OxTS Reference Frames and ISO8855 Reference Frames

Reference Frames

• OxTS navigation frame
• ISO 8855 earth-fixed system
• OxTS horizontal frame
• ISO 8855 intermediate system
• OxTS vehicle frame
• ISO 8855 vehicle system

Angles

• Heading and Yaw
• Pitch
• Roll

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

 

Reference Frames

• OxTS navigation frame (or NED: North East Down): 

This frame is attached to the vehicle, but does not rotate with it.

1. The north axis (N) is perpendicular to the gravity vector and in the direction of the north pole along the earth’s surface.
2. The east axis (E) is perpendicular to gravity, perpendicular to the north axis and is in the East direction.
3. The down axis (D) is along the gravity vector.

• ISO 8855 earth-fixed system (or ENU: East North Up):

This frame is attached to the vehicle, but does not rotate with it.

1. The east axis (E) is perpendicular to gravity, perpendicular to the north axis and is in the East direction.
2. The north axis (N) is perpendicular to the gravity vector and in the direction of the north pole along the earth’s surface.
3. The up axis (U) is co-axial with the gravity vector, and positive in the up direction.

• OxTS horizontal frame (or level frame, or FLD: Forward Lateral Down): 

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.

1. The forward axis (F) is perpendicular to gravity and is in the forward direction of the vehicle, projected onto the horizontal plane.
2. 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 onto the horizontal plane.
3. The down axis (D) is in the vertical direction of the vehicle, along the gravity vector.

• ISO 8855 intermediate system:

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.

1. The X axis is perpendicular to gravity and is in the forward direction of the vehicle, projected onto the horizontal plane.
2. 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 onto the horizontal plane.
3. The Z axis is co-axial with the gravity vector, and positive in the up direction.

• OxTS vehicle frame (or XYZ):

This frame is attached to the vehicle and rotates with it in all three axes with the heading, pitch and roll of the vehicle.

1. The X axis is parallel to the vehicle’s heading and is in the forward direction of the vehicle.
2. The Y axis is perpendicular to the X axis and is in the right direction of the vehicle.
3. The Z axis is perpendicular to the X and Y axes and is in the down direction of the vehicle.

• ISO 8855 vehicle system:

This frame is attached to the vehicle and rotates with it in all three axes with the heading, pitch and roll of the vehicle.

1. The X axis is parallel to the vehicle’s heading and is in the forward direction of the vehicle.
2. The Y axis is perpendicular to the X axis and is in the left direction of the vehicle.
3. The Z axis is perpendicular to the X and Y axes and is in the up direction of the vehicle.

Angles

1. Heading (or Yaw):

• OxTS frames: The heading angle is between the forward direction of the vehicle, projected onto 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 onto 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.

2. Pitch:

• 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.

3. Roll:

• 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.

 

• Between OxTS navigation and horizontal frames: 

These two frames share the horizontal plane (or the down axis, along gravity).

Moving from the horizontal frame to the navigation frame is equivalent to applying a rotation about the down axis (heading angle). Moving from the navigation frame to the horizontal frame is equivalent to applying the inverse rotation.

• Between OxTS horizontal and vehicle frames:

These two frames only share the heading direction (projected into the horizontal plane).

Moving from the vehicle frame to the horizontal frame is equivalent to applying two successive rotations about the forward (roll angle) and lateral (pitch angle) axes, in this order. Moving from the horizontal frame to the vehicle frame is equivalent to applying the two inverse rotations in inverted order.

• Between OxTS navigation and vehicle frames:

These two frames do not share anything apart from the origin.

Moving from the vehicle frame to the navigation frame is equivalent to applying three successive rotations about the forward (roll angle), lateral (pitch angle) and down (heading angle) axes, in this order. Moving from the navigation frame to the vehicle frame is equivalent to applying the three inverse rotations in inverted order.

• Between ISO 8855 earth-fixed and intermediate systems:

These two systems share the horizontal plane (or the up axis, co-axial with gravity).

Moving from the intermediate system to the earth-fixed system is equivalent to applying a rotation about the up axis (heading angle). Moving from the earth-fixed system to the intermediate system is equivalent to applying the inverse rotation.

• Between ISO 8855 intermediate and vehicle systems:

These two systems only share the heading direction (projected into the horizontal plane).

Moving from the vehicle system to the intermediate system is equivalent to applying two successive rotations about the X (roll angle) and Y (pitch angle) axes, in this order. Moving from the intermediate system to the vehicle system is equivalent to applying the two inverse rotations in inverted order.

• Between ISO 8855 earth-fixed and vehicle systems:

These two systems do not share anything apart from the origin.

Moving from the vehicle system to the earth-fixed system is equivalent to applying three successive rotations about the X (roll angle), Y (pitch angle) and up (heading angle) axes. Moving from the earth-fixed system to the vehicle system is equivalent to applying the three inverse rotations in inverted order.

• Between OxTS navigation frame and ISO 8855 earth-fixed system:

Moving between the OxTS navigation frame and 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 of 90 degrees about the down (up) axis and a rotation of 180 degrees about the east (north) axis.

• Between OxTS horizontal frame and ISO 8855 intermediate system:

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.

1. Between OxTS vehicle frame and ISO 8855 vehicle system:

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