GPS : Global Positioning System

GPS : Global Positioning System

  Global Positioning System
GPS (Global Positioning System) ou NAVSTAR (Navigation System by Timing And Ranging) was originally an American milirtary system. designed in the 1970s and controlled by the departement of Defense (DoD). It succeded the TRANSIT/NNSS system. operational in 1964.
GPS is a spatial radio-positioning and time transfer system. It provides position. speed and time information to an unlimited number of users throughout the world, in a single global system, whatever the weather conditions.

 1. The system
The civil operation of the GPS system must be considered from the point of view of the system is to identify its capacities as well as possible and to understand its intrinsic limits.

  1.1. The space segment
It includes all the orbital elements of  the positioning device : the platforms, the GPS signal and the navigation messahe. These elements will allow us to consider the modes of exploitation.

  1.1.1. Satellites

The quasi-permanent use of GPS has been possible since february 1994, when the constellation of 21 satellites (+3 in reserve) was declared operational.
These satellites are in quasi-polar orbit, at an altitude of 20,200 Km.
 They are distributed over six orbital planes, offst by 60 degrees (Figure 2).
The peiod of revolution of the satellites is 12 sidereal hours (i.e. 11 hours and 58 minutes). Consequently, we find the same satellite, in the same positions, twice a day (a seemingly futile detail, but often very useful in the planning of field missions!).

  1.1.2. The GPS-signal
The GPS signal is transmitted by the satellites of the constellation in the direction of the surface of the Earth.

It currently consists of two carrier frequencies :
L1 at 1575.42 MHz, and L2 at 1227.60 MHz, whose stability is ensured by otomic clocks. Theyn correspond to wavelengths of 19 cm for L1, and 24 cm for L2. They are generated from a frequency F0, called fundamental, at 10.23 MHz.

These frequencies are modulated by pseudo-random codes :
  C/A  code (Coarse/Acquisition or Clear/Access) modulating L1. It is accessible to all users.
 The P (Precise) code modilating 1.1 and 1.2 is only accessible to authorized users.
 And finally, the navigation message, at 50 Hz, which we present in the next paragraph.

  1.1.3. The navigation message
The navigation message contains fundamental information for the operation of the GPS system. In this case, it contains: :

 The GPS time, defined by the week number and the time in the week. The origin of the GPS time is January 6,1980 at 0:00, the origin of the week on Sunday at 0:00.
 The ephemeris, including the parameters useful for calculating the position of the transmitting satellite to within ten meters..
 The almanacs, contain the same information as the ephemerides, with less precision, and relate to the whole of the constellation.
 The coefficients of a global ionospheric correction model.
 Constellation status information.
 The clock behavior model and the parameters for transforming GPS time into UTC time.

  1.2. The control segment
Made up of five ground stations, thee control segment is responsible for :

 Signal recording and ephemeris prediction.
 Observing the behavior of oscillators, calculating synchronization and clocck drift parameters.
 Collecting weater information.
 The sending to the satellites of information necessary for the composition of the navigation message.

Thanks to these interventions, together with chose of measuring stations spread over the entire globe, the IGS (International GPS Service for Geodynamics) provide access to so-called precise ephemeris allowing very detailed orbitographic calculations (see. §

  1.3. The user segment
this third and last segmeent is obviously the one that interests us the most. At present, the users of the GPS system constitute a very diversified population, both in terms of its objectives and its means.
We will first look at the types of receiver (fairly representative of the public concerned and its needs), then we will look at the absolute or relative position measurement methods.

  1.3.1. Receiver Types
Several types of GPS receivers exist in various rangees of application, price, accuracy and difficulty of implementation. Here we provide a brief overview, divided into two categories: consumer devices, which ca be found in sports and leisure stores, and professional devices.
The category of consumer devices works in single frequency ( L1), by pseudodistance measurement. Currently, a large majority have an input/output in NMEA format which allows them either to export their data to an external tool (PC with GPS integration module for example), or to receive differential corrections from a station fixed transmitter (DGPS mode, often used in maritime navigation for whiich many lighthouses and signals are equipped with a GPS antenna and a radio transmission channel ) :

 Simplle navigation receiver (from 150€ to 300€). 
 navigation receiveer with cartographic tools (from 300€).

