So far the discussion was only the localization of a single object, but often one seeks to localize many objects. The classical example of this problem is robotic mapping.
In the localization algorithms before we assumed that the robot knew the map of the environment a priori. But what if it does not? Then it has to generate such a map itself. Humans have already proven their mapping skills with maps of the whole planet. Now we will give a short introduction how robots can do the same.
This problem is often referred to as simultaneous localization and mapping (SLAM). The robot does only construct a map, but it must do this without knowing where it is. A problem is that the robot may not know in advance how large the map is going to be.
The most widely used method for the SLAM problem is EKF. It is usually combined with landmark sensing models and requires that the landmarks are distinguishable. Think of a map where you have several distinguishable landmarks of unknown location. The robot now starts to move and discovers more and more landmarks. The uncertainty about the location of the landmarks and itself increases with time. When the robot finds one landmark he already discovered earlier again the uncertainty of its position and of all landmarks decreases.
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