Basically, a watchdog micro-controller is running as long as there is a battery inside a phone, and it can turn-on your phone on a request from the network operator's side.
What one should do is to either leave his phone at home, turned on (that will provide an alibi) or take out the battery. But taking out the battery would provide suspicion (yes, providers track their clients phones states and locations). I.e. FSB will be torturing you and cross-interrogating everyone involved, until you provide evidence why it was turned off at the given time.
So what I recommend is leaving your phone at home, turned on, unless you are sure you will need it. But even then it is better to get yourself a throw away phone, that cant be linked to you: i.e. never insert a battery into it near your home or places you usually visit.
Now how to get an anonymous SIM card: don't buy them online, as these sellers could be FSB honey pots for naive people. Instead pay some homeless to register a sim card on him. Now they will be tacking down that bum, instead of you.
It should be noted, that having a trackable phone on you is generally a bad idea. Here is an example of what may happen: back in 2005 I ride a tram in Moscow without buying a ticket. Then controller came, and I immediately left tram, but the controller, an old soviet-type guy, was insistent on fining me, even risking his health, therefore a fight happened outside, on the street: he assaulted me first, by grabbing my dress, but I've punched and pushed him under the moving car, and ran away, through nearby yards. Back then I had no phone, and there weren't that many security cameras, so it was impossible to track me down. Now imagine what would have happened if I had that phone. If that scummy old Russian controller died in the accident, I would have been given a life sentence for not paying a tram fare. Despite me being totally innocent (having no money for a tram ticket is not a crime). So yeah, your phone is your enemy.
If you need GPS, buy GPS receiver separately, but make sure it doesn't use wifi or BT, as these connections can be tracked too. USB is the only safe connection. Remember: there is no safe radio transmission. Most modern dissidents, starting with Dudaev and Emir Khattab, perished due to the lack of knowledge regarding radio-transmission.