As for professional devices, they can work on both frequencies, measuring :

 Single frequency geodesic recerver (up to 15k€)
 Bi-frequency geodesic receiver (from 15k€)

  1.3.2. GPS related services
In the context of large-scaale works, it is possible to use several data sources accessible via the Internet. This is notably the case of the precise ephemerides of the international GPS Service for Geodynamics (IGS).
These data are generally available with a delay of ten days, and allow real deats to be achieved both in the determination of orbits and in that of survey points.
They are obtained thanks to the measurements carried out continuously by hundreds of receiving stations and are generaly provided in the ITRF (International Terrestrial Reference Frame) system. France actively participates in this service thanks to the Permanent Geodesic Network (RGP), which is being densified.
The second GPS -related sevice is the US Coast Guard Navigation Center This service provides multiple information on the constellation: satellite status, recent failures , description of orbit files,etc  …

 2. positioning methods
In the previous paragraph, we mentioned ywo familiare of receiver:the first called nagvigation, and the second called geoditic they are distinguished by their acquisition price on the one hand, but also, and above all, by their implementation methodologies. First of all,it is necessary to present the principle of GPS measurement and the different source of errors association with it .

  2.1. Principle of GBS measurement 
The geodetic mrasurement by GPS can be split into two components: the measurement of pseudodistances by observation of the code, and the phase measurement. Each of them has its advantages, its limits and must be linked to the equipment, the desired precision and the operating mode.

  2.1.1. Code Observance
The pseudorange measurement by code observation is based on a correlation by code observation is based on a correlation analysis between the signal emitted by a satellite and the replica generated by the receiver. Thus, the time lag observed between these two signals gives us the time taken by the wave to travel the distance between its point of reception.
The position of the receiver is then calculated by intersection of spheres, hence the need to have at least four nsatellites in visibility.
Such a calculation requires extremely precise tools : stability of the replica of the code generated by the receiver, resolution of the time measurement ( a few tenths of a nanosecond for the best!) …

  2.1.2. Phase observation
Strongn inaccuracies taint the quality of positioning by code measurement. Rather than mzasuring a travel time of the electromagnetic wave, we will focus on determining the phase difference between the received signal and its replica generated by the receiver, the beat phase. Based on the Doppler effect, the variation in the distance between satellite and receiver is then determined.
The essence of the problem is then to determine the number of cycles necessary to cover this distance. This unknown, commonly called the entire ambiguity, is difficult to access, and differentiation methods are used (single; double, triple), depending on the configuration of the observation. However, they have the advantage of reducing the influence of the errors mentioned in paragraph 2.1.4.

  2.1.3. Quality factors
The principle of GPS positioning shows us that constraints exist in terms of constellation distribution.
Indeeed, a bad distribution of the satellites will generate a low precision of positioning. To qualify this geometry, we generally have indicator noted DOP (Dilution Of Precision) and whivh give, at a given moment, an assessment of the weakening of precision for:

 Planimetric positioning: HDOP (Horizontal DOP)
 Altimetric positioning: VDOP (Vertical DOP)
 A determination of time : TDOP (Time DOP)
 3D positioning (with a minimum of three satellites) : PDOP (Position DOP)

Lastly, one often retains a last factor called GDOP (Geometric DOP) which integrates the PDOP and the TDOP. It is usually only accessible on geodetic receivers and requires the visibility of at least four satellites. 
Generally, for positioning by pseudorange and if more than four satellites are visible ( which is most often the case in natural envirenments, but can sometimes be difficult in urbvan areas), the DOP parameters are used to choose the four satellites best placed, so as to affer the best results.

