Signal-in-Space Ranging Error (SISRE) is the main component of UERE. The positioning accuracy can be approximated by the formula: .SISRE reflects the influence of satellite broadcast ephemeris deviation on user ranging measurement.
Fig. GPS User SIS Ranging Error
The SISRE is the root mean square of the instantaneous SISRE value of all spatial points spread evenly across the satellite’s coverage on the surface of Earth. It can be calculated by the satellite's orbital deviation on radial, tangential and normal direction and clock offset using the following equation:
Where c is the speed of light, T is the clock offset, R is the orbit error on radial direction, A is the orbit error on along tracking direction, and C is the orbit error on cross direction. The value of and is shown in table 1.
Tab.1 The value of α and β
Fig.1 Diagram of orbit errors in Radial, Along, Cross direction and Signal-In-Space range errors formula derivation