precise location of the magnetic field sensor is not important. It must only be ensured that the magnetic field vectors (value and direction) are known exactly at the site of the magnetic field sensor or the sensor volume. To this end, FIG. 1 shows an example of an (arbitrary) orientation of the magnetic field vector 1 with the three sensor axes 2, 3, 4 to the three magnetic fields or magnetic field vectors {right arrow over (B.sub.1)}, {right arrow over (B.sub.2)}, {right arrow over (B.sub.3)}.

[0028] The suggested method is based on the reconstruction of a sensitivity vector for each monoaxial or multiaxial magnetic field sensor in the the freely orientated coordinate system of the magnetic fields. The offsets for the sensors must be known or else eliminated metrologically. This may be done for example by direct measurement of the offsets in a space where there are no magnetic fields (in a zero Gauss chamber, for example), or by eliminating the offsets through differential measurement. In the calibration of a triaxial magnetic field sensor with three magnetic fields carried out in the present example, the following vector for the sensitivity of the magnetic field sensor or a sensor axis can be constructed from the offset-free sensor measurement values O.sub.1, O.sub.2, O.sub.3, relative to the basis ĝ of the magnetic fields by sequential application and measurement of the three magnetic fields B.sub.1, B.sub.2, B.sub.3 resulting therefrom:

[00006]$\stackrel{.fwdarw.}{S_{\hat{g}}}=\left(\begin{array}{c}{E}_1\\ E_2\\ E_3\end{array}\right)=\left(\begin{array}{c}\frac{O_1}{B_1}\\ \frac{O_2}{B_2}\\ \frac{O_3}{B_3}\end{array}\right)$

[0029] Such a vector may now be generated for any further sensor axis of the magnetic field vector—and in general of multiple magnetic field sensors for any sensor axis of any of the magnetic field sensors —, thereby returning an abundance of n sensitivity vectors (in the present example n=3): S.sub.ĝ.sup.1 . . . S.sub.ĝ.sup.1

[0030] To enable further calculation, these vectors are transformed into a Cartesian coordinate system with the aid of the previously defined inverses of the transformation matrix:

{right arrow over (Sê)}=T.sub.ĝ.sup.ê.Math.{right arrow over (Sĝ)}

[0031] In the Cartesian coordinate system, the sensitivity of the respective sensor or the respective sensor axis can now be calculated using absolute value formation or determination of the norm of the sensitivity vector thereof, regardless of its individual alignment in the magnetic field. Thus, for each sensor axis 1 to n a correction factor for sensitivity is obtained:

[00007]$K_1=\frac{1}{.Math.\stackrel{.fwdarw.}{S_{\hat{e}}^1}.Math.}\mathrm{.Math.}{K}_n=\frac{1}{.Math.\stackrel{.fwdarw.}{S_{\hat{e}}^n}.Math.}$

[0032] Since the respective sensitivity vector also indicates the alignment of the sensor axis and therewith the location of the sensor axes relative to each other, the number of all angles (.sub.2.sup.n) between the n sensor axes can be determined using scalar product and cosine:

[00008]$w_{S^1{S}^2}=\arccos \frac{\stackrel{.fwdarw.}{S_{\hat{e}}^1}.Math.\stackrel{.fwdarw.}{S_{\hat{e}}^2}}{.Math.\stackrel{.fwdarw.}{S_{\hat{e}}^1}.Math..Math..Math.\stackrel{.fwdarw.}{S_{\hat{e}}^2}.Math.}\mathrm{.Math.}{w}_{S^{n-1}{S}^n}=\arccos \frac{\stackrel{.fwdarw.}{S_{\hat{e}}^{n-1}}.Math.\stackrel{.fwdarw.}{S_{\hat{e}}^n}}{.Math.\stackrel{.fwdarw.}{S_{\hat{e}}^{n-1}}.Math..Math..Math.\stackrel{.fwdarw.}{S_{\hat{e}}^n}.Math.}$

[0033] In the case of a triaxial magnetic field sensor, as in the present example which returns the measurement values M.sub.1, M.sub.2, M.sub.3, analogue to the oblique coordinate system of the magnetic fields a skewed sensor basis ŝ is obtained with the three base vectors {right arrow over (S.sub.ê.sup.1)}, {right arrow over (S.sub.ê.sup.2)} and {right arrow over (S.sub.ê.sup.3)} and the three associated angles w.sub.S.sub.1.sub.S.sub.2, w.sub.S.sub.2.sub.S.sub.3 and w.sub.S.sub.3.sub.S.sub.1. This basis is translated into a Cartesian coordinate system using the known inverse of the transformation matrix: ê=T.sub.ŝ.sup.ê.Math.ŝ

[0034] It is then possible to decide freely which position the three sensor axes will assume in an orthogonal system. For example, the following variant is chosen here: {right arrow over (S.sub.ê.sup.1)} is parallel to {right arrow over (e.sub.1)}, {right arrow over (S.sub.ê.sup.2)} lies in the plane of {right arrow over (e.sub.1)} and {right arrow over (e.sub.2)}, {right arrow over (S.sub.ê.sup.3)} is freely located in space. The transformation matrix T.sub.ŝ.sup.ê then appears as follows:

[00009]${\underset{\_}{T}}_{\hat{S}}^{\hat{e}}=\left(\begin{array}{ccc}1& 0& 0\\ -\cot \left(w_{S^1{S}^2}\right)& \frac{1}{\sin \left(w_{S^1{S}^2}\right)}& 0\\ \frac{\cot \left(w_{S^1{S}^2}\right).Math.F_Z-\cot \left(w_{S^3{S}^1}\right)}{F_N}& \frac{-1}{\sin \left(w_{S^1{S}^2}\right)}.Math.\frac{F_Z}{F_N}& \frac{1}{F_N}\end{array}\right)$$\mathrm{with}{F}_Z=\frac{\cos \left(w_{S^2{S}^3}\right)}{\sin \left(w_{S^1{S}^2}\right)}-\cot \left(w_{S^1{S}^2}\right).Math.\cos \left(w_{S^3{S}^1}\right)\mathrm{and}{F}_N=\sqrt{{\sin }^2*\left(w_{S^3{S}^1}\right)-F_Z^2}$

[0035] After translating the oblique triaxial sensor basis into an orthogonal coordinate system, it is possible to state the magnetic field vector in fully corrected form, i.e. sensitivity-corrected and in an orthogonal coordinate system. For this purpose, the correction values for the sensitivity are summarised in a diagonal matrix:

[00010]${\underset{\_}{K}}_{\hat{S}}=\left(\begin{array}{ccc}{K}_1& 0& 0\\ 0& K_2& 0\\ 0& 0& K_3\end{array}\right)$

[0036] With this correction matrix and the known transformation matrix, a measurement value for the triaxial sensor

[00011]${\stackrel{.fwdarw.}{M}}_{\hat{S}}=\left(\begin{array}{c}{M}_1\\ M_2\\ M_3\end{array}\right)$

can now be fully corrected, wherein transformation matrix T.sub.ŝ.sup.ê and correction matrix K.sub.ŝ can also be compiled as a combined correction matrix C.sub.ŝ.sup.ê=T.sub.ŝ.sup.ê.Math.K.sub.ŝ:

{right arrow over (M)}.sub.ê=T.sub.ŝ.sup.ê.Math.K.sub.ŝ.Math.{right arrow over (M)}.sub.ŝ=C.sub.ŝ.sup.ê.Math.{right arrow over (M)}.sub.ŝ