User and device localization using probabilistic device log trilateration

This paper describes a method to learn demand models and find relative locations of users and devices based on usage logs only. It therefore allows the monitoring and optimization of infrastructures using a signal that is often already available. Absolute positions can be obtained by combining the usage logs with a small number of hand-labeled positions of users and/or devices. The method exploits the characteristic that each time a user uses the infrastructure he typically interacts with the device that is closest to his physical position. This gives information about closest pairs. Special jobs that cannot be performed on all devices, the temporary unavailability of devices, or other reasons that prevent users from using the closest device, allow relative locations to be determined based on relationships beyond pairs, hence breaking the symmetries and ambiguities that would remain if only pairs could be used. This procedure is similar in spirit to the process of trilateration: a geometric method for determining the intersections of spheres given their centers and radii. Experiments show that a probabilistic model combined with Bayesian inference makes it possible to infer user and device locations relatively accurately in many settings and gives sensible descriptions of uncertainty in cases the logs do not provide enough information.