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Planes report pressure altitude via their transponders. 20-30 feet up and down is very normal for an autopilot.

GPS altitude is used for vertical guidance for certain types of GPS approaches (i.e. "LPV" approaches[1]) and requires the airplane's avionics to be equipped with a WAAS[2] receiver that provides accurate altitude information.

[1] https://en.wikipedia.org/wiki/Localizer_performance_with_ver...

[2] https://en.wikipedia.org/wiki/Wide_Area_Augmentation_System



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