  2.1.4. Multiple sources of errors
GPS measurement errors result from a complex combination of three components :

Noise : Combination of the PRN code and the noise intrinsic to the receiver. these two components are each rated at approximately0 1m.

Biases :
 Selective access (SA: until May 2, yhis voluntary deradation coused a positioning error of around 100m . Differential methods were then the only ines to provide the means to minimize it.
 Satellite clock drift : up to 1m.
 The accuracy of broadcast ephemeris data : 1m.
 The propospheric delay: 1m. Its modeling requires the exploration of this lower layer of the atmosphere, thanks to mzasurements of temperature, pressure and humidity in different  meteorological  conditions.
 The propospheric delay : 10m. The correction coefficients transmitted in the navigation message can only allow the elimination of approximately half of the delay.
Multi-path : due to multiple reflection, on surfaces close to the receiver, which interfere with the direct signal. This component is difficult to detect and avoid.

Faults : 
 Of the control segment, humain or computer, can ccouse errors from one mater to one hundred kilomètres.
 From the user. An errors in  the selection of the datum can amount from one meter to a hundred meters..
 Receiver failure, both hardware and software.

  2.2. Type of positioning based on pseudoranges
Here we discuss positioning methods based on the observation of pseudoranges, that is, the measurement of the C/A code. This is the measurement that can usually be made with navigation receivers. We will refer here to the internal studv at SERTIT ( Regional Service for Image Processing and remote sensing) conducted during the summer of 2000 on the qualification of the capabilities of a GPS navigation receiver, following the lifting of the SA .

  2.2.1. Autonomous positioning
This method consists in obtaining the position of the receiver, in absolute terms, by intersection of the spgheres (Figure4) of emission from each satellite. This  method makes it possible to obtain an average positioning error of about ten meters on the fly.
The method consists in obtaining the position of the receiver, in absolute terms, by intersection of the spheres (Figure 4) of emission from each satellite. This methood makes it possible to obtain an average positioning error of about ten meters on the fly.
The following graph (Fiugure 6) presents the histogram of the vdistribution of the deviations between the instantaneous measurements and the geodetic value (given by the data sheet of the observed point). The announced decametric precision is validated by 99.5% of the measerements.
However, it may be necessary to obtain finer results and the study carried out by SERTIT showed that calculating an average position, over approximately 10 minutes, was a good way of reducing the error on the absolute position. Two elements were considered: first, the temporal behavior of the instantaneous average of the measurements, then the validity of this averagve value with respect to the known coordinates. 
For the first point, we found that an observation period of about  twenty minutes guaranteed absolute convergence of the instrantaneous mean within 1 meter of its final value (Figure 8).
In general,on all the test points obsserved, it can be seen that the measerements are distributed randomly in a circle with an average radius of about eight meters (Figure 7 ).
Consequently, one can thus fully measure the gain of the calculation of the average, minimizing the random character of the bisolated measerement.  
Ton conculude, the accuracy of autonomous positioning is closely related to the accuracy of broadcast ephemerides.
Multiple corresctions are possible to improve the result, but the quality of the receiver used (noise level on the measurements) and the presence of multipaths on the site will be the limiting factors.

  2.2.2. Differential positioning
Differential positioning methods can be applied with all types of equipment (navigation or geodesic) and corne in two main families: post-processing and real-time.
 The first method is the simplest and least expensive; the second is more complex and requires a communication system to transmit the data.
In this type of positioning, it is considered that the main GPS errors (orbital, atmospheric and clock drift) are of the same order of magnitude in the region surrounding the control station (or hub).
This pivot records the measurements and continuously calculates the position of the satellites in visibility. It then determines the differential corrections which are sent, or applied, to all the receivers located in its sector.
This is the so-called position correction method. It nevertheless presents a major constraint : the same satellites must be observed by the two station.
A mask problem can couse this method to fail, which is therefore most often used in the maritime field. In differential positioning, the method of applying corrections to observations is preferable to that of applying corrections to positions.
Whatever the correction method,j whether applied in real time or in post-processing, it remains that the further the mobile receiver is from the pivot, the more the errors at the two locations differ.
Differential positioning then becomes increasingly inaccurate.
There are then three baseline classes:

