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...
Not sure if that's black swan territory or not, but IMO it was a great piece of forward-thinking that made GPS useful beyond just the original military applications.