If you are following the FAA rules for operating an unmanned aircraft, you must keep your drone (UAS) within sight. Then knowing the direction to fly your drone back to home should be obvious.
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If you do lose sight of your drone then you can hit the button to land your drone and it will fly back to where it was launched from or where you are currently located. That is as long as your controller has not lost connection with your drone.
Long, but we need more people, so let it fill space...
Yes you follow the FAA rules including line of site, however if you are 400' up, and 1000' away (even closer), while you can see the drone, you cannot tell what orientation it is. Depending on landscape from a birds eye, you may not be able to identify where you are standing by the video either, so it can be a guess as to what direction it is facing. In the bright sun it is surprising how quickly you lose sight of the green/red LED's (not the drone) for orientation. Regardless, you can look in the lower left corner of the controller and see the triangle. You can point it towards you and start a manual return (forward) which will get it close enough for you to orient the drone by sight. If you still cannot make it out, or too stressed per battery life, the just press land, and return to launch, or return to you and it will fly itself back.
Also, while you DO need controller connectivity to "return to you", it is not needed for "return to launch". The Karma itself remembers where it was launched, so even if you turn off the controller, it will still return to within about 10' or so of where it was launched; as long as the Karma has a GPS signal anyway. In that regard, if connectivity is lost to the controller, the Karma will stop whatever it is doing, even in autopath, hover for a short time while trying to re-establish contact, then if it still cannot connect, it will automatically return to the launch location. If it reconnects, you can take control. If it does not reconnect, such as in the instance the battery on the controller fails, it will just land where it was launched.
"Return to you" is the feature where the Karma returns to the controller. The only time you would ever do this is if you have moved and don't want to go back to where you launched it. If the connection is lost, it will not work.
The battery is similar in that if you ignore the low battery warnings, once the battery is REALLY low, the Karma will automatically start returning to the launch sight. You can cancel this, but it is not recommended. The only time I would cancel this is once it was within 20' or so, and I would prefer land it because I am more gentle, or on a boat where it needs to be a bit more precise than 10'.
As for the original poster's question, there does not appear to be a way the pilot can see the last known location of the drone. They have to contact GoPro support for that. I would like to see this changed as knowing the last point of communication helps if you crash the drone, or canceled the auto return and it lands 1000' away because the battery was too low to return all the way. Yes you should have line of sight and see the drone at all times, but at 1000' away, topology of terrain looks very different, especially if in thick vegetation and it could be tough to track it down. I think GoPro should afford us the ability to see cookies/tracking like any garden variety GPS. The maps are already there, and if real-time updates are the issue, then you should be able to send last known coordinates to a smartphone or such. Either way, this tracking would also help if someone calls the police making a claim you were harassing them, or flew in restricted areas. I have a feeling this will be in an update.
I would recommend going out to a large field and doing some testing as so you get a feeling for what will happen in emergency scenarios. It helps save the heart if you have GoPro Care, but for me knowing what to expect when something fails is a good thing. You see many out there complaining the Karma gets out of control and just flew away, but most are user mistakes. Yes there was a recall for the battery issue, though that should be resolved now. I have flown many hours and not once lost connection or control of the drone. Anyway, in my testing I did test the auto return feature on a couple levels. My first test was to fly it about 30 yards away, let it hover about 50' and shut off the controller. As designed it remained hovering, then after a short time, it rose then flew back and landed itself where it was launched. I also checked battery drain by ignoring the warnings it gave (kinda like a lost controller signal) and letting it return to launch. It did it perfectly and told me what it was doing during the process. As previously mentioned, one stress I have is that I will be on a boat, that even under anchor moves, so return to launch potentially turns the drone into a sub. As long as you have a connection, at any time you can cancel the return to launch by clicking the "X" and take control. In my testing, I did this about 30' or so away as so I could land on the boat. In that regard I have a bunch of practice where I taped out a 1' square and practiced landing the Karma there, so I have become very good. Now if the controller fails when I am in the boat, I guess I pray, or launch from land; which now that I think about it is a great option... Obviously launch from the boat to get it in the air, but then land on the shore/ launch again and proceed with flying. Looks like I have another test to see if it will fly home to the most recent launch rather than the first of the session...
As Paradise alluded to though, if you pay attention, and stay within the FAA rules which you should already know since you are required to register your drone, all this should become easy with more flying. This includes how to determine orientation. My advice as well is like any camera or electronic device, get 1 or 2 more batteries. That will help you avoid the bad practice of extending flight time beyond a safe range. Other than just being careless in flight, or flying outside of your limits, battery drain should really be the only danger to your drone and if you pay attention, it is not an issue. You hear many complain about a rogue Karma, or that they can't take control, or it just crashed/landed 100' away. In that regard, I would easily bet 99% of that is user error; again, after the recall issue anyway. It's funny, you see these guys putting up videos saying GoPro needs to resolve these issues, but when they explain what happened, you can see their mistakes, often many or misuse. These are the same people that ruin it for responsible pilots because they do stupid things such as fly it in the clouds, behind buildings, etc. Just look on YouTube and you will see numerous knuckleheads. This is where the recall really hurt since now many are on the bandwagon even though the issue was resolved.