# IMU Accuracy Error Definitions

## Summary

An Inertial Measurement Unit (IMU) combines linear accelerations from an accelerometer and rotations from a gyroscope to deliver navigation parameters and position update information. The accuracy of these parameters is influenced by a number of errors which are a function of time. This is a brief explanation of these IMU accuracy errors and their definitions.

## Gyroscope Errors

### Bias Stability

Bias Stability (or Bias Instability) is defined as the drift the measurement has from its average value of the output rate. The Bias Stability measurement tells you how stable the gyro output is over a certain period of time. Bias may be characterized as Bias Repeatability (variation over different cycles of the IMU) or Bias Stability (variation during a single operation of the IMU).

### Angle Random Walk

MEMS gyros will exhibit high frequency white noise due to thermoelectrical reactions. This random noise is an additional signal error source which cannot be modelled out with calibration. This random walk causes error growth proportional to the square root of time.

### Calibration Errors

The term ‘calibration errors’ refers to errors in the scale factors, alignments, and linearities of the gyros. Such errors tend to produce errors when the device is turning. These errors can result in additional drift.

## Accelerometer Errors

### Constant Bias

The bias of an accelerometer is the offset of its output signal from the actual acceleration value. A constant bias error causes an error in position which grows with time. It is possible to estimate the bias by measuring the long term average of the accelerometer’s output when it is not undergoing any acceleration. However, there is gravity acting on the accelerometer which will appear as a bias. It is necessary to know the precise orientation of the device with respect to the gravitational field in order to measure the bias. In practice, this can be achieved by calibration and orthogonality measurement.

### Velocity Random Walk

The outputs from an accelerometer are influenced by sensor noise of the electronics. This error in white noise grows proportionally to the square root of time. This white noise on the output of an accelerometer creates a velocity random walk, usually specified with units m/s/√h.

### Scale Factor

Scale factor is the relation of the accelerometer input to the actual sensor output for the measurement. Scale factor, expressed in ppm, is therefore the linear growth of input variation to actual measurement.

### VRE

Vibration rectification error (VRE) is the response of an accelerometer to current rectification in the sensor, causing a shift in the offset of the accelerometer. This can be a significant cumulative error, which propagates with time and can lead to over compensation in stabilization. VRE is highly dependent on the vibration profile experienced by the accelerometer, and the full scale range of the sensor. VRE is most active in high dynamic environments.