Calibration of 3D field sensors
First Claim
1. An apparatus-based method for calibration of a three-dimensional (3D) field sensor, comprising:
- accessing a plurality of samples, the samples from the 3D field sensor, each sample representing a magnitude and an orientation of a 3D field sensed by the 3D field sensor;
using the plurality of samples, determining a plurality of parameters of an ellipsoid, wherein the determining the plurality of parameters is performed so that the ellipsoid fits the plurality of samples, wherein the following is used to represent the ellipsoid;
x2+y2+z2−
U(x2+y2−
2z2)−
V(x2−
2y2+z2)−
4Mxy−
2Nxz−
2Pyz−
Qx−
Ry−
Sz−
T=0, and wherein determining a plurality of parameters determines the parameters {right arrow over (s)}LS=(U,V,M,N,P,Q,R,S,T)T;
determining a transformation that transforms the ellipsoid into a sphere;
applying the transformation to a sample to create a transformed sample; and
using the transformed sample to determine at least an orientation of the apparatus.
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Accused Products
Abstract
An apparatus-based method is disclosed for calibration of a 3D field sensor. The method includes accessing a plurality of samples, where the samples are from the 3D field sensor. Each sample represents a magnitude and an orientation of a three-dimensional field sensed by the 3D field sensor. Using the plurality of samples, a plurality of parameters is determined of an ellipsoid. The determination of the plurality of parameters is performed so that the ellipsoid fits the plurality of samples. A transformation is determined that transforms the ellipsoid into a sphere. The transformation is applied to a sample to create a transformed sample. Apparatus and signal bearing media are also disclosed.
60 Citations
41 Claims
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1. An apparatus-based method for calibration of a three-dimensional (3D) field sensor, comprising:
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accessing a plurality of samples, the samples from the 3D field sensor, each sample representing a magnitude and an orientation of a 3D field sensed by the 3D field sensor;
using the plurality of samples, determining a plurality of parameters of an ellipsoid, wherein the determining the plurality of parameters is performed so that the ellipsoid fits the plurality of samples, wherein the following is used to represent the ellipsoid;
x2+y2+z2−
U(x2+y2−
2z2)−
V(x2−
2y2+z2)−
4Mxy−
2Nxz−
2Pyz−
Qx−
Ry−
Sz−
T=0, and wherein determining a plurality of parameters determines the parameters {right arrow over (s)}LS=(U,V,M,N,P,Q,R,S,T)T;
determining a transformation that transforms the ellipsoid into a sphere;
applying the transformation to a sample to create a transformed sample; and
using the transformed sample to determine at least an orientation of the apparatus. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21)
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13. (canceled)
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22. A computer-readable medium tangibly embodying a program of machine-readable instructions executable by a processor to perform operations for calibration of a three-dimensional (3D) field sensor, the operations comprising:
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accessing a plurality of samples, the samples from the 3D field sensor, each sample representing a magnitude and an orientation of a three-dimensional field sensed by the 3D field sensor;
using the plurality of samples, determining a plurality of parameters of an ellipsoid, wherein the determining of the plurality of parameters is performed so that the ellipsoid fits the plurality of samples, wherein the following is used to represent the ellipsoid;
x2y2+z2−
U(x2+y2−
2z2)−
V(x2−
2y2+z2)−
4Mxy−
2Nxz−
2Pyz−
Qx−
Ry−
Sz−
T=0, and wherein determining a plurality of parameters determines the parameters {right arrow over (s)}LS=(U,V,M,N,P,Q,R,S,T)T;
determining a transformation that transforms the ellipsoid into a sphere;
applying the transformation to a sample to create a transformed sample; and
using the transformed sample to determine at least an orientation of the apparatus. - View Dependent Claims (23)
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24. An apparatus, comprising:
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means for measuring a three-dimensional (3D) field and for producing samples representing a magnitude and an orientation of the three-dimensional field;
means for accessing a plurality of samples from the means for measuring;
means, responsive to the plurality of samples, for determining a plurality of parameters of an ellipsoid, wherein the determining of the plurality of parameters is performed so that the ellipsoid fits the plurality of samples, wherein the following is used to represent the ellipsoid;
