Probability kernel regression for WiFi localisation

Various methods have been developed for indoor localisation using WLAN signals. Algorithms that fingerprint the Received Signal Strength Indication (RSSI) of WiFi for different locations can achieve tracking accuracies of the order of a few meters. RSSI fingerprinting suffers though from two main limitations: first, as the signal environment changes, so does the fingerprint database, which requires regular updates; second, it has been reported that, in practice, certain devices record more complex (e.g bimodal) distributions of WiFi signals, precluding algorithms based on the mean RSSI. Mirowski et al. (2011) have recently introduced a simple methodology that takes into account the full distribution for computing similarities among fingerprints using Kullback-Leibler divergence and that performs localisation through kernel regression. Their algorithm provides a natural way of smoothing over time and motion trajectories and can be applied directly to histograms of WiFi connections to access points, ignoring RSSI distributions, hence removing the need for fingerprint recalibration. It has been shown to outperform nearest neighbours or Kalman and particle filters, achieving up to 1m accuracy in office environments. In this paper, we focus on the relevance of non-Gaussian or Gaussian distributions for modeling RSSI distributions by considering additional probabilistic kernels for comparing Gaussian distributions and by evaluating them on three contrasting datasets. We discuss their limitations and formulate how the KL-divergence kernel regression algorithm bridges the gap with other WiFi localisation algorithms, notably Bayesian networks, SVMs and K nearest neighbours. Finally, we revisit the assumptions on the fingerprint maps and overview practical WiFi localisation software implementation.