The cheapest kind of altimeters use barometric pressure sensor readings to detect changes and map them as elevation. This only works well if the barometric region is somewhat static. For instance, locations along a coast like Southern California USA can have drastically different micro climates within just a few miles of the water, and the differences in water heavy coastal air and dry desert winds can get interpreted as elevation changes.
I think some older devices used a GPS location and lookup tables that contain the average elevation of the region/location.
I think newer devices use extra GPS signals from additional sats and then do the geometry calculation.
GPS sats are basically beacons that transmit/stream their location and the time. The most accurate GPS ground instruments also use the timing of the transmission signal to dial in changes. This is used by systems like the USGS earthquake monitoring sensors.
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