### Analysis of Relativistic Error Effect on the GPS Time and the Receiver Position Accuracy

#### Abstract

The Global Positioning System (GPS) is a worldwide satellite-based navigation system. The usefulness of the system for civilian users was even more pronounced, with the elimination of Selective Availability (SA) on May 2nd, 2000. The GPS accuracy relies in the precise knowledge of the satellite orbits and the time. Each GPS satellite carries an atomic clock to provide timing information for the signals transmitted by the satellites. The clocks are oscillating at a particular frequency. The oscillator clock time and the true time differ from each other both in scale and in origin. The true time reflects the atomic clock time inU.S., which also differs by 15 seconds from Coordinated Universal Time (UTC) by 2010. However, the GPS true time is calibrated byU.S.atomic time. The true time reflects the fact that the times indicated on satellite and receiver clocks are not perfectly uniform and must be calibrated by master atomic clocks on the earth. The typical error in GPS positioning due to the non synchronisation of satellite to UTC is 100 nsec and the corresponding pseudorange error is 30 meters. The GPS satellites revolve around the earth with a velocity of 3.874 km/s at an altitude of 20,184 km. Thus on account of its velocity, a satellite clock appears to run slow by 7 microseconds per day when compared to a clock on the earth’s surface. But on account of the difference in gravitational potential, the satellite clock appears to run fast by 45µs per day. The net effect is that the clock appears to run fast by 38 µs per day. This is an enormous rate difference for an atomic clock with a precision of a few nanoseconds. In this paper, the satellite clock error and the relativistic error effect on the navigation solution are carried out by collecting the several days of dual frequency (1575.42.MHz and 1227.6 MHz) GPS receiver data from the Andhra University Engineering College, Visakhapatnam (Latitude/Longitude 17.73oN/83.32oE). From the results an absolute maximum of 50.825µs satellite clock error is observed which corresponds to a pseudorange of 15.247 Km and an absolute maximum of 14.427ns relativistic error is observed which corresponds to a pseudorange of 4.328m.

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