Units
The units of the Allan Variance parameters are different depending on the research area and application. In robotics, we typically use different units from those specified by manufacturers in data-sheets. This can be confusing and often leads to mistakes in documentation and software available online. Here we try to provide an explanation of the units and their derivations.
Thanks to Martin Günther for doing much of the research.
Source: IEEE Standard 952-2020 for Specifying and Testing Single-Axis Interferometric Fiber Optic Gyros (page 18f)
| Allan variance component | unit |
|---|---|
| Q_g | ", μrad |
| N_g | °/√h, rad/√s |
| B_g | °/h, rad/s |
| K_g | (°/h)/√h, (rad/s)/√h |
| R_g | (°/h)/h, (rad/s)/s |
Unfortunately the IEEE standard is only concerned with gyroscopes, not accelerometers. However, if we substitute rad/s with m/s², we get the following units for accelerometers:
| Allan variance component | unit |
|---|---|
| Q_a | m/s |
| N_a | (m/s)/√s, (m/s)/√h |
| B_a | m/s², m/h², mg (= milli-g-force, not milligram) |
| K_a | (m/s²)/√s, (m/s²)/√h |
| R_a | m/s³ |
These units are consistent with the following table from the Kalibr wiki:
| Kalibr Parameter | Kalibr Wiki Symbol | Allan variance symbol | Units |
|---|---|---|---|
| Gyroscope "white noise" | rad/s * (1/√Hz) = rad/√s | ||
| Accelerometer "white noise" | m/s² * (1/√Hz) = (m/s)/√s | ||
| Gyroscope "random walk" | rad/s² * (1/√Hz) = (rad/s)/√s | ||
| Accelerometer "random walk" | m/s³ * (1/√Hz) = (m/s²)/√s |