2.6.1 Linear Dynamic System..................... 282.6.2 Particle Filter........................... 292.7 Least Mean Squared Error........................ 302.8 Summary................................. 313 Related Work 333.1 Radio Propagation............................ 333.1.1 2D-Raytracer Models....................... 343.1.2 3D-Raytracer Models....................... 353.2 Positioning and Tracking......................... 373.2.1 Hidden Markov Models ...................... 373.2.2 Particle Filters.......................... 393.2.3 Nearest Neighboor based Approaches.............. 413.3 Summary................................. 424 Design 434.1 General Overview............................. 434.2 Radio Propagation............................ 444.2.1 Model............................... 454.2.2 Parameter Estimation...................... 454.2.2.1 Initialization...................... 464.2.2.2 Optimization...................... 464.2.3 Device Specific Adaptation.................... 474.3 Positioning and Tracking......................... 484.3.1 Hidden Markov Model ...................... 494.3.1.1 Parameter Estimation................. 504.3.1.2 Emission Probabilities................. 504.3.1.3 Transition Probabilities................ 514.3.1.4 Pruning......................... 534.3.1.5 Result Sequence.................... 554.3.2 Particle Filter........................... 554.3.2.1 Emission Probabilities................. 554.3.2.2 Transition Probabilities................ 55