Technical Problems
SLAM can be thought of as a chicken or egg problem: An unbiased map is needed for localization while an accurate pose estimate is needed to build that map. This is the starting condition for iterative mathematical solution strategies. In comparison, the atomic orbital model may be seen as a classic approach of how to communicate sufficient results under conditions of imprecise observation.
Beyond, the answering of the two characteristic questions is not as straightforward as it might sound due to inherent uncertainties in discerning the robot's relative movement from its various sensors. Generally, due to the budget of noise in a technical environment, SLAM is not served with just compact solutions, but with a bunch of physical concepts contributing to results.
If at the next iteration of map building the measured distance and direction traveled has a budget of inaccuracies, driven by limited inherent precision of sensors and additional ambient noise, then any features being added to the map will contain corresponding errors. Over time and motion, locating and mapping errors build cumulatively, grossly distorting the map and therefore the robot's ability to determine (know) its actual location and heading with sufficient accuracy.
There are various techniques to compensate for errors, such as recognizing features that it has come across previously, and re-skewing recent parts of the map to make sure the two instances of that feature become one. Some of the statistical techniques used in SLAM include Kalman filters, particle filters (aka. Monte Carlo methods) and scan matching of range data.
Read more about this topic: Simultaneous Localization And Mapping
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