GEOFFREY BLEWITT: BASICS OF THE GPS TECHNIQUE 1. INTRODUCTION The purpose of this paper is to introduce the principles of GPS theory, and to provide a background for more advanced material. with that in mind some of the theoretical treatment has been simplified to provide a starting point for a mathematically literate user of GPS who wishes to understand how GPs works, and to get a basic grasp of GPs theory and terminology. It is therefore not intended to serve as a reference for experienced researchers however, my hope is that it might also prove interesting to the more advanced reader, who might appreciate some "easy reading "of a familiar story in a relatively short text(and no doubt, from a slightly different angle) 2. GPS DESCRIPTION In this section we introduce the basic idea behind GPS, and provide some facts and statistics to describe various aspects of the global Positionining System. 2.1 THE BASIC IDEA GPS positioning is based on trilateration, which is the method of determining position by measuring distances to points at known coordinates. At a minimum, trilateration requires 3 ranges to 3 known points. GPs point positioning, on the other hand, requires 4 pseudoranges"to 4 satellites This raises two questions: (a)"What are pseudoranges? and(b)"How do we know position of the satellites? Without getting into too much detail at this point, we address second question first 2. 1.1 How do we know position of satellites? a signal is transmitted from each satellite in the direction of the earth. This signal is encoded with the"Navigation Message, which can be read by the user's GPS receivers. The Navigation Message includes orbit parameters (often called the" broadcast ephemeris"),from which the receiver can compute satellite coordinates(X, Y, Z). These are Cartesian coordinates in a geocentric system, known as wGS-84, which has its origin at the Earth centre of mass, Z axis pointing towards the north pole, X pointing towards the Prime Meridian(which crosses Greenwich), and Y at right angles to X and Z to form a right-handed orthogonal coordinate system. The algorithm which transforms the orbit parameters into WGS-84 satellite coordinates at any specified time is called the"Ephemeris Algorithm, which is defined in GPS textbooks e.g., Leick, 1991]. We discuss the Navigation Message in more detail later on. For now, we move on to“ pseudoranges.” 2.1.2 What are pseudoranges? Time that the signal is transmitted from the satellite is encoded on the signal, using the time according to an atomic clock onboard the satellite. Time of signal reception is recorded by receiver using an atomic clock. A receiver measures difference in these times2 GEOFFREY BLEWITT: BASICS OF THE GPS TECHNIQUE 1. INTRODUCTION The purpose of this paper is to introduce the principles of GPS theory, and to provide a background for more advanced material. With that in mind, some of the theoretical treatment has been simplified to provide a starting point for a mathematically literate user of GPS who wishes to understand how GPS works, and to get a basic grasp of GPS theory and terminology. It is therefore not intended to serve as a reference for experienced researchers; however, my hope is that it might also prove interesting to the more advanced reader, who might appreciate some “easy reading” of a familiar story in a relatively short text (and no doubt, from a slightly different angle). 2. GPS DESCRIPTION In this section we introduce the basic idea behind GPS, and provide some facts and statistics to describe various aspects of the Global Positionining System. 2.1 THE BASIC IDEA GPS positioning is based on trilateration, which is the method of determining position by measuring distances to points at known coordinates. At a minimum, trilateration requires 3 ranges to 3 known points. GPS point positioning, on the other hand, requires 4 “pseudoranges” to 4 satellites. This raises two questions: (a) “What are pseudoranges?”, and (b) “How do we know the position of the satellites?” Without getting into too much detail at this point, we address the second question first. 2.1.1 How do we know position of satellites? A signal is transmitted from each satellite in the direction of the Earth. This signal is encoded with the “Navigation Message,” which can be read by the user’s GPS receivers. The Navigation Message includes orbit parameters (often called the “broadcast ephemeris”), from which the receiver can compute satellite coordinates (X,Y,Z). These are Cartesian coordinates in a geocentric system, known as WGS-84, which has its origin at the Earth centre of mass, Z axis pointing towards the North Pole, X pointing towards the Prime Meridian (which crosses Greenwich), and Y at right angles to X and Z to form a right-handed orthogonal coordinate system. The algorithm which transforms the orbit parameters into WGS-84 satellite coordinates at any specified time is called the “Ephemeris Algorithm,” which is defined in GPS textbooks [e.g., Leick, 1991]. We discuss the Navigation Message in more detail later on. For now, we move on to “pseudoranges.” 2.1.2 What are pseudoranges? Time that the signal is transmitted from the satellite is encoded on the signal, using the time according to an atomic clock onboard the satellite. Time of signal reception is recorded by receiver using an atomic clock. A receiver measures difference in these times: