We present an indoor localisation system that integrates different sensor modalities, namely Wi-Fi, barometer, iBeacons, step-detection and turn-detection for localisation of pedestrians within buildings over multiple floors. To model the pedestrian's movement, which is constrained by walls and other obstacles, we propose a state transition based upon random walks on graphs. This model also frees us from the burden of frequently updating the system. In addition we make use of barometer information to estimate the current floor. Furthermore, we present a statistical approach to avoid the incorporation of faulty heading information caused by changing the smartphone's position. The evaluation of the system within a 77m ?? 55m sized building with 4 floors shows that high accuracy can be achieved while also keeping the update-rates low.
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