![Image](http://hazeii.net/images/2004/apod/lsfit2.gif)
(click image for a larger version)
This was created by first rotating the trail so it was approximately horizontal (I used the raw data for this image), then finding the best correlation (i.e. minimum least-squares error) between an intensity template approximating the trail and the trail itself.
The horizontal axis corresponds to pixels lengthwise across the trail, the vertical axis is the pixel number perpendicular to the trail (centred at ~100). The red trace (indexed on the left) is the raw best fit, the blue trace (indexed on the right, and slightly offset for clarity) is a smoothed version of it.
The key features of note are that the general shape of the curve corresponds well to the general shape of the curves in the horizontally-compressed images, and that there appears to be a semi-periodic variation in the centreline position (corresponding to a body wobble, and at a frequency that's in the ballpark for a wing beat - 125 pixels ~= 184Hz). Also note the curve matchs well with the observation that the first half of the trail is quite linear, while the second half appears to show a tightening curvature.
The noise at each end of the trail is because the graph begins just before the trail start and ends after it; obviously before the start and after the ends, there's nothing for the algorithm to lock on to.