x2+y2+z2−
U(x2+y2−
2z2)−
V(x2−
2y2+z2)−
4Mxy−
2Nxz−
2Pyz−
Qx−
Ry−
Sz−
T=0, and wherein determining a plurality of parameters determines the parameters {right arrow over (s)}LS=(U,V,M,N,P,Q,R,S,T)T;
means for determining a transformation that transforms the ellipsoid into a sphere;
means for applying the transformation to a sample to create a transformed sample; and
means for using the transformed sample to determine at least an orientation of the apparatus. - View Dependent Claims (25)
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26. An apparatus, comprising:
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a three-dimensional (3D) field sensor, the 3D field sensor adapted to produce field samples, each field sample representing a magnitude and an orientation of a 3D field sensed by the 3D field sensor;
a calibration module adapted to access a plurality of the field samples from the 3D field sensor, the calibration module adapted to use the plurality of samples to determine a plurality of parameters of an ellipsoid, wherein the determining the plurality of parameters operation is performed so that the ellipsoid fits the plurality of field samples, wherein the following is used to represent the ellipsoid;
x2+y2+z2−
U(x2+y2−
2z2)−
V(x2−
2y2+z2)−
4Mxy−
2Nxz−
2Pyz−
Qx−
Ry−
Sz−
T=0, wherein the calibration module is adapted to determines the parameters {right arrow over (s)}LS=(U,V,M,N,P,Q,R,S,T)T, and wherein the calibration module is further adapted to determine a transformation that transforms the ellipsoid into a sphere and to apply the transformation to a field sample to create a transformed field sample; and
an application configured to use the transformed sample to determine at least an orientation of the apparatus. - View Dependent Claims (27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37)
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38. A method comprising:
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accessing a plurality of samples, the samples from the 3D field sensor, each sample representing a magnitude and an orientation of a 3D field sensed by the 3D field sensor;
using the plurality of samples, determining a plurality of parameters of an ellipsoid, wherein the determining the plurality of parameters is performed so that the ellipsoid fits the plurality of samples;
determining a transformation that transforms the ellipsoid into a sphere, wherein determining a transformation comprises;
determining a matrix, A, a bias, {right arrow over (b)}, and a scaling factor, c in a representation of an ellipsoid of ({right arrow over (x)}−
{right arrow over (b)})TA({right arrow over (x)}−
{right arrow over (b)})=c;
determining a matrix, D, where DTD=1/cA, where D is selected such that D{circumflex over (x)}=λ
{circumflex over (x)}, where λ
is an arbitrary constant and {circumflex over (x)}=(1,0,0)T, and where the transformation comprises the matrix D;
applying the transformation to a sample to create a transformed sample; and
.using the transformed sample to determine at least an orientation of the apparatus. - View Dependent Claims (39)
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40. An apparatus, comprising:
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a three-dimensional (3D) field sensor, the 3D field sensor configured to produce field samples, each field sample representing a magnitude and an orientation of a 3D field sensed by the 3D field sensor; and
a calibration module configured to access a plurality of the field samples from the 3D field sensor, the calibration module adapted to use the plurality of samples to determine a plurality of parameters of an ellipsoid, wherein the determining the plurality of parameters operation is performed so that the ellipsoid fits the plurality of field samples, wherein the calibration module is further configured determine a transformation that transforms the ellipsoid into a sphere by determining a matrix, A, a bias, {right arrow over (b)}, and a scaling factor, c in a representation of an ellipsoid of ({right arrow over (x)}−
{right arrow over (b)})TA({right arrow over (x)}−
{right arrow over (b)})=c, and by determining a matrix, D, where DTD=1/cA, where D is selected such that D{circumflex over (x)}=λ
{circumflex over (x)}, where λ
is an arbitrary constant and {circumflex over (x)}=(1,0,0)T, and where the transformation comprises the matrix D, and wherein the calibration module is further configured to apply the transformation to a field sample to create a transformed field sample; and
an application configured to use the transformed sample to determine at least an orientation of the apparatus. - View Dependent Claims (41)
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Specification