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Or against US soldiers.

You would still need a strong signal near the target, which is more difficult than setting up a drone-trap like Iran seems to have done.

Is it possible to somehow sign GPS coordinates? (Perhaps sync an internal clock at each mission's start, and check a time-based signature?)

If not, are there practical challenges to integrating the output of a drone's engine and calculating the path travelled, instead of naively believing satellite coordinates?

Actually, wind must make that difficult. For a car, you can attach a magnet to each wheel and count the surges as it passes a sensor on each rotation, to give you an idea of where you are. Due to the external forces on a drone, you would probably want to measure forces with an accelerometer/gyroscope, not engine output.)

What are the challenges involved in such? Is internal-location tracking even feasible?

All military navigation systems are inertial, not GPS. They only accept GPS corrections within the error bars of the inertial system. As a practical matter this means that you can only make a drone deviate from its intended course by a few meters assuming you did a perfect job of spoofing the GPS.

GPS spoofing/jamming only works for systems that use GPS navigation systems; military weapons and systems have never used GPS navigation. Inertial navigation systems are spoof-proof.

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