Fig. 1. Schematic illustration of contact probability calculation.

(Left to right): Raw locations, including horizontal uncertainty estimates, for two mobile devices are transformed into approximate location probability densities. The distribution of distances from points drawn randomly from these densities is computed. Sampled distances are shown here for illustrative purposes in red (when sampled device locations are within 6 feet apart) and gray (when sampled locations are more than 6 feet apart); in our implementation, the distribution of these distances is computed analytically. The shaded area under the density curve is the probability that the devices are within 6 feet.