From theory to practice, the fundamentals of GNSS positioning
Satellite tracking is part of everyone’s daily life. With a wide range of applications, its operation is often not well known. How does it work?
The origin of "GPS"
The GPS (Global Positioning System) term derives from the American army. In 1973, it created the first satellite positioning technology. Originally reserved for strictly military use, GPS will be freely available for civilian applications from 2000. Over the years, it has become an essential part of society.
And if the common language often uses the only term “GPS” to refer to this technology, it is more accurate today to talk about GNSS (Global Navigation Satellite System). Indeed, other constellations and positioning systems have joined the American GPS.
oday, there are thousands of satellites orbiting the Earth. Among them, we can mention the satellites of the American GPS constellations, Russian GLONASS, European GALILEO, Chinese BEIDOU… All are not yet 100% operational. This is the case of GALILEO and BEIDOU, which should be so in 2020.
The operating principle is based on the intersection of electromagnetic signals emitted by satellites. The user receives satellite signals defining satellite user segments whose geometric intersection allows location.
In order to be permanently functional everywhere and at all times, current solutions use signals from several constellations. This cross-referencing of information allows for better accuracy, near instantaneous convergence times and 24/7 availability around the globe.
The accuracy of the receivers is at best metric. Various calculations and strategies are used to improve this accuracy. TERIA is one of the tools for increasing accuracy. It allows the user to obtain centimetric and real-time accuracy.
The arrival of new centimetric solutions makes it possible to address areas of application that are still new: autonomous vehicle guidance, maritime applications, drones, etc.
How it works in 3 steps: 4 satellites for 1 precise position
Step 1 - Satellites serve as reference points.
The nominal operational constellations GPS, GALILEO, GLONASS, BEIDOU…, consist of several dozen satellites operating at an altitude of nearly 20,000 km in orbits equitably distributed to cover all continents.
Thanks to this coverage, the user is able to see simultaneously between five and thirty-five satellites depending on his position on Earth.
Each constellation is monitored and controlled by control stations that update the information (positions, ephemeris and time correction) of all satellites. These then broadcast their parameters to the Earth by electro-magnetic waves carrying coded signals.
Step 2 - The satellite distance / GNSS antenna, measured continuously
GPS, GALILEO, GLONASS, BEIDOU… satellites have atomic clocks that provide extremely accurate dating. The time information is placed in the codes broadcast by the satellite. The receiver then continuously determines the time at which the signal was broadcast. The signal also contains orbitography data so that the receiver can calculate the location of the satellites. This is known as navigation information.
The GNSS receiver (telephone, topography, agricultural / automotive / aeronautical guidance system…) uses the time difference between the time of reception and broadcasting of the signal to determine the distance between the receiver and the satellite. The receiver multiplies the travel time by the speed of light to calculate the receiver/satellite distance.
Thus, a GNSS mobile that receives signals from at least four satellites can accurately locate in three dimensions any point in the visibility of the satellites. To do this, it will use the intersection of these satellite-receiver vectors.
Even in the absence of obstacles, however, there are still significant disturbance factors that require correction of the calculation results. The first is the crossing of the lower layers of the atmosphere, the troposphere. The presence of moisture and changes in tropospheric pressure modify the refractive index and thus the speed and direction of propagation of the satellite signal.
Step 3 - The position is calculated by solving spherical intersection equations.
The 3rd and last step is to determine a precise position. The receiver will be able to trilate the position from the distance data collected between the receiver and several satellites.
A GNSS receiver needs a minimum of 4 satellites to be able to calculate its own position. Three satellites will determine latitude, longitude, and height. The fourth one synchronizes the receiver’s internal clock.
To popularize the demonstration, we will place ourselves on a 2D map. The principle will be the same for moving to 3D space. The circles will only be replaced by spheres.
Suppose the receiver is 25,000 km from a given first satellite. This means that the receiver can be anywhere on the 25,000km diameter circle, with the satellite as the centre.
The box will also receive a signal from a second satellite at 20,000 km for example. He will conclude that he is also on this circle. Its exact position will be at the intersection of the two circles, i.e. two possibilities.
In order to determine which of these possibilities is correct, the signal of a third satellite is required. For the demonstration we will imagine it with a diameter of 15 000km.
At the intersection of these three circles, there is only one possible point in a 2D plane. We just geolocated our receiver.
Scan from 2D to 3D
To switch to 3D, a 4th satellite would therefore be necessary, because the intersection of 3 spheres gives 2 points. However, it can be dispensed with because only one of the two points is geometrically coherent. And so, there would still be a possibility to eliminate.
However, the use of a 4th satellite is necessary, as it provides solutions in the measurement of signal propagation time. Indeed, ground-based GNSS receivers only have summary clocks that do not have the accuracy of satellite atomic clocks. The result is desynchronization, which must be resolved to properly control the receiver-satellite distance and then obtain a correct geolocation.
Towards centimetric accuracy
The example refers to the use of four satellites, but GNSS receivers are able to track many satellites at once (stations, topography, telephone, navigation device…). This improves accuracy, convergence time, coverage and reduces the possibility of errors.
On average, a receiver can catch 7 satellites from the same constellation (14 satellites on GPS – GALILEO). For a centimetric positioning, at least 5 satellites are required.
Currently, 129 positioning satellites are active and available for civil applications:
For applications where centimetric accuracy is essential (autonomous vehicle, bathymetry, topography, etc.), this is not sufficient. Indeed, distortions in signal propagation can lead to errors of several meters. This is particularly the case when crossing atmospheric layers.
Some solutions such as TERIA allow to correct these measurement errors and provide a centimetric positioning of 1-2cm in real time.
They are based on networks of receivers all connected to computer centres, which model all errors and return corrections (PPP, PPP-RTK, NRTK and RTK) in real time to users.
Towards centimetric accuracy
In order to locate an object on Earth mathematically in a unique way, it is necessary to define a geodetic datum frame that is expressed by geographical coordinates that are most often: latitude, longitude and altitude (or elevation) relative to mean sea level (orthometric elevation) or relative to a reference surface, usually ellipsoidal (ellipsoidal elevation).
Historically, geodetic systems were determined from angular measurements and some length measurements. A geodetic system was associated with a geodetic network, a set of points whose coordinates had been determined from terrestrial measurements.
Space technology has made it possible to define global geodetic systems. The most widely used geodetic system in the world is the WGS84 (World Geodetic System 1984), combined with the American GPS positioning system.
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