An alternative methodology for the mathematical treatment of GPS positioning

The basic operation of GPS involves the detection and measurement, with a GPS receiver, of data carried on electromagnetic signals transmitted by the earth-orbiting GPS satellite constellation and the computation of the travel time of these received signals. The time measurements are converted to distance measurements, which can then be used to compute the unknown position and time of the receiver from the known positions of the satellite transmitters and signal transit times. To solve the problem, at least four satellite’s measurements are needed to find user position and receiver time offset. A set of nonlinear navigation equations are formed. These nonlinear equations can be solved using iterative techniques based on linearization by Taylor model. This method is approximate since only the first term of Taylor model is used. In this paper a simple alternative method is developed to solve the GPS navigation equations directly without linearization and iteration. A practical study was done to evaluate the new model. Performance analysis was conducted using data collected by Trimble 4000SSE dual frequency receiver. The results indicated that the alternative methodology is simple, fast, and accurate as compared to Taylor method.