Bat flight model
With only a pair of microphones, there isn’t enough information to fully track the trajectory of the bat. You can only get the angle orthogonal to the baseline as a function of time. However, if we make a few assumptions, it’s possible to model data and get some idea of what the bat was doing. So, if we assume that the bat was travelling in a straight line at a constant speed, we can find a starting position and velocity that agrees with the data. After a little playing around with some geometry and a python script, here’s what I came up with. The graph shows the data I reported yesterday (angle vs time) and the model trajectory:
A model for the bat’s flight across our back garden. Data in orange and the model in blue. Starting positions and the velocity components in x, y and z are shown.
While it’s probably not a unique solution and not very well constrained, the data are consistent with a bat moving at 5 m/s at a height of 4.4m, which doesn’t sound too unreasonable.