So in anything but a dead calm or following wind, you'll continuously be missing the target. In a perfectly steady wind (which really doesn't exist outside of wind tunnels), you will fly off on a giant arc semi related to how much wind force is being exerted. It may get home after several hours of circling if it doesn't hit something first (which it will).
...
Finally, I would never want my Phantom to drunkenly wander all over the place trying to find it's way home. The first sign of a compass error, I put it in ATTI and fly it home. It's really not hard. So this idea of a compass-less RTH for the Phantom is both not possible and pointless.
But how is that possible? How can you possibly fly it home in ATTI mode with all the wind and other variables without taking a "drunken arc" and flying for hours? You said "Not knowing which way you're pointing is as good as blind"... You mean to tell me that you can tell which way you are pointing from that dot 300 meters away by looking at the dot in the sky without any RC input? Of course not. You give it a little forward pitch on the right stick and watch where it goes. Given what you see, you make adjustments until you determine how to bring it home: same exact thing this simple non-compass RTH algorithm can do. And the AC has a big advantage you don't have in that it actually knows where the AC is and which direction it is headed (after pitch is applied and movement starts). Flying in ATTI mode, you have to get its direction less directly and you will have to perform more maneuvers to do it if you are using LOS and not telemetry.
Wind, IMU, gyro accuracy,
none of that matters! This is really a very simple problem. It's the same problem you face when you have to fly home in ATTI mode: both you and the AC have the same information to work with (where the AC is and which direction it moves when you give it some forward pitch). There are multiple ways to do it but I find this the simplest (for flying the standard/default mode 2):
- +25% pitch on right stick and hold
- How did the P3 move, either by watching it in the sky or on telemetry?
- Only 3 possibilities here if you are flying LOS watching the dot in the sky that is your P3:
- Dot isn't moving: you're either flying toward or away. To find out which, hold a little yaw (left or right) on the left stick until...
- Dot is moving left: hold slight left on the left/yaw until the dot is no longer moving left
- Dot is moving right: hold slight right on the left/yaw until the dot is no longer moving right
- Keep the pitch forward while repeating the previous two steps, keeping the AC from moving left/right relative to your LOS as it approaches home
Once you've performed that procedure, your P3 is headed toward home. It makes no difference how accurate the IMU is or which way the wind is blowing. If you have a strong wind coming from one side, the P3 will be "dogging" it's way home, slightly sideways. Doesn't matter. Everything is relative because you simply set the yaw to get your line home: it doesn't mean the P3 is
pointing home, only that it is
headed home: your pitch+yaw is what is required to make it run that line. If, on the way home, you see it starting to drift to your left or right a little, make fine adjustments with the left stick to stop the left/right drift as you continue to pitch forward on the right stick. Your track home flying manual ATTI should look like an "S" around the straight home line: basically follows the home line but with slight variations side to side along that line.
A computer algorithm doing the same thing is guaranteed to follow that straight home line closer than you did manually because it can see where the AC is accurately, which way it is moving, and the moment it veers even slightly off the home line, it can apply the slight adjustments needed to keep it close to that line. And again, wind, IMU or gyro accuracy, etc. don't matter. All it has to do is pitch forward, adjust yaw until the AC is headed toward home based on its GPS movement, and then make "micro adjustments" to the yaw from that point whenever it veers to one side or the other of the home line along the way. In a couple minutes, your P3 will be overhead and you can manually land.
Shammyh has a good point: why bother? I agree: if I can see it, I personally would probably just fly it home even if we had this algorithm. But there are a lot of situations (particularly if your compass has failed) where you may lose line-of-sight. And we all know from watching the videos posted on this forum that with LightBridge, we don't all follow the FAA guidelines to keep LOS all the time.

In such cases, a simple algorithm like this could mean the difference between loss of the AC and getting back close enough to home to (re)take control.
Mike