Special Relativity Theory for One Observer?

A One-King system can be very stable.

Einstein's special theory of relativity concerns the relation between observations (of "events" without spatial extension recorded by space-time coordinates (x,t)) made by different observers using different inertial coordinate systems moving with constant velocity with respect to each other.

Suppose there is only one observer making observations in only one coordinate system in which the observer is at rest. Let us refer to this as a one-system situation. Can there be any special relativity theory for this one-system with its single observer/inertial system? Of course not. With only one  inertial system there is no room for comparison with observations in another moving inertial system. The special theory of relativity is empty for a one-system.

Now, the GPS system is a one-system based on the WGS84 spherical (ellipsoidal) coordinates system we are used to with latitude, longitude and height for spatial location, and an Earth based master clock setting common time, which is what your GPS receiver can report to you. The GPS system is thus a one-system and as such has no use for the special theory of relativity. In this one-system, the position of moving satellites are recorded by one master observer at rest on Earth and satellite clocks are synchronized with the master clock to UTC Universal Central Time (with nanosecond precision). There are no observers, sitting in the satellites making observations in moving inertial systems requiring coordination using the special theory of relativity. This is a one-master one-system for which the special theory of relativity has nothing to contribute.

This is yet another observation that GPS does not depend on the special theory of relativity.

PS We may compare with Deng Xiaopin's idea of one country - two systems, which we now see is collapsing in Hong-Kong. A one-system appears to be more stable, which is also what we expect from GPS.