Method and device for measuring directional, and computer program
AssigneeCitizen Watch Co., Ltd.
InventorsMasahiro Satoh, Kazuhiko Terashima, Junji Satoh
Life of this patent
Estimating the term…
Abstract
A method for measuring a directional of a body in a three-dimensional space defined by an X-axis (magnetic north), a Y-axis, and a Z-axis is proposed. A geomagnetic force along an x-axis, which is the direction towards which the body points and an x-axis tilt angle, which is an angle between the horizontal plane and the x-axis, are detected. The x-axis tilt angle is determined as a rotation angle, which an angle by which the x-axis needs to be rotated around the Y-axis so as to be in the XY-plane. An azimuth of the body is calculated from the geomagnetic force and the rotation angle.
Claims22
A directional measuring device that measures a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, comprising:
- an x-axis geomagnetic force detector that detects a geomagnetic force along the x-axis;
- an x-axis tilt angle detector that detects an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- a y-axis geomagnetic force detector that detects a geomagnetic force along a y-axis that is orthogonal to the x-axis;
- a z-axis geomagnetic force detector that detects a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis;
- a y-axis tilt angle detector that detector detects a y-axis tilt angle that is angle between the horizontal plane and the y-axis;
- a determining unit that determines the x-axis tilt angle as a rotation angle that is an angle by which the x-axis needs to be rotated around the Y-axis so as to be in the horizontal plane;
- a rotation angle calculator that calculates a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis, and
- an azimuth calculator that calculates an azimuth of the body based on the geomagnetic force and the rotation angle wherein
- the azimuth calculator calculates an azimuth of the body based on the geomagnetic forces detected by both the y-axis geomagnetic force detector and the z-axis geomagnetic force detector and the rotation angle calculated, and the rotation angle calculator calculates the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A directional measuring device that measures a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, comprising:
- a y-axis geomagnetic force detector that detects a geomagnetic force along a y-axis that is orthogonal to the x-axis;
- a z-axis geomagnetic force detector that detects a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis;
- an x-axis tilt angle detector that detects an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- a y-axis tilt angle detector that detects a y-axis tilt angle that is angle between the horizontal plane and the y-axis;
- a rotation angle calculator that calculates a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis;
- and
- an azimuth calculator that calculates an azimuth of the body based on the geomagnetic forces detected by both the y-axis geomagnetic force detector and the z-axis geomagnetic force detector and the rotation angle
- where the rotation angle calculator calculates the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A directional measuring device that measures a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, comprising:
- a y-axis geomagnetic force detector that detects a geomagnetic force along a y-axis that is orthogonal to the x-axis;
- a z-axis geomagnetic force detector that detects a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis;
- a total geomagnetic force input unit that receives a total geomagnetic force at a present position of the body, wherein the total geomagnetic force is a vector addition of geomagnetic forces along the X-axis, the Y-axis, and the Z-axis;
- a geomagnetic force calculator that calculates a geomagnetic force along the x-axis based on the total geomagnetic force and the geomagnetic forces along both the y-axis and the z-axis;
- an x-axis tilt angle detector that detects an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- a y-axis tilt angle detector that detects a y-axis tilt angle that is angle between the horizontal plane and the y-axis;
- a determining unit that determines the x-axis tilt angle as a rotation angle that is an angle by which the x-axis needs to be rotated around the Y-axis so as to be in the horizontal plane;
- a rotation angle calculator that calculates a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis and
- an azimuth calculator that calculates an azimuth of the body based on the geomagnetic force along the x-axis and the rotation angle wherein
- the azimuth calculator calculates an azimuth of the body based on the geomagnetic forces detected by both the y-axis geomagnetic force detector and the z-axis geomagnetic force detector and the rotation angle calculated, and the rotation angle calculator calculates the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A directional measuring device that measures a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, comprising:
- a first-axis geomagnetic force detector that detects a geomagnetic force along a first axis from among the x-axis, a y-axis that is orthogonal to the x-axis, and a z-axis that is orthogonal to both the x-axis and the y-axis;
- a second-axis geomagnetic force detector that detects a geomagnetic force along a second axis other than the first axis from among the x-axis, the y-axis, and the z-axis;
- a total geomagnetic force input unit that receives a total geomagnetic force at a present position of the body, wherein the total geomagnetic force is a vector addition of geomagnetic forces along the X-axis, the Y-axis, and the Z-axis;
- a geomagnetic force calculator that calculates a geomagnetic force along an axis other than the first axis and the second axis, from among the x-axis, the y-axis, and the z-axis based on the total geomagnetic force and the geomagnetic forces along both the first axis and the second axis;
