What is an inertial sensor?
Strictly speaking, an inertial sensor is a device that uses inertia to perform a
a measurement. As a practical matter, when people say "inertial sensor" they are
referring to an accelerometer or a gyroscope.
What is an accelerometer and a gyroscope, and how do they differ?
An accelerometer is a sensor that measures acceleration or translational
motion. A gyroscope is an angular rate sensor - it measures the rate of angular
rotation. While angular accelerometers (devices that measure the rate of change of
angular rotation) do exist, they are rarely used. Generally, accelerometers are
thought of as devices that measure linear acceleration.
Where would you use an accelerometer?
There are many uses for an accelerometer. Here are a few examples:
- Accelerometers can be used to measure vibration. Often machinery that is failing
has a characteristic vibration pattern - a motor bearing for example. Smooth and quiet
when in good order, gradually getting rougher and noisier as it wears out. An
accelerometer can be used to detect the impending failure by measuring the changing
vibration signature of that machine
- Shock can be thought of as a non-periodic vibration. An accelerometer can,
therefore, be used to measure shock. As an example, accelerometers are used to measure
if shipping containers have been subjected to abusive handling. Generally this is done
by recording the accelerometer's measurement during shipping and then uploading and
analyzing the data after delivery
- An accelerometer can be used to measure change in velocity. An automobile airbag
crash sensor is a example. The crash module is looking for a large, sudden, reduction
in velocity (sudden reduction of velocity is the only reliable indication of a crash
- potholes can generate lots of shock, but should not trigger an airbag).
- Many accelerometers (including all those made by Analog Devices) can measure
static acceleration, such as the force of gravity. The gravity vector always points
toward the center of the Earth. By measuring the effect of gravity on each of the
accelerometer's axes you can determine the tilt of the accelerometer relative to the Earth.
Where would you use a gyroscope?
Gyroscopes are used when you want to know how fast or how much something is turning.
There are many ways to determine rotational rate (optically, magnetically, etc), but a
gyroscope is unique in requiring nothing external to make this measurement. Here are a few examples:
- In automobile electronic stability control systems the rotation rate of the car is measured
by the gyro and compared to what is expected from the wheel speed and steering wheel sensors.
If there is a discrepancy between them, differential braking is applied to bring the car back
into control.
- Optical image stabilization in digital cameras is accomplished by having a gyro measure
the unintentional rotational movement of the camera. The image is then steered by moving lens
elements such that it remains relatively stationary compared to the image sensor. In this way
images remain blur-free even though the camera moved during exposure.
- In navigation systems, a gyro's angular rate output is integrated to determine angular
heading which in turn is used to determine if you have been turning and by how much. When
combined with displacement information you can figure out your position.
What are the major error sources for inertial sensors?
Most inertial sensors have several error sources. Some are easy to deal with, others less so.
Here are a few:
- Null bias error (or zero g bias error in the case of accelerometers)
Null bias error is simply the deviation from zero when the inertial sensor is experiencing no stimulus
- zero g for an accelerometer or no rotation for a gyro. In general, all sensors exhibit at least two
forms of null bias error: initial null bias error and null bias error due to temperature. Initial bias
error is very easy to correct for - simply measure the sensor's output with no stimulus present and
subtract it from what it should be ideally. Store that value and add it to all subsequent measurements.
Null bias error due to temperature is harder to deal with since the correction coefficient generally
varies from sensor to sensor and each unit must be individually temperature compensated. Data sheets
should provide specifications for both null bias errors.
- Scale factor error
Scale factor error is the deviation from ideal of the sensor's sensitivity. There may be an initial as
well as an over temperature component. Just as with null bias errors, both can be corrected by
calibration. Scale factor calibration is more difficult as it requires the user to apply known stimulus
to the sensor. Analog Devices inertial sensors generally have little initial scale factor error and
even less scale factor error due to temperature.
- Noise
All inertial sensors suffer from noise. In general, noise is proportional to bandwidth so the user
must calculate the significance of noise based on the bandwidth they will be using. The noise of all
Analog Devices inertial sensors is Gaussian in nature (the noise energy is the same at all frequencies),
so it is rather simple. With a single pole output filter, the RMS noise of a sensor is: RMS NOISE =
Noise Density * √(Bandwidth * π/2). Noise density should be specified in the sensor's data sheet.
- There are several other error sources that are much less significant such as nonlinearity, ratiometricity,
etc. that are beyond the scope of this FAQ
What is the limit of resolution of an inertial sensor?
Noise usually sets the limit of resolution of an inertial sensor. Simply calculate the RMS noise as
described above. It is generally impossible to resolve signals below the RMS noise.
I need finer resolution. What do I do?
You can always select a sensor with lower noise (Analog Devices makes several models with various noise
densities to suit most applications). If that is still not enough, there are two avenues to explore -
bandwidth and noise density. As mentioned previously, noise floor is determined by noise density and bandwidth.
Since the user has no control over a sensor's noise floor, you can try to reduce the bandwidth as much as
possible for a given application. If more adjustment is required, you can average the signal from multiple
sensors. As noted earlier, the noise of all Analog Devices inertial sensors is random (Gaussian). Therefore
the noise of each sensor is uncorrelated with the other. So for n sensors averaged there is an improvement
in noise of √n.
