In the last post I discussed the methods I looked into for cancelling the gravity vectors measured by the ACC, if you haven’t seen that I would recommend reading that first. The way I compared the two methods was by seeing how well they follow the raw acceleration signal from an angular movement, this was done by mounting the sensor on the side of a servo motor and moving between different angles with varying starting positions(in reference to gravity) and magnitudes of angle change. Below is the graph from a 5-degree movement.
The blue graph is the raw acceleration signal on the Z axis,red is the cos method and the yellow is the tan method, looking at the full graph(left picture) they seem to be overlapped and looks like they both follow the raw signal fairly well but in the zoomed in picture(right), both are slightly off the middle of the raw acceleration so neither seems better than the other, the Y axis showed the same result that neither stood out. I did another test where the angle change was 35 degrees and the result of the of the two axes is below: