# US 11,442,118 B2 · Method for self-calibrating multiple field sensors having three or more sensing axes and system performing the same

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- Number: US 11,442,118 B2
- Document ID: US11442118B2
- Status: Granted
- Kind: B2
- Application number: 17/102,553
- Filed: 2020-11-24
- Published: 2022-04-21
- Granted: 2022-09-13
- Earliest claimed: 2020-10-19
- Assignees: Korea Institute of Science and Technology
- Applicants: Korea Institute of Science and Technology
- Inventors: Ig Jae Kim; Je Hyeong Hong; Donghoon Kang
- Web page: https://patentgrep.com/patent/US11442118B2

## CPC

- G01R 33/0041: {using feed-back or modulation techniques}
- G01L 25/00: Testing or calibrating of apparatus for measuring force, torque, work, mechanical power, or mechanical efficiency
- G01P 15/18: in two or more dimensions
- G01P 21/00: Testing or calibrating of apparatus or devices covered by the preceding groups
- G01R 33/0035: {Calibration of single magnetic sensors, e.g. integrated calibration}
- G01R 33/0094: {Sensor arrays}
- G01R 33/0206: {Three-component magnetometers}
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- G01L: MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE (weighing G01G)
- G01P: MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT (measuring or recording blood flow A61B5/02, A61B8/06; monitoring speed or deceleration of electrically-propelled vehicles B60L3/00; vehicle lighting systems adapted to indicate speed B60Q1/54; determining position or course in navigation, measuring ground distance in geodesy or surveying G01C; combined measuring devices for measuring two or more variables of movement G01C23/00; measuring velocity of sound G01H; measuring velocity of light G01J7/00; measuring direction or velocity of solid objects by reception or emission of radiowaves or other waves and based on propagation effects, e.g. Doppler effect, propagation time, direction of propagation, G01S; measuring speed of nuclear radiation G01T; measuring acceleration of gravity G01V; {measuring or recording the speed of trains B61L23/00; speed indicators incorporated in motor vehicles B60K35/00; measuring frequency or phase G01R; traffic control G08G})

## Abstract

Embodiments relate to a method including obtaining m measured values for each field sensor by measuring with respect to a first sensor group including first type of field sensors and a second sensor group including different second type of field sensors, which are attached to the rigid body, at m time steps; and calibrating a sensor frame of the first type of field sensor and a sensor frame of the second type of field sensor by using a correlation between the first type of field sensor and the second type of field sensor based on measured values of at least some of the m time steps, wherein the multiple field sensors include different field sensors of a magnetic field sensor, an acceleration sensor, and a force sensor, and a system therefor.

## Claims

### Claim 1

A method for self-calibrating multiple field sensors attached to a rigid body, which is performed by a processor, the method comprising the steps of:
obtaining m measured values for each field sensor by measuring with respect to a first sensor group including first type of field sensors and a second sensor group including different second type of field sensors, which are attached to the rigid body, at m time steps, wherein m is a natural number of 2 or more; and
calibrating a sensor frame of the first type of field sensor and a sensor frame of the second type of field sensor by using a correlation between the first type of field sensor and the second type of field sensor based on measured values of at least some of the m time steps.

### Claim 2 (depends on 1)

The method of claim 1, wherein the calibrating of the sensor frame of the first type of field sensor and the sensor frame of the second type of field sensor comprises:
determining pairs of different time steps in the m time steps and obtaining correlations in pairs of multiple time steps; and
calculating a relative rotation matrix from one of the first and second types of field sensors to the other field sensor based on the correlations in the pairs of multiple time steps.

### Claim 3 (depends on 2)

The method of claim 2, wherein in order to obtain the correlations in pairs of multiple time steps, four time steps are selected from m time steps to designate three independent pairs of time steps, and
the calculating of the relative rotation matrix comprises:
calculating multiple solutions of the relative rotation matrix by applying a nonlinear optimization algorithm to the correlations in the three pairs of time steps; and
determining one of the multiple solutions as the relative rotation matrix.

