Russ Brown points us toward these two products:

http://www.engadget.com/2014/06/16/airdog-drone/

The battle in the skies this week is the autonomous action-sports
drone apparently. Why? Because, what if you want to be the star in your as yet
un-made aerial epic? With a regular drone that's a tricky one. You could film
yourself, as you stand flying the drone, but where's the fun in that? Airdog is
a quadcopter drone that follows you, using GPS and movement tracking to keep up
as you get down (the slope, or whatever). Action camera selfie videos are cool
and all, but wouldn't an epic aerial shot following you...

https://www.kickstarter.com/projects/sqdr/hexo-your-autonomous-aerial-camera

We initially began thinking about HEXO+ because we needed a
solution that would make aerial filming possible in the most remote places: on
mountains, in the snow, and in all sorts of unpredictable situations that were
quite a pain to deal with when trying to sync a drone pilot, a cameraman and a
rider.

When we started toying with the idea, we realized that it had the potential to
change the face of all kinds of aerial filming, making it dead simple. So we
combined our expertise in action-sports movie-making, drone design and
aeronautic software to create a drone capable of autonomously flying, filming
and following, giving you access to amazing aerial shots with the bare minimum:
a drone, a camera and an app on your smartphone.

HEXO+ is just that – an intelligent aerial follow camera: no pilot, no
cameraman, no headache.