Also, I don't think turning off you cell phone will prevent the powers that be from locating the phone. You should remove the battery.
+1
Even back in the day of the analog cell phone (remember those?), it was possible to locate a phone to the coverage area of the cell tower nearest to the phone. It was because of how cellular phones work.
Even when off, a cell phone is always scanning for a broadcast signal from the cell towers. It will then send a message to identify and announce itself to the tower with the strongest signal. It's so that the network knows where your phone is and what cell tower your phone is in contact with at any time. When someone calls your phone, the network already knows where your phone is in order to "ring" and to route the call to your phone via that cell tower.
Think about the above. When you are abroad, the GSM network in the foreign country you are visiting "knows" that you are there because your phone announces itself, even when you think your phone is off. The foreign network then alerts your home network of your whereabout. All that so that you can
receive and to make calls, and also to charge you for the service. Amazing technology, is it not?
Here's a bit more about what's going on behind the scene. When you are moving while talking on the phone, you may be getting away from the cell tower that your phone is connected to. When the signal strength decreases, a "handoff" to another tower may be needed. How does the network know which of the surrounding towers to handoff your connection to? It instructs adjacent towers to listen in on your phone signal, and when another tower reports that its reception of your phone signal is getting stronger, that is the tower that the network will switch your connection to. All that should happen seamlessly without the user knowing what is going on.
In new digital phones (not really new since they have been out for almost 20 years), the phone will also scan for adjacent towers and reports which tower signal is getting stronger than that of the current one. This is to assist the network in determining which should be the best tower for the handoff. This is call "MAHO" (Mobile Assisted Handoff).
PS. Using trilateration, the new cell network can locate the mobile with better accuracy than the old analog system that can only place the phone within the coverage of a tower, which can be tens of miles in radius. However, network trilateration does not work anywhere as accurate as GPS. The technology existed and was talked about more than 10 years ago when I was working in this field. I do not know how widespread the implementation is currently.