18 2. Backgrounda model can easily be projected into an indoor scenario, but here, also allowing achange in the opposite direction should also be considered.The last class of mobility models rely on exploiting the behaviour of multiple syn-chronously moving devices. Therefore, they are called Group mobility models. It isfor example plausible to assume, that vehicles on a street that are near to each other,have correlated speed and direction properties. The same holds true for swarms ofanimals or human movement on crowded places.2.3.2 ErrorThe error of a Tracking result sT1can be given in the form of the Root Mean SquareTracking Error(RMS-TE). The RMS-TE between the correct sequence of positionsr1Tand the estimated sequence s1Tis defined as:RM S- T E( s1T, r1T)=tT=1(|| rt, st||)2Twith|| rt, st|| as the 2D or 3D euclidian distance between the real positions rtandst. The performance of a localization system can be given by evaluating the errorover multiple tracking attempts stored in an evaluation corpus C.RM S- LE( C)=1NNc=11TcTc(|| rc,t, sc,t||)2t=1where Tcis the length of a sample from the corpus. This error can also be evaluatedfor the positioning problem by assuming that Tc= 1 for all pseudo-paths of thecorpus. In literature a variant of this error is also given by using the simpler l1-norm:1N1TcLE( C)=Nc=1Tc| rc,t- sc,t|t=1This error should be referred to as the averaged Localization Error evaluated ona collected corpus of tracked paths. All three error variants are given in the unitmeter.2.4 Bayesian Pattern RecognitionFor understanding the approaches to the localization problem, that are presented inthe following sections, a general understanding of the basic principles of Bayesianinference is needed. Therefore, a short introduction into this very popular approachto the problem of machine learning and pattern recognition is given.In Bayesian inference, the Bayes theorem is used to compute how the degree of beliefin a proposition changes due to available evidence. In the context of RSSI informa-tion based localization, the proposition is:"The device is there." with the evidence:"It has received these RSSI readings". Since such a proposition is inherently a de-cision for a state2in a however modelled environment, it will be represented by s.2Another convention for formalizing the concept of the proposition is given by the notion of aclass that will be decided upon.