That is surprising, you must have had an extremely accurate accelerometer and gyro, or employed tricks [1]. There are two problems with determining position from acceleration measurements:
1. You're integrating twice (acceleration to obtain velocity, then velocity to obtain position). So if you have any noise or error, you're integrating that, and integrate that again. Hello, parabola.
2. Gravity. It's strong. So you have to subtract it (as it induces an apparent acceleration upwards).
If the difference between actual down and where your model thinks is down is just a fraction of a degree, you'll be totally off within minutes.
> As a concrete example consider a tilt error of just 0.05 [degrees]. This error will cause a component of the acceleration due to gravity with magnitude 0.0086 m/s2 to be projected onto the horizontal axes. This residual bias causes an error in the horizontal position which grows quadratically to 7.7 m after only 30 seconds [and thus to 770 m after 5 minutes, unless I'm mistaken, and 110 km after an hour]
[1] such as assuming that your foot has velocity zero while on the ground, which does not hold when you're in an elevator, for example, and which you can't use in a drone without some serious sensor fusion.
I had 2 tricks - really high-order filter borrowed from some paper and the assumption that a walking human doesn't gain constant acceleration. Even in an elevator you stop on a floor which resets your speed to 0.
I agree that there is no way you could extend this directly for flying, but with modern devices and things like ground-distance radar, relative airspeed indicators and so on I don't think it is beyond the realm of possibility. Plus we have detailed hightmap of the world, which, when combined with a radar should allow for terrain tracking. That makes the accuracy of sole INS much less crucial.
1. You're integrating twice (acceleration to obtain velocity, then velocity to obtain position). So if you have any noise or error, you're integrating that, and integrate that again. Hello, parabola.
2. Gravity. It's strong. So you have to subtract it (as it induces an apparent acceleration upwards).
If the difference between actual down and where your model thinks is down is just a fraction of a degree, you'll be totally off within minutes.
See eg here: https://www.youtube.com/watch?v=C7JQ7Rpwn2k&t=1401s
Or here: https://www.cl.cam.ac.uk//techreports/UCAM-CL-TR-696.pdf
> As a concrete example consider a tilt error of just 0.05 [degrees]. This error will cause a component of the acceleration due to gravity with magnitude 0.0086 m/s2 to be projected onto the horizontal axes. This residual bias causes an error in the horizontal position which grows quadratically to 7.7 m after only 30 seconds [and thus to 770 m after 5 minutes, unless I'm mistaken, and 110 km after an hour]
Or here: https://liqul.github.io/blog/assets/rotation.pdf (search for "Accuracy of Velocity and Position Estimates").
[1] such as assuming that your foot has velocity zero while on the ground, which does not hold when you're in an elevator, for example, and which you can't use in a drone without some serious sensor fusion.