What is the Coriolis Effect?
The Coriolis effect is an inertial effect which occurs when a mass is moved in a rotating frame. This produces a deflection effect whereby the moving object seems to run off its course to the right in Northern Hemisphere and on the left in the Southern Hemisphere as viewed within the rotating frame.
When it comes to IMUs (Inertial Measurement Units), the Coriolis effect is more than a geographical oddity, it is a principle at the heart of the functioning of vibratory MEMS gyroscopes, key components of modern navigation. See What is a Gyro Sensor for gyroscope fundamentals systems.
IMU Essentials
An IMU usually incorporates three gyroscopes and three accelerometers (sometimes three magnetometers, too), giving a 9-degree-of-freedom motion tracking capability. IMUs using MEMS (Micro-Electro-Mechanical Systems) gyroscopes can measure angular velocity without external references because they utilise the Coriolis effect.
Fundamental ideas of Coriolis in IMUs
Reference Frames
To occur, there must be a mismatch between an inertial reference frame and a rotating reference frame, which is the case in MEMS gyroscopes.
Force Calculation
The Coriolis force is determined as F = -2m(Ω × v), where m is the mass, Ω is the angular velocity, and v is that of linear velocity in the rotating frame.
Vibrating Mass
MEMS gyroscopes utilize a vibrating proof mass. As the device rotates, it causes the Coriolis effect to make a secondary vibration orthogonal to the first.
Measurement
The gyroscope can measure the rate of rotation by measuring the displacement of Coriolis induced vibration.
How the MEMS Gyroscopes use the Coriolis Effect
1. Drive Mode Vibration
A proof mass is forced by the electrostatic forces into sustaining an oscillation at a constant frequency and amplitude along the drive axis.
2. Rotation Detection
When the gyroscope is rotated, the Coriolis force is applied in a direction cross to the drive direction and axis of rotation.
3. Sense Mode Displacement
This Coriolis force makes the proof mass vibrate in the sense direction whose amplitude is proportional to the angular rate.
4. Capacitive Sensing
The sense-direction displacement is measured by use of electrodes that convert the mechanical motion into electricity.
Challenges and Error Sources
Although the Coriolis based IMUs have ushered in a revolution in motion sensing, there are certain drawbacks associated with the physical phenomenon that they utilize:
| Error Source | Description | Impact on Measurement |
|---|---|---|
| Bias Instability | Gradual modifications in offset in the zero-rate output | Drifting in orientation with time |
| Scale Factor Errors | Errors Inaccuracy in the conversion between the input rate and the output signal | Bad angular velocity reading |
| Cross-Axis Sensitivity | Response to rotation about non sensitive axes | An off-axis rotation contamination of measurement |
| Temperature Effects | Their performance can change due to shifts in temperature | Inconersistent measurements in different environments |
| G-Sensitivity | The response to linear acceleration | False rotation signals in the case of linear acceleration |
Mitigation Techniques
To eliminate the shortcomings of Coriolis-based IMUs, engineers have designed a number of methods:
Temperature Compensation
Applying temperature sensors and calibration values to adjust the measured values to existing operating temperature.
Multi-Axis Designs
Using two or more proof masses or sensing elements to reject common-mode errors to improve accuracy.
Advanced Calibration
The in-field and laboratory IMU calibration steps to characterise and compensate systematic errors.
Sensor Fusion
Using IMU in conjunction with GPS, magnetometers and barometers through Kalman filtering to provide more reliable navigation.