The most interesting thing to me about relativistic corrections for GPS is that we didn't even have to know about or understand relativity in advance in order for GPS to work.
That sounds strange .. but .. there are many small corrections that need to be applied to "straight forward" triangulated fixing off of moving monuments (term from surveying), relativitic time shift being just one.
There are several recent HN threads about Kalman filters [e].
It's possible (and more or less roughly what already happens) to record GPS fixes against a fixed master station and compute the time series error twixt the naive computation and known location (or, indeed, mesh of locations across (say) Australia) and generate a Kalman filter to correct and return more precise positions for moving recievers in the mesh area.
Had we not been aware of relativity we very likely would have discovered it via the time slip 'error' terms in the correction filter.
In a similar manner we have improved our understanding for atmospheric wobble, continental drip [1], and other fine effects.
That sounds strange .. but .. there are many small corrections that need to be applied to "straight forward" triangulated fixing off of moving monuments (term from surveying), relativitic time shift being just one.
There are several recent HN threads about Kalman filters [e].
It's possible (and more or less roughly what already happens) to record GPS fixes against a fixed master station and compute the time series error twixt the naive computation and known location (or, indeed, mesh of locations across (say) Australia) and generate a Kalman filter to correct and return more precise positions for moving recievers in the mesh area.
Had we not been aware of relativity we very likely would have discovered it via the time slip 'error' terms in the correction filter.
In a similar manner we have improved our understanding for atmospheric wobble, continental drip [1], and other fine effects.
[1] https://en.wikipedia.org/wiki/Continental_drip
[e] https://hn.algolia.com/?dateRange=pastYear&page=0&prefix=fal...