Gyroscopes and Accelerometers.jpgMEMS gyroscopes typically rely on the Coriolis effect to measure angular velocity. It consists of a resonating proof mass mounted in silicon. The gyroscope is, unlike an accelerometer, an active sensor. The proof mass is pushed back and forth by driving combs. A rotation of the gyroscope generates a Coriolis force that is acting on the mass which results in a motion in a different direction. The motion in this direction is measured by electrodes and represents the rate of turn.


IMU Inertial Measurement Unit


Several parameters are important when choosing a gyroscope for a typical application.

One of the parameters the gyroscope is most judged on is the in-run bias stability. However, the accuracy and usability of a gyroscope is also influenced by other parameters. Depending on the application, some parameters become more important than others. The in-run bias stability is often used to classify gyroscopes from consumer grade up to a navigation grade system.

The Allan Variance method generates curves such as shown in the figure below from which the statistical properties of the random processes responsible for data noise of the MEMS inertial sensor can be deduced/analyzed. Typical technical data sheet values of white noise and bias stability (in-run) are derived from the Allan Variance characterization curves.

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 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 an 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 fall 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.


A gyroscope requires a high bandwidth in order to capture all movements and vibrations. A too low bandwidth will result in aliasing and drift in orientation.  In addition, coning motions, if not properly captured, will cause apparent drift in the output. The bandwidth should be chosen high enough, taking into consideration the proper capturing of coning motion, removing high frequency noise components and aliasing.

On top of the sensitivity to angular rate, the proof mass of the gyroscope is also sensitive to gravitational acceleration. A gyroscope rotating at the same rate along the same axis has a different output depending on the orientation with respect to gravity if not compensated for, which is called g-sensitivity. MEMS manufacturers are able to reduce g-sensitivity by taking the effects into account in the designs.

Vibration rejection is the mechanical ability of the sensing structures inherent in the design to reject vibrations. Vibrations put mechanical stress on the gyroscope structure, compromising the rate of turn estimation. In this video, it is explained what happens when vibration rejection (or vibration rectification) is not correctly designed.

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 magnetic disturbed environments or during long-lasting accelerations). In those cases, integration of the gyroscope signal is the only data is used to estimate orientation. With a non-linearity of e.g. 0.1 % FS, the error after a 360º turn can be 0.36º from non-linearity alone. Especially when the rotation is constantly in one direction, e.g. when a robotic vacuum cleaner only makes right-hand turns, the non-linearity is important.

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. Bias repeatability is caused by relaxation, temperature and start-up effects. The gyroscope output should be 0º/s when the gyroscope is not moving, so it is relatively easy to compensate for the bias after startup. Robust sensor fusion algorithms can also compensate for changing bias during use without the need to keep the gyroscope static.

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. AHRSs use reference signals, so orientation changes over longer times can be detected more easily. Lowering the bandwidth, in good signal process pipelines done by lowering the output data rate, will lower the RMS noise. This can be helpful when low-frequency angular rotations need to be measured.

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 handles appropriately during operation.

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