Introduction Of Gps

By Author: sudarshan singh
Total Articles: 327
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The purpose of this Artical 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.

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.

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, 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, and Y at right angles to X and Z to form a right-handed orthogonal coordinatesystem. The algorithm which transforms the orbit parameters into WGS-84 satellite coordinates at any specified time is called the “Ephemeris Algorithm,” which is defined inGPS textbooks . We discuss the Navigation Message in more detail later on. For now, we move on to “pseudoranges.”

Time that the signal is transmitted from the satellite is encoded on the signal, using the timeaccording to an atomic clock onboard the satellite. Time of signal reception is recorded byreceiver using an atomic clock. A receiver measures difference in these timesNote that pseudorange is almost like range, except that it includes clock errors because the receiver clocks are far from perfect. How do we correct for clock errors?

The satellite constellation is designed to have at least 4 satellites in view anywhere, anytime, to a user on the ground. For this purpose, there are nominally 24 GPS satellites distributed in 6 orbital planes. So that we may discuss the orbit design and the implications of that design, we must digress for a short while to explain the geometry of the GPS constellation. According to Kepler’s laws of orbital motion, each orbit takes the approximate shape of an ellipse, with the Earth’s centre of mass at the focus of the ellipse. For a GPS orbit, the eccentricity of the ellipse is so small (0.02) that it is almost circular. The semi-major axis (largest radius) of the ellipse is approximately 26,600 km, or approximately 4 Earth radii. The 6 orbital planes rise over the equator at an inclination angle of 55o to the equator. The point at which they rise from the Southern to Northern Hemisphere across the equator is called the “Right Ascension of the ascending node”. Since the orbital planes are evenly distributed, the angle between the six ascending nodes is 60o.

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