Von Mises distribution to detect outliers

I don't quite understand what you're doing, and I had to look at Wikipedia to remind myself about von Mises, so take my answers with a grain of salt. If you could create an analogous problem with just real numbers instead of angles on a circle, would it make sense to you? von Mises is like a Gaussian on the circle. Are the angle differences all actually small enough to approximate the distribution as a Gaussian?

1. Angle differences also live within 0 to $2pi$, so von Mises could be appropriate. But only if it is! Just like points on the real axis may or may not be described by a Gaussian.

2. You could calculate the "circular variance" and then set the $kappa$ parameter to match using $<cos delta theta> = I_1(kappa)/I_0(kappa)$. Then detect outliers that have small values of the von Mises distribution, recalculate $kappa$, and repeat. Assuming zero mean here. Basically do the analogue of what you'd do with a sample drawn from the real numbers.