Accelerometers

Accelerometers

MEMS accelerometers consist of a damped mass system on a spring, etched in silicon. When the accelerometer is accelerating, the proof mass will move with respect to the casing. This movement is measured by electrodes. The analog measurement signal goes through a sequence of signal processing stages and gets converted to digital. Subsequently the digital signal is converted to acceleration (SI unit, m/s2) by applying pre-defined calibration parameters. For inertial sensors the evaluation and thereby characterization of the MEMS-design and signal processing chain is typically done using Allan Variance graphs, which are typically used in the  study of frequency stability of oscillators.

An example of an Allan Variance curve is shown in the figure below from which the statistical properties of the random processes causing the inherent noise in the signal from the MEMS inertial sensor can be deduced and analyzed. Typical technical data sheet values of white noise and bias stability (in-run) are derived from the Allan Variance characterization curves.

For accelerometers, the three parameters a system integrator pays attention to are the Velocity Random Walk, Bias Instability and Rate Random walk. The Velocity Random Walk is equivalent to the integral of white noise in accelerometer output. A more detailed explanation is given below:

• Velocity Random Walk – It is the equivalent of the integral of white noise in the accelerometer 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 mg/√(Hz) or m/s²/√(Hz). A low noise density value is desired when low amplitude signals are of interest.
• Bias instability or in-run bias stability – not to be confused with bias repeatability or turn-on turn-on bias stability (addressed later). This is represented by the flat portion at the bottom of the curve. The value in this section is called the in-run bias instability of an accelerometer and indicates the minimum bias that cannot be estimated. In the Allan Variance graph above this value is ~3*10-4 m/s2 (30 μg) for the MTi 10-series and MTi 100-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.

In Attitude and Heading Reference Systems, the filter parameters are modelled with stochastic information derived from the Allan Variance curves.  The choice of the accelerometer is therefore dependent on and important to the intended use in an application.

Accelerometers need to be calibrated to let them output useful information. Calibration algorithms and methods generally calibrate for gain, also called scale factor; offset/bias; temperature dependency of the gain and offset; cross-axis sensitivity/misalignment in case of a 3D accelerometer or assembly.

How to choose your accelerometer?

Depending on the design, accelerometers behave differently. Especially 3D accelerometers that may have different designs for each axis have different characteristics depending on the orientation. The availability of 3D accelerometers makes it possible to have 3D IMUs and AHRSs on a SMD-chip, as shown in the MTi 1-series. Apart from the stochastic measures discussed previously other specifications that play an important role are the following:

Non-linearity is an important parameter to take into account, especially for applications where accelerations larger than 1g can be expected, e.g. aircraft. Non-linearity in 3D accelerometers is caused by geometry of the proof mass, the mounting and the capacitive measurement. A 0.1% non-linearity in the ± 1g range can result in errors of 0.1 deg in roll and pitch.

Bias repeatability also called the (turn-on to turn-on) bias stability is often mistakenly used for referring the in-run bias stability discussed previously. Accelerometers calibrated by the system integrators or IMU/AHRS manufacturer like Xsens show shift in biases especially from turn-on to turn-on during its lifetime usage. As this parameter is not deterministic it cannot be calibrated out. It is generally not specified and often mitigated by software means where the accelerometer bias is estimated in a sensor fusion framework. A value of e.g. 0.05 m/s2 will result in an initial roll/pitch error of around 0.3º.

The bandwidth of an accelerometer is important for proper functionality in industrial applications. Typical vibrations in industrial applications can be up to 150 Hz (9000 rpm in an engine), with sculling motion an addition error source up to around 400Hz. If not properly captured the sculling motion cannot be compensated for. The bandwidth should be chosen taking into consideration the proper capturing sculling motion for compensation later and also removing high frequency noise components and aliasing.

Accelerometers are available with different full scale options parameters. The full range of accelerometers lies typically between 2g and 15g. The negative implications of choosing a non-optimal full range can be significant. As most industrial applications experience vibrations, the vibrations may exceed the full range of the accelerometer. As in many signal processing pipelines accelerometers are sampled at a high frequency (e.g. 10 kHz) and then converted to a lower frequency (e.g. 1 kHz or 2 kHz), short term clipping may not be noticed but does affect the output. Although the resolution of the accelerometer decreases and noise is higher, it is advised that that the full range is higher than the expected maximum vibrations or accelerations. Vibrations can easily be up to 10g in vehicles with engines. Military standards such as MIL-STD 202 prescribe immunity against vibrations of 6g RMS.