I just saw an ad for this
https://shop.soloshot.com
The device tracks an arm-band that you wear, up to 2000 feet away. There is an "indoor" accessory for up to 100 feet away.
A bit expensive...
Based on a _"self tracking camera" search, here are some vaguely similar devices:
Dolphin for iPhone
http://dolphin.com/your-personal-cameraman-with-swivl-self-tracking-camera-for-iphone/
Lily UAV
https://www.lily.camera/
Snap UAV
https://vantagerobotics.com/?gclid=CKSKkPPq9coCFQIfhgodR3YCcw
FOSCAM baby monitor
http://www.amazon.com/Foscam-FBCAM3502-FBM3502-Digital-Monitor/dp/B00O4J4ZFE/ref=sr_1_1?ie=UTF8&qid=1455404193&sr=8-1&keywords=tracking+camera
There are discussions on the web about frame rate - you may need poor resolution, extra software to get high enough for skating.
Swivl
http://www.swivl.com/#top
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Has anyone used any tracking cameras? Reviews?
Relevant issues could include possible interference inside your rink by various WIFI devices, cordless phone systems, walkie talkies, other people's camera systems, bounces from walls and ceilings, etc.
I've seen ads for such devices and they are cleverly engineered, but at my rink we can't even take cell phones on the ice during freestyle.
I could probably work with the rink staff to get around those general restrictions, but then I'm left with what to take videos of. At my current (dwindling) skill level, that's not what I'd want to see.
On the other hand, someone working much more seriously might make use of one. It might be easier than trying to find a friend with enough videography skills to do a good job with regular equipment.
I looked at the soloshot very seriously sometime last year, but the cost put me off. :-\