Gyroscopes

For gyroscopes, the three parameters a system integrator pays attention to are the Angular Random Walk, Bias Instability and Rate Random walk. A more detailed explanation is given below:

• Angular Random Walk It is the equivalent of the integral of white noise in the gyroscope output. It is characterized by a slope of -0.5 and is contributed by random fluctuations in signal with correlation time much shorter than the sample rate. The value is read for T=1 second, and it directly represents the noise density in deg/s/√(Hz) or rad/s/√(Hz).  A low noise density value is desired when low amplitude signals are of interest. Small gyroscopes, such as gyroscope used in the MTi 1-series have a very low noise level since they resonate at a higher frequency than larger gyroscopes.
• Bias instability or in-run bias stability – not to be confused with bias repeatability or turn-on turn-on bias stability (addressed later). The value in this section is called the in-run bias instability of a gyroscope and indicates the minimum bias that cannot be estimated. In the Allan Variance graph above this value is ~12º/h for the 100-series and 1-series and 20º/h for the 10-series.
• Rate random walk – Characterized by power spectral density that falls off as 1/frequency² and represents bias fluctuations caused in the long term primarily due to temperature effects. A low rate random walk is important for long-term dead reckoning performance.

Which gyroscopes for which application?

Choosing the right gyroscopes depends on several parameters, where the importance of each is application-specific.

Non-linearity is an important parameter, especially when gyroscope integration is the only way to retrieve orientation (e.g. in magnetically disturbed environments or during long-lasting accelerations). 

Bias repeatability is also called the (turn-on to turn-on) bias stability. Gyroscopes are calibrated by the manufacturer of IMUs and AHRSs, but bias repeatability cannot be calibrated for. 

Noise density is a parameter that can be interesting when signals with a low amplitude need to be distinguished. Also, for short term dead-reckoning, noise density is the dominating factor.

The full range of gyroscopes determines which motion can be measured. Typical gyroscope full ranges are 450, 1000 and 2500 deg/s. A full range of 450 deg/s is sufficient for most industrial applications, such as maritime applications, satellite stabilization, camera stabilization and aerospace applications. Hand held applications may go up to 1000 deg/s, whereas most sports applications exceed this value (a golf swing or a baseball pitch is performed with an angular velocity up to and above 2000 deg/s). Xsens’ products have different full ranges: the MTi 10-series and MTi 100-series are available in 450 and 1000 deg/s, where the MTi 1-series is available with 2000 deg/s gyroscopes.

A higher angular velocity than required reduces the resolution and is therefore not recommended. However, when data is missed because the angular velocity cannot be measured, sensor fusion algorithms may have troubles coping with that: when the angular velocity is above 500 deg/s for 0.05 sec, the gyroscope integration when the sensors cannot measure higher than 500 deg/s will be above 25 deg after 0.05 sec. Most IMU and AHRS manufacturers supply the user with clipping flags so that this can be handled appropriately during operation.