Global Positioning System (GPS) is a satellite-based navigation system that provides a three-dimensional user position (x,y,z), velocity and time anywhere on or above the earth surface. The satellite-based position accuracy is affected by several factors such as satellite clock error, propagation path delays and receiver noise due to which the GPS does not meet the requirements of critical navigation applications such as missile navigation and category I/II/III aircraft landings. This paper emphasizes on modelling the satellite clock error and orbital solution (satellite position) error considering the signal emission time. The transmission time sent by each satellite in broadcast ephemerides is not accurate. This has to be corrected in order to obtain correct satellite position and in turn a precise receiver position. Signal transmission time or broadcast time from satellite antenna phase center is computed at the receiver using several parameters such as signal reception time, propagation time, pseudorange observed and satellite clock error correction parameters. This corrected time of transmission and broadcast orbital parameters are used for estimation of the orbital solution. The estimated orbital solution was validated with the precise ephemerides which are estimated by Jet Propulsion Laboratory (JPL), USA. The errors are estimated for a typical day data collected on 11^th March 2011 from dual frequency GPS receiver located at Department of Electronics and Communication Engineering, Andhra University College of Engineering, Visakhapatnam (17.73°N/83.319°E).