Weighted Curve Fitting

In an attempt to fit more points along the trajectory, we tried a simple weighting scheme to favor points with larger magnitudes (distance from the origin). We define a set of concentric rings around the origin with radii of multiples of 50 pixels. Then, for a point in ring with radius n*50, we use n*THRESHOLD as the threshold for determining whether or not a point agrees with a model generated by RANSAC (where THRESHOLD is the threshold we were using for all points before).

The results using this scheme:





The model fit for the upswing is actually worse than it was before, but the downswing curve follows the actual trajectory better for longer.

In general, this doesn't seem like a promising approach. One related possibility is to take the extreme points (the left-most, bottom-most, etc) and force RANSAC to fit at least those points. But this does not sound like a robust approach either.