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[ GPS ]

GPS (Global Positioning System)
(Sistema de Posicionamento Global)

The GPS is a geographical positioning system that gives us the coordinates of any place on Earth, provided that we have a GPS signals receptor. This system was developed by the American Defence Department for civilian and military purposes.

Our position on Earth is determined in relation to the Equator and the Greenwich Meridian, and consists of three figures: latitude, longitude and altitude. So in order to find out where we are on Earth, we only need to know these three figures. For example, airports have three precise coordinates, which are actually written on large signs near the runways. Automatic navigation systems use this information to calculate flight paths between airports.

Nowadays, artificial satellites make it possible for us to have a global positioning system. In total, there are 24 satellites which orbit the Earth every 12 hours sending continuous radio signals. No matter where we are on Earth, four of these satellites are always visible, and with the different signals sent by these four satellites, the GPS receptor calculates the latitude, longitude and altitude of our location.


Latitude is the distance from the Equator measured along the Greenwich Meridian. This distance is measured in degrees and ranges between 0º to 90º North and South. For example, the latitude of Lisbon is 38º 4´N, Rio de Janeiro 22º 55´S, and Macao 22º 27´N.


Longitude is the distance from the Greenwich Meridian measured along the Equator. This distance is measured in degrees and ranges from 0º to 180º East and West. For example, the longitude of Lisbon of 9º 8´W, Rio de Janeiro 34º 53´W and Macao 113º 56´E.


The Earth is a rough spheroid slightly flattened at both poles. In order to determine the altitude of a point on Earth, we use a sphere – a geoid – with a radius of 6378 km. The altitude of any given point on Earth is the vertical distance from the surface of this geoid. For example, the average altitude of Lisbon Airport is 114m, but the average height in Holland is actually negative.

There are several internet pages that contain information about the latitude and longitude of different cities:


The GPS system

The technological framework of the GPS system comprises three sub-systems:

1- satellite sub-system --- space segment. 2- control sub-system --- control segment. 3- user sub-system. --- user segment.

1- The satellite sub-system is composed of 24 satellites that orbit the Earth twice a day at a height of 500km. The orbit of the satellites was designed so that between 5 and 8 satellites could be seen from any given place on Earth. However, in order to calculate your position with relative accuracy, you only need to receive good signals from four of these satellites.

2- The control sub-system is made up of several stations on Earth, where GPS satellite trajectories are monitored and time is recalculated with great precision. Using this data, the computerised system on each satellite recalculates and corrects its position and then corrects the information sent to Earth. The primary control station of the GPS constellation is situated in the United States, in the state of Colorado.

3- The user sub-system consists of a radio receptor with a processing unit that decodes information sent by each satellite in real time and calculates the position. Each satellite sends different characteristics signals at intervals of 30 seconds and 6 seconds. In order to determine position accurately, we need at least 12 and a half minutes of good reception of the different types of signals. The information transmitted by the satellites also includes mathematical techniques that enable the recuperation of information lost in the transmission owing to bad atmospheric and ionospheric conditions. Even so, during periods of high solar activity, most of the information sent by the satellites is lost and, as a result, the information processed by the GPS signal receptors is not reliable. Depending on the type of user and their objectives (civilian or military) the signals from the different satellites can be decoded accordingly. There are in fact two ways of decoding GPS signals: the Precise Mode (military) and the Standard Mode (civilian). The accuracy of these two positioning modes is as follows:

Precise Mode:

Latitude and longitude accuracy: 22 m
Altitude accuracy: 27.7 m
Time accuracy: 200 nanoseconds

Standard Mode:

Latitude and longitude accuracy: 100 m
Altitude accuracy: 156 m
Time accuracy: 340 nanoseconds

The GPS can also function in differential mode, DGPS system. In this case, the GPS signal is stored on computer and later processed, cross-referencing data requested from the Earth stations (control segment). System errors can be eliminated using this process and GPS can be accurate to about 1 metre. This is particularly useful in cartography where spatial coordinates are fixed in time.

There are many excellent web pages with detailed information about the GPS system. Some of the best are:


Rui Dilão
Non-Linear Dynamics Group, IST

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