2BackgroundIn this chapter the background to the two main topics of this thesis is presented.These are radio propagation models and localization algorithms. A radio propa-gation model is used to compute the propagation of Wi-Fi signals and lays thefoundation for the localization methods developed in this thesis. Therefore, thechallenges of radio propagation will be discussed in general and different technolo-gies to compute the signal propagation of Wi-Fi terminals are presented. Thereby,the raytracing technology is discussed in more detail because it is able to computemost accurate propagations and is therefore used for the further work of this the-sis. Furthermore, a technique for automatic training of the material parameters,thereby enabling the generalization to unknown scenes, will be provided. The tech-nique of choice is optimization with Genetic Algorithms . Finally, the two main errormeasures for evaluating the quality of the model are defined.The chapter continues by introducing the two different variants of the localizationproblem: Positioning and Tracking. Furthermore, the possible sources of informa-tion, that can be exploited by a localization algorithm, are described. A focus wasplaced on the signal strength information given by RSSI values that are receiv-able with Wi-Fi capable devices. For the tracking problem, additional informationsources are presented in the form of mobility models. For both sub-problems, thecorresponding error measures will be defined.After describing the basic ideas of simple positioning approaches in 2.2.1, this chapterwill end with a detailed presentation of more sophisticated models. These are theHidden Markov Model and the Particle Filter, as both of them are more suited tothe tracking problem and have therefore been evaluated in this thesis.2.1 Radio Propagation ModelIn this thesis, two main approaches for modelling the propagation of radio signals aredistinguished by the following reasoning: Propagation models are used to construct