- an x-axis tilt angle detector that detects an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- a y-axis tilt angle detector that detects a y-axis tilt angle that is an angle between the horizontal plane and the y-axis;
- a rotation angle calculator that calculates a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis;
- and
- an azimuth calculator that calculates an azimuth of the body based on the geomagnetic forces along the y-axis and the z-axis and the rotation angle
- wherein the rotation angle calculator calculates the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A directional measuring method of measuring a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, comprising:
- detecting a geomagnetic force along the x-axis;
- detecting an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- detecting a geomagnetic force along a y-axis is orthogonal to the x-axis;
- detecting a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis′
- detecting a y-axis tilt angle that is angle between the horizontal plane and the y-axis;
- determining the x-axis tilt angle as a rotation angle that is an angle by which the x-axis needs to be rotated around the Y-axis so as to be in the horizontal plane;
- calculating a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation to the x-axis and
- calculating an azimuth of the body based on the geomagnetic force and the rotation angle, wherein
- the step of calculating the azimuth includes calculating the azimuth of the body based on the geomagnetic forces along both the y-axis and the z-axis and the rotation angle calculated, and the calculating the rotation angle includes calculating the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A directional measuring method of measuring a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, comprising:
- detecting a geomagnetic force along a y-axis that is orthogonal to the x-axis;
- detecting a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis;
- detecting an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- detecting a y-axis tilt angle that is angle between the horizontal plane and the y-axis;
- calculating a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis;
- and
- calculating an azimuth of the body based on the geomagnetic forces detected along both the y-axis and the z-axis and the rotation angle wherein
- the step of calculating the rotation angle includes calculating the rotation angle, based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- a
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A directional measuring method of measuring a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, comprising:
- detecting a geomagnetic force along a y-axis that is orthogonal to the x-axis;
- detecting a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis;
- receiving a total geomagnetic force at a present position of the body, wherein the total geomagnetic force is a vector addition of geomagnetic forces along the X-axis, the Y-axis, and the Z-axis;
- calculating a geomagnetic force along the x-axis based on the total geomagnetic force and the geomagnetic forces along both the y-axis and the z-axis;
- detecting an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- detecting a y-axis tilt angle that is angle between the horizontal plane and the y-axis;
- determining the x-axis tilt angle as a rotation angle that is an angle by which the x-axis needs to be rotated around the Y-axis so as to be in the horizontal plane;
- calculating a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the axis:
- and
- calculating an azimuth of the body based on the geomagnetic force along the x-axis and the rotation angle wherein
- the azimuth calculating step includes calculating an azimuth of the body based on the geomagnetic forces along both the y-axis and the z-axis and the rotation angle calculated, and the calculating the rotation angle step includes calculating the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A directional measuring method of measuring a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, comprising:
- detecting a geomagnetic force along a first axis from among the x-axis, a y-axis that is orthogonal to the x-axis, and a z-axis that is orthogonal to both the x-axis and the y-axis;
- detecting a geomagnetic force along a second axis other than the first axis from among the x-axis, the y-axis, and the z-axis;
- receiving a total geomagnetic force at a present position of the body, wherein the total geomagnetic force is a vector addition of geomagnetic forces along the X-axis, the Y-axis, and the Z-axis;
- calculating a geomagnetic force along an axis other than the first axis and the second axis, from among the x-axis, the y-axis, and the z-axis based on the total geomagnetic force and the geomagnetic forces along both the first axis and the second axis;
- detecting an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- detecting a y-axis tilt angle that is an angle between the horizontal plane and the y-axis;
- calculating a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis;
- and
- calculating an azimuth of the body based on the geomagnetic forces along the y-axis and the z-axis and the rotation angle wherein
- the rotation angle calculating step includes calculating the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A computer program that realizes on a computer a directional measuring method of measuring a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, the computer program making the computer execute:
- detecting a geomagnetic force along the x-axis;
- detecting an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- detecting a geomagnetic force along a y-axis that is orthogonal to the x-axis;
