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The official specification for the GPS signal is an Interface Control
Document. I think the one of most interest is the first on the page,
Interface Specification IS-GPS-200.

https://www.gps.gov/technical/icwg/

See p. 103 in that document for the format of the ephemerides broadcast
by the satellites. The orbit parameters have the appearance of the
Keplerian orbital elements long used in astronomy, but they actually
yield the WGS84 coordinates of the satellites. In other words, the
rotation of the Earth and wandering of the pole have been absorbed into
the ephemeris.

But what about the encrypted military signal ("Y-code")? Does it include
additional data for improved accuracy? Apparently not: "The NAV data,
D(t), includes SV [Space Vehicle] ephemerides, system time, SV clock
behavior data, status messages and C/A to P (or Y) code handover
information, etc. The 50 bps data is modulo-2 added to the P(Y)- and
C/A- codes; the resultant bit-trains are used to modulate the L1 and L2
carriers. For a given SV, the data train D(t), if present, is common to
the P(Y)- and C/A- codes on both the L1 and L2 channels."

Upgrades have made new GPS signals available to civil users, such as the
"CNAV" data described in Appendix III of the document. They include
Earth orientation parameters: x and y of the pole, UT1-UTC, and the time
derivatives of those values. See p. 176. I don't know how many
satellites broadcast the new data, or to what extent consumer grade
devices apply the corrections.

   

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