Actually, there is no need for an independent battery for your PS3. Get one of these (battery brain):

http://batterybuddy.com/

1/2 the price of an Optima battery & you don't need to figure out where to put it.

Basically you could get the battery brain & a power inverter and have the whole thing up & running in about 30 minutes.

We installed some equipment on vehicles for the boarder patrol years ago and added the old device (battery buddy) & they worked great.