Obtain velocity by using accelerometer data

Question

I have an accelerometer sensor, which obviously measures acceleration along the $x$, $y,$ and $z$ axes.What I would like to do is to obtain the velocity along these axes by using the accelerometer readings. I have thought the following procedure:

1. Get the accelerometer readings

2. Filter the data by some kind of filter (Lowpass, moving average etc)

3. Select a small time interval of the order $\text{Δt} = 0.01\text{sec}$

4. Use the velocity formula $v = v_0 + a\cdot\Delta t$

5. Update $v_0$ at each time step by using the previous calculated value $v$

I would really appreciate any thought on how precise this procedure would be or even any suggestion that would improve it. The goal is to obtain the velocity along the $x$, $y$, and $z$ by using the accelerometer data.

Answer 1

First of all a couple of pointers:

• Essentially what you are proposing is integration.
• Whether the result is acceptable that is depended on the problem specifications.

Now, some details on the main problems:

1. Numerical integration and rounding error over a long period of time: The fact that you are using a filter (any filter for that matter) will not remove small rounding errors and (at the end of the day) numerical differences from the actual value. This will create the problem that eventually, after a (not so long time), a significant difference with the raw data will occur.

2. Orientation of accelerometer: I don't know the exact problem you are trying to apply (I've worked with this on human gait and it was a nightmare), but even a slight tilt or a wobble during the motion of the accelerometer will cause the readings of the accelerometer to be pointing to a direction different from the global xyz. So again, after a while the error accumulates and you seem to have a higher velocity.

There are ways to partially rectify this (e.g. using a gyroscope and rotating the local axis of the accelerometer to the global axis, or using a Kalman filter for the velocity if you have another method of measurement), however, --at least to my knowledge-- it is not feasible to get an accurate measurement of velocity only from acceleration measurements.