- detecting a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis;
- determining the x-axis tilt angle as a rotation angle that is an angle by which the x-axis needs to be rotated around the Y-axis so as to be in the horizontal plane;
- calculating a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis and
- calculating an azimuth of the body based on the geomagnetic force and the rotation angle wherein
- the calculating the azimuth step includes calculating the azimuth of the body based on the geomagnetic forces along both the y-axis and the z-axis and the rotation angle calculated, and the calculating the rotation angle step includes calculating the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A computer program that realizes on a computer a directional measuring method of measuring a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, the computer program making the computer execute:
- detecting a geomagnetic force along a y-axis that is orthogonal to the x-axis;
- detecting a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis;
- detecting an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- detecting a y-axis tilt angle that is angle between the horizontal plane and the y-axis;
- calculating a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis;
- and
- calculating an azimuth of the body based on the geomagnetic forces detected along both the y-axis and the z-axis and the rotation angle wherein
- the calculating the rotation angle step includes calculating the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A computer program product that records a computer program for realizing on a computer a directional measuring method of measuring a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, the computer program making the computer execute:
- detecting a geomagnetic force along a y-axis that is orthogonal to the x-axis;
- detecting a geomagnetic force along a z-axis that is orthogonal to both the x-axis and the y-axis;
- receiving a total geomagnetic force at a present position of the body, wherein the total geomagnetic force is a vector addition of geomagnetic forces along the X-axis, the Y-axis, and the Z-axis;
- calculating a geomagnetic force along the x-axis based on the total geomagnetic force and the geomagnetic forces along both the y-axis and the z-axis;
- detecting a y-axis tilt angle that is angle between the horizontal plane and the y-axis;
- determining the x-axis tilt angle as a rotation angle that is an angle by which the x-axis needs to be rotated around the Y-axis so as to be in the horizontal plane;
- calculating a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis;
- and
- calculating an azimuth of the body based on the geomagnetic force along the x-axis and the rotation angle wherein
- the azimuth calculating step includes calculating an azimuth of the body based on the geomagnetic forces along both the y-axis and the z-axis and the rotation angle calculated, and the calculating the rotation angle step includes calculating the rotation angle based on a coordinate expression for rotations three times expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
A computer program product that records a computer program for realizing on a computer a directional measuring method of measuring a direction of a body of the directional measuring device in a three-dimensional space including an X-axis indicating magnetic north on a horizontal plane, a Y-axis orthogonal to the X-axis on the horizontal plane, and a Z-axis orthogonal to the horizontal plane, assuming that the body points towards an x-axis, the computer program making the computer execute:
- detecting a geomagnetic force along a first axis from among the x-axis, a y-axis that is orthogonal to the x-axis, and a z-axis that is orthogonal to both the x-axis and the y-axis;
- detecting a geomagnetic force along a second axis other than the first axis from among the x-axis, the y-axis, and the z-axis;
- receiving a total geomagnetic force at a present position of the body, wherein the total geomagnetic force is a vector addition of geomagnetic forces along the X-axis, the Y-axis, and the Z-axis;
- calculating a geomagnetic force along an axis other than the first axis and the second axis, from among the x-axis, the y-axis, and the z-axis based on the total geomagnetic force and the geomagnetic forces along both the first axis and the second axis;
- detecting an x-axis tilt angle that is an angle between the horizontal plane and the x-axis;
- detecting a y-axis tilt angle that is an angle between the horizontal plane and the y-axis;
- calculating a rotation angle based on both the x-axis tilt angle and the y-axis tilt angle, wherein the rotation angle is an angle by which the y-axis needs to be rotated around the X-axis so as to be in the horizontal plane when the x-axis is rotated by the x-axis tilt angle around the Y-axis so as to be in the horizontal plane to cause the y-axis to rotate following rotation of the x-axis axis;
- and
- calculating an azimuth of the body based on the geomagnetic forces along the y-axis and the z-axis and the rotation angle wherein
- the rotation angle calculating step includes calculating the rotation angle based on a coordinate expression for rotations three time expressed by an expression
- [
- cos
-
-
- θ
- sin
-
-
- θ
- 0
- -
- sin
-
-
- θ
- cos
-
-
- θ
- 0
- 0
- 0
- 1
- ]
- ×
- [
- cos
-
-
- β
- 0
- -
- sin
-
-
- β
- 0
- 1
- 0
- sin
-
-
- β
- 0
- cos
-
-
- β
- ]
- ×
- [
- 1
- 0
- 0
- 0
- cos
-
-
- α
- sin
-
-
- α
- 0
- -
- sin
-
-
- α
- cos
-
-
- α
- ]
- where α is a rotation angle around the X-axis, β is an x-axis tilt angle as a rotation angle around the Y-axis, and θ is a rotation angle around the Z-axis as an azimuth of the body.
Dependencies are inferred from the claim text.