- OxTS navigation frame
- ISO 8855 earth-fixed system
- OxTS horizontal frame
- ISO 8855 intermediate system
- OxTS vehicle frame
- ISO 8855 vehicle system
Conversions between Reference Frames
- Between OxTS navigation and horizontal frames
- Between OxTS horizontal and vehicle frames
- Between OxTS navigation and vehicle frames
- Between ISO 8855 earth-fixed and intermediate systems
- Between ISO 8855 intermediate and vehicle systems
- Between ISO 8855 earth-fixed and vehicle systems
- Between OxTS navigation frame and ISO 8855 earth-fixed system
- Between OxTS horizontal frame and ISO 8855 intermediate system
- Between OxTS vehicle frame and ISO 8855 vehicle system
Examples of Measurements in OxTS and ISO8855 Reference Frames
This frame is attached to the vehicle, but does not rotate with it.
- The north axis (N) is perpendicular to the gravity vector and in the direction of the north pole along the earth’s surface.
- The east axis (E) is perpendicular to gravity, perpendicular to the north axis and is in the east direction.
- The down axis (D) is along the gravity vector.
This frame is attached to the vehicle, but does not rotate with it.
- The east axis (E) is perpendicular to gravity, perpendicular to the north axis and is in the east direction.
- The north axis (N) is perpendicular to the gravity vector and in the direction of the north pole along the earth’s surface.
- The up axis (U) is co-axial with the gravity vector, and positive in the up direction.
This frame is attached to the vehicle, it rotates by the heading of the vehicle, but does not rotate with the roll and pitch of the vehicle.
The forward and lateral axes remain parallel to the horizontal plane and the forward axis is parallel to the vehicle’s heading.
- The forward axis (F) is perpendicular to gravity and is in the forward direction of the vehicle, projected into the horizontal plane.
- The lateral axis (L) is perpendicular to gravity, perpendicular to the forward axis and is in the lateral direction of the vehicle, pointing to the right, projected into the horizontal plane.
- The down axis (D) is in the vertical direction of the vehicle, along the gravity vector.
This frame is attached to the vehicle, it rotates by the heading of the vehicle, but does not rotate with the roll and pitch of the vehicle.
The X and Y axes remain parallel to the horizontal plane and the X axis is parallel to the vehicle’s heading.
- The X axis is perpendicular to gravity and is in the forward direction of the vehicle, projected into the horizontal plane.
- The Y axis is perpendicular to gravity, perpendicular to the X axis and is in the lateral direction of the vehicle, pointing to the left, projected into the horizontal plane.
- The Z axis is co-axial with the gravity vector, and positive in the up direction.
This frame is attached to the vehicle and rotates with it in all three axes with the heading, pitch and roll of the vehicle.
- The X axis is parallel to the vehicle’s heading and is in the forward direction of the vehicle.
- The Y axis is perpendicular to the X axis and is in the right direction of the vehicle.
- The Z axis is perpendicular to the X and Y axes and is in the down direction of the vehicle.
This frame is attached to the vehicle and rotates with it in all three axes with the heading, pitch and roll of the vehicle.
- The X axis is parallel to the vehicle’s heading and is in the forward direction of the vehicle.
- The Y axis is perpendicular to the X axis and is in the left direction of the vehicle.
- The Z axis is perpendicular to the X and Y axes and is in the up direction of the vehicle.
- OxTS frames: The heading angle is between the forward direction of the vehicle, projected in to the horizontal plane, and the North. The range of the heading angle is from 0 to 359.99 degrees, with positive rotation from the North (clockwise when looking from above) about the down direction axis of the vehicle.
- ISO 8855 frames: The yaw angle is between the forward direction of the vehicle, projected in to the horizontal plane, and the East. The range of the yaw angle is from -180 to +180 degrees, where positive rotation is from the East and counter-clockwise when looking from above, about the up direction axis of the vehicle.
- OxTS and ISO 8855 frames: Starting with the vehicle in the horizontal plane, the pitch angle is obtained with a rotation about the lateral direction axis of the vehicle. The range of the pitch angle is -90 to +90 degrees, where positive rotation is from horizontal and clockwise when looking in the same direction of the lateral axis.
- OxTS and ISO 8855 frames: Starting with the vehicle in the horizontal plane, the roll angle is obtained with a rotation about the forward direction axis of the vehicle. The range of the roll angle is -180 to +180 degrees, where positive rotation is from horizontal and clockwise when looking from behind.
Conversions between Reference Frames
Symbols used for basic angles:
OxTS frames: |
ISO 8855 frames |
Heading angle: ψ |
Yaw angle: γ |
Pitch angle: θ |
Pitch angle: λ |
Roll angle: ϕ |
Roll angle: η |
Symbols used for basic matrices:
H is the OxTS Heading Matrix
P is the OxTS Pitch Matrix
R is the OxTS Roll Matrix
Y is the ISO8855 Yaw Matrix
T is the ISO8855 Pitch Matrix
L is the ISO8855 Roll Matrix
A, B and C are fixed matrices.
