Identify which of the three signals is closest to a sinusoidal curve
Is it sufficient to identify the «most sinuoidal» of those 3, or would you also want linear projections of those (consistent with a IMU sensor tilted vs the plane of motion)?
A simple solution might be to do a windowed fft and pick the direction where the «crest factor» of the fft magnitude was largest (best explained by a single sinoid).
Edit:
It appears thah your «sine» is somewhat variable. If the above approach fails, then perhaps removing the DC component («highpass filter») followed by removing the high frequency edges and impulses (lowpass filter) for an effective tuned bandpass filter, followed by squaring and summing the samples could be used.