What is Scale Factor in IMUs?
Scale factor of Inertial Measurement Unit (IMU) is a concept that shows the connection of popular sensor output in the real-world physical input under measurement. It is the ratios between IMU output and the physical input . This ratio is ideal and there is no perfect fit and in practice, each sensor will have some degree of a scale error that is a variation of this perfect fit.
A parameter of high importance when calibration IMU is scale factor and is applied to bring the raw sensor values into a meaningful physical value. An example would be in accelerometers and gyroscopes, where the scale factor would be expressed as the ratio between the output signal and what is being measured, e.g. acceleration or angular rate.
Core Concepts of Scale Factor
1. Definition
Scale factor is the change in sensor output to change in physical quantity being measured. In the case of an accelerometer: SF = ΔOutput / ΔAcceleration. It is normally given in terms of counts/(m/s²).
2. Error Sources
Scale factor errors are caused by manufactory tolerances, temperature changes, mechanical stress and aging. Temperature is especially profound where it leads to the scale factor drift of 100-500 ppm/°C of MEMS sensors.
3. Impact on Navigation
In inertial navigation, the proportional factor error of the accelerometer will cause the velocity error to accumulate linearly over time and the position error to increase quadratically with time. Error in gyro scale factor of 0.1 percent will cause a position error of ~1.8km after 1 hour of use.
4. Linearity
An ideal scale factor would hold no variations all through the measurement range of the sensor. As a matter of fact, scale factor usually changes a little with input magnitude- this is known as scale factor nonlinearity.
Scale Factor Calibration Techniques
Motion sensing requires the ability to be properly calibrated. The best ways of calculating scale factor are as follows:
Static Multi-position Test
Put the IMU at various orientations to determine the gravity (1g) on axis. Scale factors of accelerometers can be computed by comparing the outputs with respect to known gravity vector.
Rate Table Testing
For the gyroscopes mount the IMU on precision rotation table. Output is then measured at known rates of rotation (usually 10-1000deg/s). Change in the output is divided by the change in the rotation rate to obtain the scale factor.
Temperature Compensation
Scale factor will be affected by temperature, so calibrate at a number of temperatures. Store the coefficients of compensation in the memory of the sensor in order to achieve correction in real time.
In-Field Calibration
Smart algorithms take advantage of vehicle motion constraints (e.g. zero when the vehicle is stationary) or a combination with GPS to track scale factors in real-time.
Applications of Accurate Scale Factor
Aerospace & Drones
In UAV navigation the accurate scale factors can eliminate position drifts in the GPS-denied. For a deeper understanding of drift mechanisms, see IMU Drift: Causes, Effects and Solutions condition. Scale factor stability must have better than 0.01 percent of military drones in order to be successful in the missions.
Smartphones & AR/VR
Correct gyro scale factors are of great importance to the augmented reality applications where virtual objects have to remain pinned on the real world. Modern smart phone adopt continuous calibration algorithm.
Medical Robotics
The IMUs used in surgical robots use highly stable scale factors (less than 0.1%), in order to accurately track instrument position and orientation during a minimally invasive surgery.
Autonomous Vehicles
The data of IMU is used when the GPS update is not active in self-driving cars. When there are issues of lane-level positioning accuracy in urban surroundings, scale factor errors should not exceed 0.2 percent.