These two frames share the horizontal plane (or the down axis, along gravity).
Moving from the navigation frame to the horizontal frame is equivalent to applying a rotation about the down axis (heading angle). Moving from the horizontal frame to the navigation frame is equivalent to applying the inverse rotation.
These two frames only share the heading direction (projected into the horizontal plane).
Moving from the horizontal frame to the vehicle frame is equivalent to applying two successive rotations about the lateral (pitch angle) and forward (roll angle) axes, in this order. Moving from the vehicle frame to the horizontal frame is equivalent to applying the two inverse rotations in inverted order.
These two frames do not share anything apart from the origin.
Moving from the navigation frame to the vehicle frame is equivalent to applying three successive rotations about the down (heading angle), lateral (pitch angle) and forward (roll angle) axes, in this order. Moving from the vehicle frame to the navigation frame is equivalent to applying the three inverse rotations in inverted order.
These two systems share the horizontal plane (or the up axis, co-axial with gravity).
Moving from the earth-fixed system to the intermediate system is equivalent to applying a rotation about the up axis (heading angle). Moving from the intermediate system to the earth-fixed system is equivalent to applying the inverse rotation.
These two systems only share the heading direction (projected into the horizontal plane).
Moving from the intermediate system to the vehicle system is equivalent to applying two successive rotations about the Y (pitch angle) and X (roll angle) axes, in this order. Moving from the vehicle system to the intermediate system is equivalent to applying the two inverse rotations in inverted order.
These two systems do not share anything apart from the origin.
Moving from the earth-fixed system to the vehicle system is equivalent to applying three successive rotations about the up (heading angle), Y (pitch angle) and X (roll angle) axes. Moving from the vehicle system to the earth-fixed system is equivalent to applying the three inverse rotations in inverted order.
Moving between the OxTS navigation frame to the ISO 8855 earth-fixed system is equivalent to swapping the north and east axes and inverting the sign of the vertical axis. This is in turn equivalent to applying a rotation +90 degrees about the down (up) axis and a rotation of 180 degrees about the east (north) axis.
Moving between the OxTS horizontal frame and the ISO 8855 intermediate system is equivalent to inverting the sign of the lateral (Y) and vertical (Z) axes, which is in turn equivalent to applying a rotation of 180 degrees about the forward (X) axis.
Moving between the OxTS vehicle frame and the ISO 8855 vehicle system is equivalent to inverting the sign of the Y and Z axes, which is in turn equivalent to applying a rotation of 180 degrees about the X axis.
Examples of Measurements in OxTS and ISO8855 Reference Frames
Measurement |
OxTS Measurement Coordinate Frame |
ISO 8855 Measurement Coordinate Frame |
OxTS Measurment Name |
ISO 8855 Measurment Name |
OxTS CAN Message Name |
ISO8855 CAN Message Name |
Yaw rate of the vehicle |
OxTS Vehicle frame |
ISO 8855 Vehicle System |
Angular Rate Zv |
ISO v.s. Yaw Velocity |
AngRateZ |
IsoVsYawVelocity |
Pitch Rate of the vehicle |
OxTS Vehicle frame |
ISO 8855 Vehicle System |
Angular Rate Yv |
ISO v.s. Pitch Velocity |
AngRateY |
IsoVsPitchVelocity |
Roll Rate of the vehicle |
OxTS Vehicle frame |
ISO 8855 Vehicle System |
Angular Rate Xv |
ISO v.s. Roll Velocity |
AngRateX |
IsoVsRollVelocity |
Yaw Angle of the vehicle |
OxTS Vehicle frame |
ISO 8855 Vehicle System |
Heading |
ISO Yaw Angle |
AngleHeading |
IsoYawAngle |
Pitch Angle of the vehicle |
OxTS Vehicle frame |
ISO 8855 Vehicle System |
Pitch |
ISO Pitch Angle |
AnglePitch |
IsoPitchAngle |
Roll Angle of the vehicle |
OxTS Vehicle frame |
ISO 8855 Vehicle System |
Roll |
ISO Roll Angle |
AngleRoll |
IsoRollAngle |
longitudinal velocity of the vehicle |
OxTS Horizontal Frame |
ISO 8855 Intermediate System |
Velocity Forward |
ISO i.s. Longitudinal Velocity |
VelForward |
IsoVsLongitudinalVelocity |
lateral velocity of the vehicle |
OxTS Horizontal Frame |
ISO 8855 Intermediate System |
Velocity Lateral |
ISO i.s. Lateral Velocity |
VelLateral |
IsoVsLateralVelocity |
vertical velocity of the vehicle |
OxTS Horizontal Frame |
ISO 8855 Intermediate System |
Velocity Down |
ISO i.s. Vertical Velocity |
VelDown |
IsoVsVerticalVelocity |
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