### Claim 4 (depends on 2)

The method of claim 2, wherein in order to obtain the correlations in pairs of multiple time steps, nine time steps are selected from m time steps to designate eight independent pairs of time steps, and
the calculating of the relative rotation matrix comprises:
calculating a matrix T through the following Equation 1, which is obtained from the correlations in the eight pairs of time steps; and
calculating a solution of the relative rotation matrix based on the calculated value of the matrix T,
Tvec(Rm→a)=0
or
Tvec(Ra→m)=0 Equation 1
wherein, Rm→a represents a relative rotation matrix based on the sensor frame of the first sensor group, and Rm→a represents a relative rotation matrix based on the sensor frame of the second sensor group.

### Claim 5 (depends on 2)

The method of claim 2, wherein in order to obtain the correlations in pairs of multiple time steps, 17 time steps are selected from m time steps to designate 16 independent pairs of time steps, and
the calculating of the relative rotation matrix comprises:
calculating a variable M associated with a relative rotation matrix by applying measured values in the 16 pairs of time steps to the following Equation 2; and
obtaining the relative rotation matrix based on the variable M,
(
K
a
-
1
(
y
a
,
j
-
b
a
)
)
T
⁢
R
m
→
"\[Rule]"
a
(
K
m
-
1
(
y
m
,
j
-
b
m
)
)
=
[
y
a
,
j
1
]
T
⁢
M
[
y
m
,
j
1
]
=
cos
⁢
θ
,
or
⁢
(
K
a
-
1
(
y
a
,
j
-
b
a
)
)
T
⁢
R
a
→
"\[Rule]"
m
(
K
m
-
1
(
y
m
,
j
-
b
m
)
)
=
[
y
a
,
j
1
]
T
⁢
M
[
y
m
,
j
1
]
=
cos
⁢
θ
Equation
⁢
2
wherein, ya represents a measured value of the field sensor of the second sensor group, ym represents a measured value of the field sensor of the first sensor group, j and k represent different time steps, Km represents an intrinsic variable of the field sensor of the first sensor group, Ka represents an intrinsic variable of the field sensor of the second sensor group, and η represents an angle between a field vector direction of the first sensor group and a field vector direction of the second sensor group, respectively.

### Claim 6 (depends on 5)

The method of claim 5, wherein the calculating of the variable M associated with the relative rotation matrix comprises:
calculating multiple solutions of the variable M by applying a nonlinear optimization algorithm to the correlations in the 16 pairs of time steps; and
determining one of the multiple solutions as the variable M,
wherein the variable M is expressed by the following Equation 3,
[
y
a
,
j
1
]
T
⁢
M
[
y
m
,
j
1
]
-
[
y
a
,
k
1
]
T
⁢
M
[
y
m
,
k
1
]
=
0.
Equation
⁢
3

### Claim 7 (depends on 2)

The method of claim 2, wherein the calibrating of the sensor frame of the first type of field sensor and the sensor frame of the second type of field sensor comprises:
obtaining a correlation in each of at least some of m time steps; and
calculating a relative rotation matrix from one of the first and second types of field sensors to the other field sensor based on the correlation in each of at least some time steps,
wherein the correlation at each time step is expressed by the following Equation 4,
ĝa,jTRm→aĥm,j−cos θ=0
or
ĥm,jTRa→mĝa,j−cos θ=0 Equation 4
wherein, g and h represent a field vector of the first sensor group and a field vector of the second sensor group, respectively, and η represents an angle between a field vector direction of the first sensor group and a field vector direction of the second sensor group.