 Very short bases (less than 5 Km). In this case, a single-frequency (2 ppm) or dual-frequency (1 ppm) receiver can be used indiscriminately, these precision criteria alone being submerged in the overall error report. Practically, the difference will be seen in the initialization time of the receiver. for single frequency, measurement, 5min are required for initialization and 10min  for centimeter determination. In dual frequency, the initialization takes about 30s and calculates a point in 6min.

 Medium bases (from 5 to 20 Km). In metropolitan France, it is quite rare to have to build bases of this order of magnitude, except in the case of very specific work sites. 
Here again, the initialization time will play the decisive role. On a basis of 5 to 10 Km, a single frequency will need 30 to 60min while a dual frequency will onkly require 7 to 15. And if the base value is pushed between 10 and 20 Km, we go to duration of 1 ro 2h, and 15 to30min, respectively.  .

 Long bases (over 20km). It is then very difficult to reasonably fix the entire ambiguities. The observation times and the computation volumes become extremely heavy in these cases.

  2.3. Phase-based positioning type
Phase measerements are usually (at least in surveying) not done alone and are accompanied by code measurements. They can be performed in two modes: static and dynamic. 

  2.3.1. The sstaticn mode
Static GPS consists in observing the phase information at two ^points (at least) for a long period of time (from ojne to severak hours depending on thee type of application).
The remarks set ont in the previous paragraph obvionsly remain valid. The interest of long pbservation times is to be able to take advantage of the evolutions of the geometry of the constellation, thus contributing to an improvement of the solution. 

  2.3.2. The dynamic mode
The dynamic mode is available in several observation methodologies, the ease of implomentation of which is strongly conditioned by the purpose of the measerements..

 Kinelatics. When it is based on the phase measerement, the kinematic mode requires thee complete determination of the ambiguities to obtain decimetric precisions. Formerly, it was necessary to initializee the mobile on a fixed position but now,"on the fly" calculation algoritms are commonly integrated into controllers. It is generaly applied to establish a relationship between physical elements and data collected on board a moving vehicle (plane for aerial shots).

 Semi-kinematic, from English stop-and-Go. This method consists of standing on each of the points to be measured for about ten seconds. Before the rover departs. the full ambiguities must be determined and the rover depart, the full ambiguities must be determined and the rover must maintain lock to at least four satellites. If the lock is lost, the operator must then return to the last correctly measured point and restart thr initialization.
This method is therefore very fast and effective but requires working in clear areas.  .

 Pseudo-kinematics. Similar to the two previous methods, it consists of stationing each point twice, for a few minutes, at least one hour apart. The advantages of two geometrier of the constellation and the comulative measurement times are then combined. However, from a practical and logistical point of view, this method is not often used.

 Fast static. This technique is based on the resolution of ambiguities over very short periods of observation. We then rely on additional information (observation of the P code, or redundant satellites). These surveys must  be taken on short baselines to achieve centimeter accuracy. Very close to semi kinematic acquisition, this technique has the advantage of not requiring locking onto four satellites while movingb between points.
 3. Planning and preparation
The list of GPS signal observation methods clearly shows that it isb imperative to much the type of receiver used, the measerement methodology with the objectives of the field mission. It is also advisable to carry out reconnaissance of the terrain before the measurement compaigns. Thus, the design of the compaign is improved, its effectiveness increased. The interest is above all to avoid bad surprises and to identify the most difficult points to propose an adequate planning.

