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A system for mobile users' position and heading estimation in IEEE 802.11 WLAN (WiFi) using received signal strength (RSS) approach is introduced. The basic contribution the system introduces is that it doesn't need offline training or extra special hardware. It makes use of the fact that only few online RSS measurements from visible access points (AP) around the user is needed to build local propagation model at run-time. Gaussian Process Regression (GPR) is used as a non-parametric modeling that handles non-equally spaced sparse data. Due to the few learning data points, Gaussian kernels calibration and prediction happen in a single step. This enables the system to autonomously adapt to environment changes. The estimated ranges from multiple access points (AP) are used to determine position using weighted least squares. Then, the rate of change of signal strength from multiple APs is used by a novel algorithm to estimate heading. Experiments show reliable meter-level positioning accuracy and heading estimation accuracy of 16.5 degrees.