L Overview of Basic Relativistic Theory 3.1 Special Relativity Why have to consider relativistic effect on GPS L. Lorentz transformation measurement? 2. Time dilation Velocity of GPS (TIME) 3. Lorentz Contraction Earth rotation(SPACE) 4. Second-Order Doppler Effect 5. Mass relation 3.2 General Relativity I. Relevant relativistic Effects on gps The theory of special and general An accelerated I. Relativity Affecting to Satellite Orbit relativity must be taken into RF (each GPS) 2. Relativity Affecting to Satellite Signal Relativistic effects are relevant for 1. Satellite orbit 2. Satellite signal propagation 3. Relativity Affecting to Satellite Clock 4. Relativity Affecting to Receiver Clock un, moon, all other masses in the solar system( negligible). The correction is usually performed by the receiver software at rest. in the the gravitational field of the earth must be considered earth Two Center: The phase center of the antennas is a point to which the radio signal measurement referred and generally is not identical with the geometric antenna center. 4. Antenna phase center offset variation azimuth, and the intensity of the satellite signal and is different for LI and L2 Two effects offset The precision of an antenna should be based on the antenna phase center variation and not on the offset.4 Why have to consider relativistic effect on GPS measurement? • Velocity of GPS (TIME) • Earth rotation (SPACE) 3.1 Special Relativity 1. Lorentz Transformation 2. Time Dilation 3. Lorentz Contraction 4. Second-Order Doppler Effect 5. Mass Relation I. Overview of Basic Relativistic Theory 3.2 General Relativity II. Relevant Relativistic Effects on GPS The theory of special and general relativity must be taken into account. Relativistic effects are relevant for 1. Satellite orbit 2. Satellite signal propagation 3. Satellite and receiver clock 4. Sun, moon, all other masses in the solar system ( negligible). RF(relatively) at rest: in the center of the earth. With respect to general relativity, Ash shows that only the gravitational field of the earth must be considered. An accelerated RF (each GPS) 1. Relativity Affecting to Satellite Orbit 2. Relativity Affecting to Satellite Signal Example: 3. Relativity Affecting to Satellite Clock 4. Relativity Affecting to Receiver Clock The correction is usually performed by the receiver software. 4. Antenna Phase Center Offset & Variation Two Center: The phase center of the antennas is a point to which the radio signal measurement is referred and generally is not identical with the geometric antenna center. Results: The offset depends on the elevation, the azimuth, and the intensity of the satellite signal and is different for L1 and L2. Two effects: • offset • variation of the antenna phase center The precision of an antenna should be based on the antenna phase center variation and not on the offset