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Does GPS compensate for lower c in air?


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They pretty much have to. The precision required is something like 8 orders of magnitude. They have to correct for gravitational time dilation, among other things. Atmospheric index of refraction is not insignificant at this point. That's easy enough to correct for, however. What it probably doesn't correct for are pressure fluctuations due to weateher and some lensing effects in upper atmosphere. These will be some of the factors that will result in limited precision of the GPS system. But they do average out between multiple satellites, so the more of them you have the lock on, the less of a precision loss this causes.

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GPS receivers can do some pretty complicated modelling of the Earth's atmosphere. Specifically there are ionospheric correction terms in the almanac section of the GPS signal. The almanac isn't real time data and the ionospheric correction terms can only be as accurate as our models and measurements of the ionosphere, but this correction is usually better than nothing.
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