Let there be $n$ points on a unit circle. It is known they come from "normal" distribution around particular unknown direction (i.e. sum of 2 "normal" distributions on circle - one centered at point $p$ and the other at its opposite $-p$). 
What is the best way to estimate this direction? By best I mean an algorithm that is a. analytical, b. efficient and c. simple.



Estimating direction from a distribution on a circle
This seems too simple to be true, but, combining some of the ideas posted earlier,
I think you could just interpret the vectors as complex numbers and take the RMS.


Squaring will turn the bimodal distribution into a unimodal one.
Then the square roots of the mean should give a good estimate of the modes of the original distribution.


