I have a data from $3$-axis $50$ Hz accelerometer, acceleration over each of $3$-axis: $acc_X,\ acc_y,\ acc_z$.
I want to decompose acceleration into gravity and movement components.
First question:
Should I introduce some notation of magnitude, for example $mag = \sqrt{acc_x^2 + acc_y^2 + acc_z^2}$ and then apply all transformations to the magnitude rather than component-wisely?
The second question is the decomposition itself.
One solution I've found is to apply lowpass Butterworth filter. However, I don't know how to interpret ButterWorth filter return values, namely numpy arrays $a$ and $b$, in terms of gravity and movement component.
So, how can I implement decomposition using the Butterworth filter?