Underwater ROV

I am trying to create a underwater ROV that follows me as I swim.

a) how would I control it with a remote?
b) how do I use Matlab to follow me?

a) how would I control it with a remote?

That would really depend on what kind of remote you are talking about, and what you want to control.

b) how do I use Matlab to follow me?

Install matlab on the PC. Duct tape the PC to the outside of the ROV. Pray that the laptop survives the submersion.

What, EXACTLY, is Matlab going to get as input? Create as output? How is it going to communicate with the Arduino?

I presume a tether isn't an option!

38kHz near-IR beacon? Like a line-follower robot but in 2 dimensions to steer the thing, and use
signal-strength to estimate distance.

Ultrasound is another possibility, but transducers expensive, only work under water - IR
is cheap and easy to test on dry land.

Shark!

A shark would do the trick. All you need is to design a shark muzzle.

-jim lee