The filtering, smoothing, and the fixed-lag smoothing distributions of (a) the bar position variables m
and (b) the velocity variables n
. The lag in the fixed-lag smoothing distribution is selected to be 2 s (i.e., lagging one bar behind in 120 beats per minute). It can be observed that introducing a certain amount of lag yields smoother estimates and at the same time introduces a fixed amount of latency. Note that this experiment contains a dramatic tempo change where the tempo is increased by 40 BPMs in approximately 8 s.