  3.1. Choice of survey method
It will be noted that the figure above indicates the technique to be used to achieve a given accuracy and not the range of accuracies that a technique makes it possible to obtain. In other words, if the range of precision sought is within the limits of a technique (for example, metric), it will be a question of establishing an order of priority between this desired final precision of the survey, the material and human means available. , the time needed to implement a method.
The suitability of using a semi-kinematic, rapid static, or conventional static GPS survey for a project requiring decimeter to meter level of accuracy depends on the nature of the location and the and the spacing points. Semi-kinematic surveys pose the greatest number of constraints since they require that the paths followed when moving from one point to another be free of any obstacle.
A semi-kinematic survey would therefore be ideal if a large number of points must be positioned in an open area such as a large field for exemple.
Fast static surveys should, as a general rule, be limited to short vector, if centimeter accuracy is desired. For fast semi-kinematic and static surveys, the chance of success are much hisg accuracy over longer distances or when satellite geometry is poor, it may be wiser to use traditional static GPS techniques.
Moreover, it will be noted that the previous figure illustrates the techniques to be used according to planimetric accuracy rather than altimetric accuracy. The corresponding altimetric accuracies depend on the nature of the magnitude. Their relationship is illustrated in paragraph 3.2.3.
The cost of GPS positioning is closely linked to the technique used, which itself depends mainly on the level of accuracy required. The two main variables that influence the costs for the same technique are the observation time required at each location and the cost of the receivers required. As a general rule, the shorter the observation period required at each point, the less costly the survey will be.

₪ 3.2. Choosing a Receiver  
GPS receivers can be rented or purchased. Whatever the case, it is recommended to use only receivers of the same brand for relative positioning, if you want to avoid problems such as systematic errors, complications in data processing and incompatibilities in synchronization. recording of observations often resulting from the use of several different types of receivers. 

The receiver used must be able to collect the observations required by the chosen positioning technique. In autonomous positioning, as in differential positioning based on pseudo-distance observations, a receiver performing only observations from the code is sufficient (note that some receivers only use phase observations to smooth the observations from the code and improve the resulting accuracy).

For semi-kinematic , rapid static , and conventional static GPS surveys , pseudo ranges and phase observations should be used. For short vectors surveyed by conventional techniques, single frequency receivers are sufficient.

In conventional static GPS and for long vectors, when high precision is sought, it is desirable to use dual-frequency receivers which make it possible to correct most of the ionospheric errors. For fast static surveys, it is strongly recommended to use dual frequency receivers since they allow the application of advanced data processing methods to resolve ambiguities and thus offer a much better chance of success.
Choosing a receiver can be a complex process due to the large number of types of GPS receivers now available, the wide range of possibilities offered and the many applications for which they are intended.

Un grand nombre d’éléments dont il faut tenir compte sont énumérés à la figure suivante et devraient faciliter le choix d’un récepteur. Cette liste n’est pas exhaustive et ne vise qu’à faciliter un choix éclairé. Pour chacun des aspects mentionnés les priorités varieront naturellement en fonction de l’application à laquelle le levé est destiné.
On se référera utilement aux publications spécialisées pour obtenir des comparatifs, en termes de prix et de performances, des matériels sur le marché (GPS World, GIS World, XYZ, …)

  3.3. Validation des matériels et procédures
La phase de planification d’un projet GPS devrait comporter des essais des procédures et de l’équipement qui seront utilisés, depuis la collecte des données jusqu’au résultat final, afin de s’assurer qu’ils permettent de satisfaire de manière fiable aux exigences en matière d’exactitude. Toutefois, si un utilisateur a déjà utilisé avec succès les mêmes procédures et le même équipement GPS pour une application semblable, il peut ne pas être nécessaire d’effectuer une nouvelle validation.

