34 3. Related Work4. Are the physical properties of the geometry homogeneously modelled or doesthe system distinguish between different materials?5. How are these material parameters obtained?6. If the material parameters were trained from measurements, what was thestrategy? What was the optimization target?7. Which error rates have been reached by comparing the simulation results toreal world measurements? How complex were the testbeds?One of the simplest analytical models for the radio propagation problem has beengiven by the RADAR system with the so called Wall Attenuation Factor model(WAF). The path-loss of the signal is described as a function of the number of inter-secting walls on the straight line between localization hypothesis and the transmitterof the signal. The Wall Attenuation Factor influences the rate of power decay ateach intersection and has to be found manually. Different factors for different wallmaterials are possible although not used. The reduction of the signal strength is em-pirically determined to be 3. 1 dBm for a wall intersection in the analysed scenario.This model can be understood as a very reduced ray-tracing approach. The line ofsight is the only simulated ray and the attenuation factor corresponds to the trans-mission parameter of the employed PHOTON raytracer. Although the evaluation ofRADAR has lead to the conclusion that the fingerprinting based approach reachesbetter localization accuracy than an also compared analytical model, this has notstopped interest in this area of research.3.1.1 2D-Raytracer ModelsA more complicated model is given by 2D-raytracers. These models are enhancedby adding the simulation of reflection effects at the ray intersection points. 2D-raytracers were investigated in[12] and[13]. The system, presented in[12] usesheterogeneous reflection and transmission coefficients for different materials, similarto the PHOTON system. In contrast, the ARIADNE system[13] does not distin-guish between different materials.In the ARIADNE system a rasterized 2D-floor plan is automatically converted to a2D-model of the environment. They have employed a 2D-raytracer that simulatesthe basic physical effects like transmission and reflection. Refraction or scatteringhave not been simulated. The model ignores rays with a power below a fixed thresh-old. Similar to the PHOTON raytracer, the individual power values of overlappingrays are combined by simple summing without anticipating interference effects. Thefree parameters of the raytracer model are given by the antenna gain of a singleAP and a transmission and reflection coefficient. Hence, only one material type isconsidered. An optimization of these free parameters has been done by running asimulated annealing optimizer against the RSSI value of only one measured loca-tion. As described in 2.1.2, the presented localization framework has shown betterconvergence with a genetic algorithm optimizer. But modelling different materialparameters and separate antenna gains for different AP classes leads to a higherdimensional search-space and has therefore probably other convergence properties.