The task of localizing a smartphone in a building can be solved in various ways. The most simplest one may be triangulation, where the signal strength information is first transformed into distance estimates between smartphone and beacons and, afterwards, a least-squares approach delivers the position estimate. In ideal environments with only slightly erronous measurements the approach works well.
However, in real environments BLE RSSI signal measurements tend to have large errors and thus triangulation will fail. In the upper example the system tries to combine the observations from different beacons, where a subset of beacons have very erronous oberservations. The result is large localization error. In comparison the result of a grid-based approach is depicted. Without the need of identifying the outliers the grid-based approach remains a robust estimator. Its core implementation models all signals as random variables and tries to estimate the most likely position given all observations.