### Claim 8 (depends on 7)

The method of claim 7, wherein in order to obtain a correlation at each of at least some of time steps, nine time steps are selected from m time steps, and
the calculating of the relative rotation matrix comprises:
calculating a matrix T through the following Equation 5, which is obtained from the correlation in each of nine time steps; and
calculating a solution of the relative rotation matrix based on the calculated value of the matrix T.
T
[
vec
⁡
(
Rm
→
"\[Rule]"
a
)
cos
⁢
θ
]
=
0
⁢
or
⁢
T
[
vec
⁡
(
Ra
→
"\[Rule]"
m
)
k
]
=
0
Equation
⁢
5
wherein, Rm→a represents a relative rotation matrix based on the field sensor of the first sensor group, and Ra→m represents a relative rotation matrix based on the field sensor of the second sensor group.

### Claim 9 (depends on 7)

The method of claim 7, wherein in order to obtain a correlation at each of at least some of time steps, 17 time steps are selected from m time steps, and
the calculating of the relative rotation matrix comprises:
calculating a variable M associated with the relative rotation matrix by applying measured values in pairs of 17 time steps to the following Equation; and
obtaining the relative rotation matrix based on the variable M,
[
y
a
,
j
1
]
T
⁢
M
[
y
m
,
j
1
]
-
cos
⁢
θ
=
0.
Equation
⁢
6

### Claim 10 (depends on 9)

The method of claim 9, further comprising:
removing measured values of outlier components,
wherein a time step at which measured values of inlier components are measured is used to obtain the correlation.

### Claim 11 (depends on 2)

The method of claim 2, further comprising:
updating variables of sensor frames of the multiple field sensors to minimize a difference between an expected value of the sensor frame based on the relative rotation matrix and an actual measured value.

### Claim 12 (depends on 11)

The method of claim 11, wherein a new value of the variable to be updated is calculated through the following Equation 7,
min
⁢
∑
(
i
,
j
)
∈
Ω
m
ρ
⁡
(

A
i
⁢
h
ˆ
m
,
j
+
b
i
-
y
i
⁢
j

2
)
+
∑
(
i
,
j
)
∈
Ω
a
ρ
⁡
(

A
i
⁢
g
ˆ
a
,
j
+
b
i
-
y
i
⁢
j

2
)
⁢
s
.
t
.
g
^
a
,
j
T
⁢
R
m
→
"\[Rule]"
a
⁢
h
^
m
,
j
=
cos
⁢
θ
,

g
^
a
,
j

=
c
g
,

h
ˆ
m
,
j

=
c
h
⁢
∀
j
,
or
⁢
min
⁢
∑
(
i
,
j
)
∈
Ω
m
ρ
⁡
(

A
i
⁢
h
ˆ
m
,
j
+
b
i
-
y
i
⁢
j

2
)
+
∑
(
i
,
j
)
∈
Ω
a
ρ
⁡
(

A
i
⁢
g
ˆ
a
,
j
+
b
i
-
y
i
⁢
j

2
)
⁢
s
.
t
.
h
^
m
,
j
T
⁢
R
a
→
"\[Rule]"
m
⁢
g
^
a
,
j
=
cos
⁢
θ
,

g
^
a
,
j

=
c
g
,

h
ˆ
m
,
j

=
c
h
⁢
∀
j
Equation
⁢
7
wherein, i represents an index of the field sensor included in the corresponding sensor group, A and b represent intrinsic variables of the field sensor, g and h represent a field vectors of the first sensor group and a field vector of the second sensor group, and η represents an angle between a field vector direction of the first sensor group and a field vector direction of the second sensor group, respectively.

### Claim 13 (depends on 11)

The method of claim 11, wherein a new value of the variable to be updated is calculated through a least squares algorithm, a manifold optimization algorithm, a spherical manifold optimization algorithm, or a Lagrangian method algorithm.

### Claim 14 (depends on 1)

The method of claim 1, wherein the multiple field sensors include at least one of a force sensor, an acceleration sensor, and a magnetic field sensor, and a combination of the first type of field sensor and the second type of field sensor includes a three-axis magnetic field sensor and a three-axis acceleration sensor, a three-axis magnetic field sensor and a three-axis force sensor, or a three-axis force sensor and a three-axis acceleration sensor.

