Applied Science and Computer Mathematics

Higher order multi-point iterative methods for finding GPS User Position

  • By Kalyanasundaram Madhu
  • Applied Science and Computer Mathematics, 1(1) (2020): 15-23


The basic operation of Global Positioning System 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 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 is formed. These nonlinear equations can be solved using iterative techniques based on newly developed Newton type methods. One of these methods is most efficient and converges faster than other compared iterative methods. A practical study was done to evaluate the new models. El-naggar performance analysis was conducted using data collected by Trimble 4000SSE dual frequency receiver. The results indicate that the improved Newton type methods are simple, fast, and accurate as compared to Newton’s method.