Positioning and reference/ Geodesy

Positioning and reference/ Geodesy

Cartesian and three-dimensional geodetic coordinates

The best known terrestrial reference systems are :

- NAD83 (North American Datum 1983);

- WGS84 (World Geodetic Datum 1984);

- ITRS (International Terrestrial Reference System).



The terrestrial reference system is materialized on the territory with the help of landmarks. All these markers form the geodetic network. In Quebec, the Ministry of Natural Resources ensures the integration and dissemination of information related to the geodetic network.

Today, the measurements used to determine the position of a landmark in a terrestrial reference system or to position oneself in it come mainly from these four space techniques :

- VLBI (Very Long Baseline Interferometry): very long baseline radio interferometry;

- SLR (Satellite Laser Ranging): satellite laser telemetry;

- DORIS (Doppler Orbitography by Radio-positioning Integrated on Satellite): positioning system based on the Doppler effect;

- GPS (Global Positioning System), probably the best known (global positioning system).

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The field of gravity

The gravity field plays an important role in the shape of the Earth. The Earth is a complex plastic body composed of solid, semi-rigid, and liquid parts. Since these different parts are not made of identical materials, the gravitational field differs from one place to another.

The measurement of gravity makes it possible to define another surface representing the shape of the Earth: the geoid. This surface gives an approximation of the mean sea level. It is made up of hollows and bumps caused by the uneven distribution of masses of various densities.

Moreover, being a plastic body, the shape of the Earth changes continuously. It is subject to different internal and external forces.


For a person, these changes may be perceptible, such as the tide, or imperceptible, such as the land tide (amplitude of about 30 cm) and the drift of lithospheric plates (tectonics). To track the movement of the plates, a four-dimensional reference frame (three axes and time) independent of the earth's surface is required. The International Terrestrial Reference System (ITRS) has this temporal capability. Unlike the ITRS, the NAD83 system is fixed to the North American tectonic plate. The position of the points is invariable in time unless they are located on an unstable part of the plate.

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The GPS

In the past, the stars allowed navigators to position themselves. Today, GPS satellites have replaced the stars and unlike the stars, satellites are accessible 24 hours a day despite the clouds.

The arrival of the GPS (Global Positioning System) has revolutionized the way of doing things in the field of positioning and navigation. Set up, controlled, and operated by the United States Department of Defense (DoD), the GPS system is based on a constellation of satellites that allow a position to be determined at any time and in any place on Earth. This constellation is made up of at least 24 satellites operating at an altitude of approximately 20,200 km.





Each satellite transmits on two carrier waves different coded messages containing civil and military information, including its position in the WGS84 terrestrial reference system. Civilian information is broadcast on a single carrier wave.

The principle for obtaining a position is very simple. Using the coded message transmitted by a satellite, a GPS receiver determines the time it took for the signal to travel the distance to that satellite, approximately 0.07 seconds. By multiplying the time obtained by the speed of light (300,000 km/s), the receiver can determine this distance. Thus, measurements on four satellites allow the position of the receiver to be determined. The accuracy of this position varies from ten meters to one centimeter and better depending on the type of receiver used.

When calculating its position, the GPS receiver synchronizes its clock with the atomic clocks of the GPS satellites. Once synchronized, the receiver displays the time with a very high degree of accuracy and in turn, becomes a very precise time reference.

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Consumer receiver

The vast majority of users of GPS receivers have a positioning need of the order of ten meters. This is the accuracy obtained with a single receiver reading the coded message from a minimum of four satellites.

Receiver for differential positioning

Another level of accuracy is between 0.5 and 5 meters. To obtain it, it is necessary to read the coded message with two GPS receivers simultaneously. This is called differential positioning.

Receiver for carrier wave positioning

Carrier wave positioning is the most accurate, ranging from 30 cm to better than one centimeter. Instead of reading the coded message with two receivers, the receivers measure the wave that carries the coded message. Usually, these are specialized receivers. However, this method is very sensitive to obstructions that can cut off the signal.

Differential positioning and carrier wave positioning requires the processing of data collected by both receivers. 

This processing can be done in specialized software once all the data has been collected, commonly called post-processing, or in real-time if there is a communication link between the two receivers. 

This link is used to transmit data from one receiver (called the base) to the other. The receiver that receives the data (called the cell phone) has software to process the received data on its own. 

The accuracy of the position can vary from a centimeter to about two meters depending on :

- the distance between the two receivers;

- the time it takes to capture the data;

- the type of receiver used in the field;

- the way the data is processed.

The Ministère des Ressources Naturelles has set up permanent GPS reference stations throughout Québec to serve as a base for applications requiring differential positioning or carrier wave positioning. These stations allow positioning by post-processing and the majority of them offer real-time centimetric positioning by cellular telephony.

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Why use geodesy and GPS?

Although little known to the general public, geodesy is the basis of everything related to terrestrial positioning.

 A reference system resulting from geodesy allows to position oneself and then to position different works in a common reference frame.

 Its infrastructure of points (geodetic network) is indispensable not only for the precision and homogeneity of maps but also :

- to navigation (land, sea, or air);

- geophysics;

- Space science;

- Atmospheric sciences;

- Prospecting;

- knowledge of continental drift;

- monitoring of oceanic phenomena;

- everything related to earth sciences.

Thus, for geophysics, geodesy provides :

- information for the study and modeling of the deformation of the Earth's crust over time;

- Gravimetric data to study irregularities in the distribution of crustal density and its variation over time.

For space sciences, geodesy provides :

- the geometry of the gravitational field necessary for the prediction of satellite orbits. This contribution will further increase in view of the current and future exploitation of increasingly efficient space resources.

The advent of geographic information systems has exploded the need for location in a single repository in order to integrate and share data from different sources.

Thanks to the advent of GPS, the notion of positioning has become democratized.

There is a multitude of fields in which this cutting-edge technology is used with or without the help of a geodetic network :

- air transport

- cartography

- surveying

- navigation

- telecommunications

- remote sensing

- regional/recreotourism development

- civil security

- agriculture

- forestry

Pilots use GPS to guide their aircraft.

Geodetic points are used for photogrammetric purposes, thus for map-making and the collection of data from geographic information systems.

GPS and geodetic points are used, among other things, for topographic surveys, subdivisions, and infrastructure construction (bridge, road, dam, etc.). Cities and other service agencies use them to locate their infrastructures such as power lines, fire hydrants, and even streets.

At sea, fishermen and sailors use them as a guide to navigate or to locate places.

GPS receivers are used to synchronize telecommunications networks.

The addition of GPS receivers aboard low altitude satellites allows for more precise measurement of their location and more accurate analysis of their orbit.

Hikers, campers, and hunters use it to avoid getting lost.

It is used to track vehicles in real-time (fire, ambulance, or other 911 services), to locate persons in distress, etc.

Farmers use it to better manage their farms (precise application of seeds and herbicides, etc.).

Foresters use geodetic points and GPS to carry out forest inventories and to locate forest roads.