# Why not to calibrate accelerometer in IMU filters?

I have been reading various research papers regarding IMU filters and I came to the question of why do we not need to calibrate the accelerometer values as we do for the gyroscope and magnetometer?

The first thing that one needs to point out is the following that )usually):

• accelerometers report acceleration in 1, 2 or 3 orthogonal directions (i.e. second derivatives of length)
• gyroscopes report angular velocity (i.e. first derivative of angular position)
• magnetometer report amplitude and orientation of a magnetic field.

## Magnetometers

Magnetometers can be used to obtain the orientation using earth's magnetic field. However, magnetometers are very prone to magnetic field disturbances. It is very similar to having a magnet needle near a compass. It essentially introduces a bias/offset. So the idea is to try, and remove the offset with that calibration.

## Gyroscopes

Gyroscopes although similar in construction to accelerometers, they serve another purpose altogether. They are usually used for "attitude-sensing". I.e. they are used to find the orientation of an object. However, what they do, is they report the rate of change (i.e. the angular velocity). Given the angular velocity, it is possible to integrate to the angular position.

The problem is that there is always a small error in the measurement. if that error is large, then in the long run you get accumulation and significant error. Algorithms exist that can combine input from sensors (e.g. GPS) and using various techniques (e.g. kalman filtering), it is possible to correct for that error. However, for a gyroscope that remains static it is very difficult (/impossible) to make that type of correction.

## Accelerometers

The MEMS accelerometers are based on a very simple principle. Its basically a mass on spring which oscillates.

Based on the oscillation which is generated by the acceleration on the object (see Base induced Vibration), there is a very clear understanding and theory which allows prediction of the acceleration from the mass oscillation. Since the masses. are really small, there is very little that can change over the period of time (no drift). Therefore, modern MEMS accelerometers don't really require much calibration.

One might say, that I can also use accelerometers to get acceleration and integrate that to velocity and then integrate again over time to obtain position. However then you'd be integrating twice the error (let alone that the axis on the accelerometer change over time), and the error accumulates a lot faster. So usually, accellerometers are not used for orientation but they are used to gauge the resultant acceleration of all three accelerations and then do smart things with that (e.g. identify movement, walking etc). (There are -of course - some exceptions).

## why calibration is not as important on accelerometers

gyroscopes and magnetometers are used to obtain orientation in space. Both measurements are prone to errors for different reasons (see error accumulation and electromagnetic offset).

Accelerometers are not usually used for orientation measurements (although is some cases they can be used under static conditions). Therefore, the very small error (usually less than 1%) doesn't affect much effective operation.