IMU Coordinate systems Introduction
Inertial Measurement Units (IMU) are electronic sensors that measure and report the specific force, angular rate, and some times the magnetic field around the body comprising of a combination of accelerometers, gyroscopes, and sometimes magnetometers. Interpretation of IMU data is impossible without the knowledge of coordinate systems, not to mention transferring measurement findings into understandable information.
IMUs also work in more than one coordinate system at a time, and the nature of the relationship between the systems must be clearly determined to achieve accurate orientation, position and motion measurements.
IMU core coordinates systems
There are four basic coordinate systems that are applicable to IMU operation and data interpretation:
Sensor Coordinate System
The reference frame of the IMU itself, specified by the manufacturer, and relative to the physical sensors.
Body Coordinate System
Affixed to the vehicle or device to which the IMU is mounted, such that the axes are in the forward, right, and down directions of the body.
World Coordinate System
A frame of reference fixed to the world (such as East-North-Up or North-East-Down) that is used to navigate and orient with.
Global Coordinate System
Earth-centred coordinate systems like ECEF (Earth-Centred, Earth-Fixed) in location of the global positioning.
Sensor Coordinate System
The sensor coordinate system is the reference frame of the IMU, the basis is given by the structure of the accelerometer and gyroscope chips on the printed circuit board.
The majority of IMU abide by the right-hand rule convention, which states that:
- X-axis: Normally pointing in the direction of the “forward” sensitivity of the sensor
- Y-axis: Normal to the X, and generally symbolizing the aspect of “right”.
- Z-axis: Perpendicular to X and Y and completing the right handed system
Body Frame vs World Frame
The difference between body-fixed and world-fixed coordinate systems is essential to IMU data fusion and interpretation.
Body Coordinate Frame
The frame is attached to the device or vehicle in which IMU is mounted. Its axes rotate with the body and this makes it suitable in the quantification of relative motions and orientation variations. The body frame is vital to control systems requiring reaction to the immediate movement of the device.
World Coordinate Frame
It is a fixed reference frame, usually geared towards the gravity and the magnetic north of the earth. The most used conventions are ENU (East-North-Up) and NED (North-East-Down). Conversion of the IMU measurements into the world frame will allow absolute orientation estimation and navigation.
| Aspect | Body Frame | World Frame |
|---|---|---|
| Reference | Attached to moving device | Fixed to Earth |
| Orientation | Changes with device movement | Remains constant |
| Acceleration | Includes gravitational component | Gravity can be separated |
| Use Case | Relative motion tracking | Absolute positioning |
Conversion formulae for Coordinate Systems
To convert measurements between any two coordinate systems will involve mathematical transformations, usually a rotation matrix, quaternion, or Euler angles.
Rotation Matrices
The matrices that relate rotation between two coordinate systems are 3 by 3 matrices. Orthogonal with determinant = 1.
Quaternions
Numbers with four dimensions that represent rotations and avoid some of the problems of gimbal lock. Favored in computer graphics and in modern IMU filtering.
Euler Angles
Intuitive display with three angles (roll, pitch, yaw), with possible gimbal lock at specific orientations.
Axis-Angle Representation
Specifies the rotation of an axis around another by a value of angular measure Handy in some of the operations of mathematics.
Practical Applications
Knowledge of the IMU coordinate systems allows real world applications in multiple industries
Aircraft Navigation
IMUs are used to provide attitude and heading reference and they convert. For more on integrated navigation, see our GNSS/INS positioning and navigation systems body-frame measurements to a world frame, to counteract aircraft maneuvers.
Smartphone Orientation
Screen rotation and motion gaming are based on proper transformation between body frame of the device and the world reference frame.
Robotics
The data given by the IMU is in body frame when it comes to balancing and controlling a robot, when it comes to navigating and mapping the world the IMU data is transformed into world frame.
Virtual Reality
VR systems combine IMU outputs with other sensors to monitor the head orientation in real time so as to create immersive experiences.
Conclusion
The coordinate systems in IMUs are an essential aspect to this field of study in that they help make a profound deduction of accurate and desirable information out of these invaluable sensors. The sensor-body-world transformation can be applied to many fields ranging all the way to consumer electronics and aerospace navigation.
As IMU technology is further developed, with further refinements in MEMS fabrication and sensor fusion algorithm, the efficient management of coordinate systems will still be a crucial element of inertial measuring and navigation systems.