Trois composantes principales sont éprouvées dans le cadre du processus de validation : la technique de positionnement adoptée, l’équipement à utiliser et la méthode de traitement retenue. La méthode de positionnement adoptée peut être l’une des techniques décrites précédemment ou encore une procédure plus récente. Quel que soit le cas, on devra vérifier si la méthode permet de répondre de manière fiable aux besoins de l’utilisateur. L’équipement GPS varie grandement en complexité, en coût et en possibilités. On ne peut présumer que les niveaux d'exactitude avancés par les fabricants ou par tout autre utilisateur seront obtenus de façon constante dans toutes les conditions d’exploitation sur le terrain.

Il importe donc de soumettre l’équipement à des essais et de l’évaluer. Pour les mêmes raisons, il importe de mettre à l’essai et d’évaluer le logiciel et les méthodes de traitement.

Le processus de validation offre également l’avantage de permettre aux utilisateurs de détecter et de résoudre les problèmes avant d'entreprendre de coûteux levés, de rationaliser les opérations et de vérifier les exactitudes auxquelles on peut s’attendre avec les procédures mises à l’épreuve.

  3.4. La reconnaissance de terrain
La reconnaissance consiste à vérifier sur place les lieux d'un projet avant d’entreprendre des observations GPS. Il est nécessaire de vérifier si les emplacements conviennent au GPS, l’existence de points géodésiques et les exigences logistiques. Sont énumérées dans le tableau suivant les composantes clés de la reconnaissance d'un terrain.
La reconnaissance sur le terrain a pour résultat final l’obtention d’un ensemble de points prêts pour les observations GPS ainsi que d’une description à jour de chacun des emplacements, de l’information concernant l’accès à ces emplacements et d’une description des différentes mesures particulières à adopter à chaque endroit.

 4. Rattachement de chantiers GPS

Quel que soit le mode d’observation des points GPS et le matériel employé, il est souvent utile de rattacher le levé à un système de coordonnées. Le problème du rattachement de la campagne de mesure se pose de façon d’autant plus cruciale que la précision du résultat final souhaité est élevée.

  4.1. Le changement de système géodésique
Déjà évoqué dans le premier chapitre, le changement de système géodésique regroupe toutes les étapes de calcul nécessaires à l’expression des coordonnées d’un point d’un système vers un autre.

Le moyen le plus simple reste d’utiliser les outils logiciels à disposition de tout utilisateur ayant accès à Internet. Cette recommandation est valable exclusivement pour les mesures réalisées avec un récepteur de navigation, non converties directement par le récepteur.

Pour les mesures réalisées avec des récepteurs géodésiques, la transformation est prise en charge soit pendant la mesure (temps réel), soit au post-traitement.
Une recommandation particulière est à prendre en compte concernant les changements de systèmes à la volée, en particulier pour les récepteurs de navigation. Les paramètres utilisés sont généralement ceux d’une transformation de Molodensky (dadfdxdydz), et sont souvent fournies à des précisions métriques.

La non-maîtrise du calcul de la transformation par le récepteur pousse à recommander l’enregistrement des déterminations des latitudes et longitudes des points dans le système WGS 84. La transformation peut alors être réalisée au bureau, avec des outils plus éprouvés (Figure 11).

  4.2. Considérations pratiques
L’essentiel du travail de rattachement d’un levé GPS doit être réalisé sur le terrain. Ce rattachement peut être effectué dans un système soit global, soit local. Dans tous les cas, un minimum d’observations est à recueillir. Le procédé le plus souvent employé est la colocation de points.
Le principe de rattachement de chantier par observation de points en colocation est relativement simple : il suffit de disposer de quelques points connus dans la zone de travail. Ces points connus, soit en WGS 84 soit dans le système local, permettent de calculer un ajustement des observations sur le réseau de points GPS.
At a minimum, a point must be known , and in this way, one can calculate the values ​​of the three translations allowing to pass from the GPS coordinates to the user coordinates . It is obviously desirable to observe several known points .

Thus, the calculated adjustment will take into account both translations, rotations and scale factors on each axis (also called Helmert transformation). Different types of these transformations are commonly implemented in many commercial or free (downloadable online) software .

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