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FOSS app to record GPS location, saving it locally?
(discuss.tchncs.de)
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
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RunnerUp and Another Activity Tracker seem like your best options.
I used AAT about 5 years ago. It worked well.
Had to turn off battery-optimisation to allow recording in the background.
AAT is nice, also can load OpenStreetMap for the tracked area.