### Claim 15 (depends on 1)

The method of claim 1, further comprising:
calculating a sensor frame of the first sensor group or the second sensor group by calibrating the sensor frame for each field sensor,
wherein the sensor frame of the first type of field sensor or the sensor frame of the second type of field sensor to be calibrated is a sensor frame of the first sensor group or the second sensor group.

### Claim 16 (depends on 15)

The method of claim 15, wherein when the first sensor group or the second sensor group consists of multiple three-axis field sensors, the calculating of the sensor frame of the first sensor group or the second sensor group includes calculating calibration variables A and b for each field sensor using at least some of the m measured values to calibrate the sensor frame for each field sensor in the corresponding sensor group,
wherein the calculating of the calibration variables A and b for each field sensor comprises:
calculating multiple intrinsic variables including the calibration variable b based on at least some of the m measured values;
calculating extrinsic variables including a rotation matrix R based on at least some of the m measured values; and
calculating the calibration variable A based on the intrinsic variable and the extrinsic variable.

### Claim 17 (depends on 16)

The method of claim 16, wherein the calculating of the multiple intrinsic variables comprises:
removing measured values of outlier components from the m measured values; and
calculating an intrinsic variable including the variable b based on the measured values of inlier components,
wherein the intrinsic variable includes a sub-matrix K or P of the calibration variable A that satisfies the following Equation 8, and
the intrinsic variable K is a matrix in a positive definite upper triangular form, and the intrinsic variable P is a matrix in a symmetric positive definite form.
A=KR
or
A=PR Equation 8
wherein, R represents the rotation matrix as an extrinsic variable of the field sensor.

### Claim 18 (depends on 16)

The method of claim 16, wherein the calculating of the extrinsic variables based on at least some of the measured values comprises:
calculating a relative rotation matrix of sensor pairs by forming the sensor pairs in the sensor group to calculate a relative direction between the sensor frames in the sensor group; and
calculating an absolute rotation matrix for each field sensor to calculate each absolute direction of each sensor frame of an individual sensor in the sensor group, wherein the absolute rotation matrix is an extrinsic variable R.

### Claim 19 (depends on 15)

The method of claim 15, wherein when the first sensor group or the second sensor group consists of field sensors having Q axes, wherein Q is a natural number of 4 or more, the calculating of the sensor frame of the first sensor group or the second sensor group includes calculating calibration variables A and b for each field sensor using at least some of the m measured values to calibrate the sensor frame for each field sensor in the corresponding sensor group,
wherein the calculating of the calibration variables A and b for each field sensor comprises:
obtaining a vector b as an intrinsic variable;
calculating a matrix A by applying a rank-4 matrix decomposition algorithm to a measurement matrix Y consisting of the measured values; and
calibrating the obtained variables A and b values so that the size of a direction vector is as close as possible to a specified value c in the sensor frame including the obtained variables A and b,
wherein the vector b is designated as an arbitrary vector, and the value c is a size value of a unit vector of the direction vector of the field sensor.

### Claim 20

A computer-readable recording medium having a computer program recorded thereon, the computer program execatable by a processor to cause the processor;
to obtain m measured values for each field sensor by measuring with respect to a first sensor group including first type of field sensors and a second sensor group including different second type of field sensors, which are attached to a rigid body, at m time steps, wherein m is a natural number of 2 or more; and
to calibrate a sensor frame of the first type of field sensor and a sensor frame of the second type of field sensor by using a correlation between the first type of field sensor and the second type of field sensor based on measured values of at least some of the m time steps.

### Claim 21

A system comprising:
multiple field sensors outputting m measured values by measuring the measured values at m time steps and including a first type of field sensor and a different second type of field sensor which are attached to rigid bodies, wherein m is a natural number of 2 or more; and
a computing device including a processor configured to obtain m measured values from each of the multiple field sensors and to calibrate a sensor frame of the first type of field sensor and a sensor frame of the second type of field sensor using a correlation between the first type of field sensor and the second type of field sensor.