diff --git a/geographie-informatique.pdf b/geographie-informatique.pdf
index d9f5d0c..ec49ebc 100644
Binary files a/geographie-informatique.pdf and b/geographie-informatique.pdf differ
diff --git a/geographie-informatique.tex b/geographie-informatique.tex
index c536da3..41cf5e3 100644
--- a/geographie-informatique.tex
+++ b/geographie-informatique.tex
@@ -1532,6 +1532,64 @@ L'autre solution est de disposer d'un téléphone permettant un partage de conne
De plus, l'accès au positionnement satellite est possible permettant là encore une cartographie de meilleure qualité. Mais, il faut rester prudent, tant le positionnement est encore aléatoire si on ne veut pas passer par une géolocalitation par wifi, généralement possible uniquement sous condition de transmission des données à Google. Avec un positionnement uniquement satellitaire, la précision reste limitée, comme on va le voir.
\subsubsection{Positionnement GPS}
-Le monde du positionnement par GPS mériterait un ouvrage à lui seul tant il est vaste.
+Le monde du positionnement par GPS mériterait un ouvrage à lui seul tant il est vaste. Les quelques mots que nous allons en dire n'ont pour prétention que d'évoquer le sujet à travers quatre mesures réalisées par comparaison avec l'estimation relative de leur positionnement.
+
+L'idée est d'utiliser un smartphone pour effectuer un positionnement GPS à l'aide de trois application libres : GPSTest, Here GPS Location et phyphox. Les deux premières ont pour unique but de donner la position par GPS. La dernière est une application permettant d'accéder à de nombreux capteurs du smartphone, dont le GPS.
+
+Les mesures ont été faites en deux points du parc Gallet. Pour le premier, seul Here GPS Location a été utilisé et pour le second les trois logiciels l'ont été.
+
+Les résultats sont donnés à la figure \ref{figure:positionnementgps}.
+
+\begin{figure}
+ \centering
+ \begin{subfigure}{\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{images/GPS_umap.eps}
+ \caption{Les points de mesures et leur estimation.}
+ \label{figure:umap}
+ \end{subfigure}
+
+ \smallskip
+ \begin{subfigure}{0.24\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{images/GPS_GPSTest.eps}
+ \caption{GPSTest}
+ \label{figure:gpstest}
+ \end{subfigure}
+ \begin{subfigure}{0.24\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{images/GPS_HereGPS_1.eps}
+ \caption{HereGPS 1}
+ \label{figure:heregps1}
+ \end{subfigure}
+ \begin{subfigure}{0.24\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{images/GPS_HereGPS_2.eps}
+ \caption{HereGPS 2}
+ \label{figure:heregps2}
+ \end{subfigure}
+ \begin{subfigure}{0.24\textwidth}
+ \centering
+ \includegraphics[width=\textwidth]{images/GPS_Phyphox.eps}
+ \caption{Phyphox}
+ \label{figure:phyphox}
+ \end{subfigure}
+ \caption{Positionnement GPS : comparaisons.}
+ \label{figure:positionnementgps}
+\end{figure}
+
+On reconnait sur la figure \ref{figure:umap} la partie du parc Gallet entre les deux zones de jeu. En bleu les points mesurés et en rouge l'estimation relative de leur position par rapport au distances à différents points déjà placés. La mesure de droite est unique, réalisée avec Here GPS Location et correspond à la mesure présente à la figure \ref{figure:heregps1}. La mesure de gauche est double, c'est-à-dire que deux points sont superposés : celui fait avec GPSTest et au-dessus celui fait avec Here GPS Location. Ils correspondent respectivement aux figures \ref{figure:gpstest} et \ref{figure:heregps2}. Enfin, la mesure de la figure \ref{figure:phyphox} n'est pas présente sur la carte, car elle se situait au centre de la ville de la Chaux-de-Fonds.
+
+\medskip
+Ces figures questionnent plusieurs choses~:
+\begin{itemize}
+ \item le positionnement relatif, tout d'abord, puisqu'on voit que le décalage entre celui-ci et les mesures GPS est relativement important. La question est donc de savoir dans quelle mesure on peut se fier à un positionnement relatif. Une expérience intéressante pour en juger serait d'effectuer des mesures de positionnement depuis des points établis avec précision comme des bâtiments vers un point particulier comme l'intersection d'un chemin et de la positionner par triangulation. On pourrait ainsi juger de la précision de l'estimation visuelle et en faire un estimation géométrique. Géométrique, car relative à des points qui eux-mêmes ne sont pas forcément correctement placés du point de vue des coordonnées géographiques.
+ \item le positionnement GPS, ensuite, car il est entaché d'erreur. Généralement, il est admis que sans corrections Wifi, celui-ci a une précision de plusieurs mètres (généralement deux ou trois). Il est donc très difficile de dire si les points GPS relevés fournissent un positionnement correct sans recourir à une triangulation Wifi. Or celle-ci est aujourd'hui essentiellement propriétaire (Google) et soumise à l'acceptation d'un traçage du téléphone que le RGPD (Référentiel Généralisé de Protection des Données) européen rend illégal, puis il spécifie que chacun doit pouvoir le refuser sans que cela nuise au service fourni. Sauf donc à utiliser un tel service qui méprise la loi européenne, il n'est pas encore possible d'effectuer un positionnement Wifi améliorant la précision du GPS\footnote{Des alternatives sont en cours de construction, notamment venant de la part de Mozilla qui cherche à fournir une prestation identique compatible avec le RGPD.}.
+ \item la disponibilité des valeurs de marge d'erreur pour les outils GPS utilisés. Dans quelle mesure, peut-on estimer cette marge d'erreur et quelle action peut-on avoir sur celle-ci en utilisant par exemple un plus ou moins grand nombre de satellites. GPSTest est a cet égard intéressant, puis il spécifie les satellites utilisés. Un travail intéressant pourrait donc être d'effectuer des mesures avec un nombre variable de satellites pour les comparer entre elles et de mener avec les élèves une réflexion sur le positionnement satellitaire.
+\end{itemize}
+
+La pertinence de l'utilisation du positionnement relatif apparait rapidement quand on tente de pacer des éléments sur une carte. Ce travail permet donc de mieux apprécier celui des géomètres qu'on voit parfois au travail avec leur goniomètre et dont on se demande vaguement le pourquoi de l'utilisation de cet appareil. Une introduction à la goniométrie pourrait être très intéressante dans le cadre de celle de la cartographie avec des élèves de niveau lycée.
+
+Remarquez enfin que la carte de la figure \ref{figure:umap} a été réalisée avec un logiciel en ligne dédié à la création de cartes à usage collectif ou personnel à partir du fond cartographique d'OSM, nommé Umap\footnote{Voir~: \url{https://umap.openstreetmap.fr/fr/}}. La création de cartes avec celui-ci est décrite dans le corps du présent travail et nécessiterait une annexe approfondie à lui tout seul. Il est cependant très aisé de faire rapidement une carte avec umap et en apprendre l'usage des bases est certainement nécessaire.
\end{document}
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