KL-divergence kernel regression for non-Gaussian fingerprint based localization

Probability kernel regression for WiFi localisation

“…when measuring RSSI from J multiple access points), Mirowski et al (2011) make the assumption of local independence of each AP's marginal distribution and use the chain rule for relative entropy (Cover and Thomas, 2006) to express the KL-divergence of a joint distribution of independent variables. One can indeed argue that the WiFi software most likely queries and receives answers from the APs independently, and that the fluctuations in signal propagation for various APs happen along somewhat different paths.…”

“…One can indeed argue that the WiFi software most likely queries and receives answers from the APs independently, and that the fluctuations in signal propagation for various APs happen along somewhat different paths. Mirowski et al (2011) propose to combine the KL-divergence with kernel 2 methods and to use kernelbased regression algorithms. Following (Moreno et al, 2004), and for a data-dependent range of values α, it is possible to define such positive semi-definite kernels by exponentiating the symmetrized KL-divergence:…”

“…It has however been reported (di Flora and Hermersdorf, 2008;Vauper et al, 2010) that this is not always the case: the signal can be multimodal, different recording devices can measure quite different distributions at the same location and simple changes in antenna orientation can impact the RSSI by 10dBm (Curran et al, 2011). In their experiments, Mirowski et al (2011) reported that the RSSI of an immobile receptor can be distributed in a bimodal way and that they oscillate between two extreme values distant by as much as 10dB (see Figure 1).…”

“…This is an intuitive scheme since RSSI values recorded by such software as NetStumbler R (http: //www.netstumbler.com) or WiFi Scanner R (http://wlanbook.com) are integers. In the most general case that accounts for the multi-modality of the signals, Mirowski et al (2011) consider multinomial distributions as a model for RSSI distributions, and compare such multimodal distributions using the divergence metric developed by Kullback and Leibler (1951).…”

“…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 then 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.…”