Mathematical Modelling of The Global Positioning System Tracking Signals

Abstract: Recently, there has been increasing interest within the potential user community of Global Positioning System (GPS) for high precision navigation problems such as aircraft non precision approach, river and harbor navigation, real-time or kinematic surveying. In view of more and more GPS applications, the reliability of GPS is at this issue. The Global Positioning System (GPS) is a space-based radio navigation system that provides consistent positioning, navigation, and timing services to civilian users on a continuous worldwide basis. The GPS system receiver provides exact location and time information for an unlimited number of users in all weather, day and night, anywhere in the world. The work in this thesis will mainly focuss on how to model a Mathematical expression for tracking GPS Signal using Phase Locked Loop filter receiver. Mathematical formulation of the filter are of two types: the first order and the second order loops are tested successively in order to find out a compromised on which one best provide a zero steady state error that will likely minimize noise bandwidth to tracks frequency modulated signal and returns the phase comparator characteristic to the null point. Then the Z-transform is used to build a phase-locked loop in software for digitized data. Finally, a Numerical Methods approach is developed using either MATLAB or Mathematica containing the package for Gaussian elimination to provide the exact location or the tracking of a GPS in the space for a given a coarse/acquisition (C/A) code.