Research Paper : Computation of Time Error in GPS Signals: Using Schwartzchild Time Dilation Equation

T.S. Oluwadare... [et.all];

Global Positioning System (GPS) is a satellite based navigation
system that can be used to locate positions anywhere on earth and proper timing determination. The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. As a result of their motion and being in the earth gravitational field, these clocks are subject to one of the relativity effects known as time dilation and without carefully accounting for this effect, the system would not work. This research work discussed the concept and effect of special and general relativity on GPS navigation as well as using Karl Schwarzschild time
dilation equation to estimate time error. Signals exchanged by atomic clocks at different altitudes are subject to general relativistic effects described using the Schwarzschild metric and neglecting these effects would make the GPS errorfull.
Applying the Kerl Schwarzchild time dilation equation in the obtained GPS data set, as measured at the orbit of the satellite, we found a difference between the proper time and the coordinate time whish gave us the dilated time within the
range of 0.7-0.9 seconds. The dilated time for signal to travel from the orbit to the receiving station is what we regarded as Time Error.