Doggy Door with Sensor

I've seen lots of doggy doors that have sensors that are triggered by a FOB on the collar. They're usually pretty pricey. I just want one that unlocks the flap, not the full on automatic doors. Think that can be done with an arduino. I have little experience using arduinos, but not afraid to try something out.

Search the forum, this has been discussed many times. Or google "arduino pet door".

The problem is not in having an Arduino unlock a door.

The problem is having the Arduino know when to unlock the door, i.e. the "dog wants to go through the door now" detection.

I I have a dog and a cat.
My problem is not, knowing when to let them in, but to not let the cat in with one of his 'presents'