How does accelerometer calibration work?

Question

Inside a MEMS accelerometer there are some miniature spring-mass structures that displace under gravity or external force (acceleration). These forces are proportional to or can be indirectly quantified by capacitive changes due to their displacements. If an accelerometer is made ideal (perfect) and is laid flat on a surface, it would theoretically read \$ A_x = 0g \$, \$ A_y = 0g \$, and \$ A_z = 9.81 m/s^2 = 1g \$. In reality, we have to calibrate it, but I can't think of any sensible way of offsetting (calibrating) theses g values other than comparing the accelerometer values against a known mechanical design (pendulum of known inertia, free falling from a known height, rails of known direction and length etc.) then offset the measured values against a known physical values. Like calibrating a weight scale, we compare the reading against a physical, calibrated mass then either tune the bridge balance or hardcoding it in the firmware.

But in countless tutorials I found on google or youtube (e.g. Calibrating the BNO055 9-axis Inertial Measurement Sensor), the accelerometer calibration are carried out just by leveling and holding the accelerometer at different angles. If \$ A_z = 10.1 m/s^2\$ to begin with, in a minute or less of calibration, \$ A_z \$ then will magically correct itself to \$ 9.81 m/s^2 \$.

How is that possible? How does an accelerometer correct itself just by having it positioned at different angles? And if the accelerometer can correct itself, why do we need calibration in the first place (it may as well calibrate itself in operation)?

Answer 1

Calibration is frequently done on a centrifuge also. This allows precise acceleration to be applied.

Answer 2

The accelerometer controller knows that, when held stationary, it should see an acceleration of 9.81 in one direction, and zero in the two directions orthogonal to the 9.81 reading.

If held at an arbitrary angle, all three axes may read something, but the combined magnitude of those three readings should always be 9.81. If it isn't, the sensor needs to adjust itself.

If you take multiple readings at different angles, the controller can work out an offset and multiplier to apply to each of the three axes to get an answer of 9.81 every time. There are six unknowns to solve.

You can't constantly calibrate the sensor while it's moving, because there may be other accelerations going on.

Answer 3

Doesn't it do something like this: -

Internally, the device knows that \$9.81 \text{ m/s²}\$ is the gravitational constant for earth. It has this value burnt in to hardware (so to speak). So, when you calibrate a particular axis, you need to align the accelerometer to "receive" the maximum effects of gravity on that axis. You need to do this with care and accuracy (if you want accuracy). So, now, it can take the number it was producing and fix the gain of that axis so that it then reads \$9.81 \text{ m/s²}\$.

For the other two axis (if you have done this carefully) there are no gravity pulls and these can be zeroed. Step and repeat for the other axes and you should be good to go. This method of course does not work on any other celestial body in our solar system other than earth.

if the accelerometer can correct itself, why do we need calibration in the first place (it may as well calibrate itself in operation)?

The accelerometer has no idea what angle the device is at nor whether it is actually accelerating.