GPS doesn’t send information from your phone, it just listens to what is essentially a signal reporting the time from satellites in different locations. Airplane mode stops your phone from sending signals to eliminate the risk (which is basically zero, but people still worry about it) of the signals from the phone interfering with the electronics on a plane. GPS will continue to function in airplane mode as long as the map of your current location was already loaded before shutting off wifi and cell signals.
Airplane mode only prevents your phone from sending signals. It doesn’t restrict it from receiving them. The way GPS works is that satellites are constantly transmitting highly accurate time data. By receiving that data from multiple satellites, you can pinpoint your position on the Earth using the delays in transmission. However, you don’t need to send any signals to the satellites themselves.
Accelerometers are devices that measure acceleration/rotation in 3 axes. You can use these devices for positioning information, but they have enormous drift over long distances and you need a known starting position to get an absolute position/orientation.
Other comments covered the why. I’ll add that what you’re referring to is called dead-reckoning – position tracking using accelerometers and/or gyroscopes.
This is *wildly* inaccurate for consumer grade sensors. Useful for seconds to *maybe* minutes with a really well tuned system, if you expect anything resembling accuracy. Beyond that the drift will be extreme, as the error increases with the square of time – t^(2)
I’m not aware of any phone or app that actually does it. There was some talk years ago of Google navigation using it just to know that you made a turn, before the GPS can “catch up.” They still haven’t done it, nor have Waze or Apple Maps.
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