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They could, but multiple governments now publicly broadcast from similar constellations, so it wouldn't have nearly as much benefit for them to do so.

Modern dirt cheap receivers can pick up European, Chinese, Russian, etc. constellations for location just as well as the American one.

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Always wondered about this, can overlapping systems be used simultaneously for higher reliability or precision?

Surprisingly the answer is most often no, however in poor signal areas like in a city or under canopy the answer is yes as you are more likely to get a signal from the remaining bits of sky view.

The other benefit is when doing PPP the convergence time is dramatically shorter with multi constellation.

When doing RTK most receivers will use only GPS, as it is generally the most accurate, but it can and will use GLONASS occasionally. I have never seen one use beidu or Galileo

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