"Ben nerede olduğumu biliyorum."
Translation:I know where I am.
I think you mean "Benim nerede oldugumu biliyorum" and that raises an excellent question because grammatically I believe it must be benim not ben if you choose to use it. (Nerede oldugumu biliyorum is correct on its own.)
You actually can't, you can leave out 'Ben' totally if you want to, but benim does not work here. You would say 'Senin nerede olduğunu biliyorum." (I know where you are.) but it does not work for I/ben here.