MacM,
The use of SR and GR is implied, inferred, stated or whatever term you want to use in paragraphs 1, 2, 3 and 4 on page 11 of the link you provided.
http://metrologyforum.tm.agilent.com/pdf/AN1272.pdf
From paragraph 1:
"...Fortunately, an understanding of relativity is not necessary to gain an understanding of how GPS works.
The relativistic terms are accounted for in the design of the satellite clocks and in the receivers that properly process the data..."
Paragraph 2:
"The orbit period for GPS places them at a distance of about 4.2 earth radii from the center of the earth as illustrated by the feet of the tripod in Figure 5.
The relativistic velocities of the space vehicle (SV) clocks cause them to lose about 7.2 millionths of a second (7.2 microseconds) per day with respect to the earth. On the other hand, their altitude (often called the gravitational redshift) causes them to gain 45.6 microseconds per day. The net is a gain of 38.4 microseconds per day. This accumulation is enormous compared to the few nanoseconds synchronization accuracy desired for the system, since a microsecond is 1,000 times a nanosecond. The SV clocks are constructed on earth to lose 38.4 microseconds per day, so that when they are in space they appear to be running at the right rate."
Paragraph 3:
"
Because the earth is rotating and generally all receivers are moving, the relative velocities and positions between SV clock and receiver clock have to be accommodated in the receiver software. It is not known that all receivers are performing this calculation correctly. This is a receiver manufacturer’s responsibility. Just due to the rotating earth alone, hundreds of nanoseconds of error can occur in synchronizing clocks around the globe unless the calculations are done correctly."
Paragraph 4:
"The U.S. Air Force has created an interface control document (ICD 200-B) which describes how to perform these calculations.
Once the relativity is properly included, GPS can be thought of in a traditional time-of-flight way. By measuring the time of arrival (TOA) of a signal — knowing the time it began and its velocity — the range or distance between the sender and the receiver can be easily calculated."
.