{"id":5181,"date":"2018-05-03T15:21:27","date_gmt":"2018-05-03T13:21:27","guid":{"rendered":"http:\/\/www.sigterritoires.fr\/?p=5181"},"modified":"2018-10-17T12:10:36","modified_gmt":"2018-10-17T10:10:36","slug":"accuracy-uncertainty-and-linear-alteration-of-geographic-data-2","status":"publish","type":"post","link":"https:\/\/www.sigterritoires.fr\/index.php\/en\/accuracy-uncertainty-and-linear-alteration-of-geographic-data-2\/","title":{"rendered":"Accuracy, uncertainty and linear alteration of geographic data (2)"},"content":{"rendered":"

In\u00a0\u00a0the \u00a0previous article<\/a>\u00a0\u00a0\u00a0we discussed the different geographic coordinate systems: astronomical, geocentric and geodetic coordinates.\u00a0Let’s have a look at the possible sources of error.<\/p>\n

Ellipsoidal and real distance<\/strong><\/h2>\n

Now, let’s see a practical case.\u00a0You invest in a GPS that allows an accuracy of 10 cm.\u00a0You map a network that is one kilometre long.\u00a0Question: What is the difference between the actual positions of the first and the last point of the network?<\/p>\n

There are two answers depending on whether you are using geocentric or geodesic coordinates.\u00a0In the first case, the answer is: maximum 10 cm.\u00a0In the second, the answer is: it depends on the place, but, obviously, it is more than 10 cm and you can be surprised to find yourself with tens of meters!<\/p>\n

Let’s see the explanation:<\/p>\n

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The starting point of the network is M and the arrival point is M ‘, you see in the figure that the real distance between the points is M-M’, which you can calculate exactly with geocentric coordinates, and if you use the geodesic coordinates you can calculate the distance P-P ‘, clearly different from the real distance. The more distant the points are, the greater the difference.<\/p>\n

Ellipsoidal precision<\/strong><\/h2>\n

Geodetic systems were designed centuries before the advent of GPS and electronic measurements.\u00a0Since the modelling of the ellipsoid is a mathematical process, it has an intrinsic precision that cannot be exceeded.\u00a0This precision, for geodetic systems which were used throughout the world until the 90s, is a metric precision.\u00a0What does that mean?\u00a0It means that a longitude latitude expressed on an IGN map in Lambert 2 NTF, where a position on a chart in Mercator Europe 50, or a UTM WGS84, has an uncertainty of one meter due, only, to the fact that this calculation locates this place on the ‘ellipsoid\u2019.<\/p>\n

It is because of this precision, largely sufficient with the old positioning means, but unsuitable for satellite positioning, that a new, more accurate geodetic system has been put in place.<\/p>\n

This is the reason for the withdrawal in France of the NTF system and the adoption of the RGF93.<\/p>\n

New global geodetic systems<\/strong><\/h2>\n

There are two types of geodetic systems:<\/p>\n