Context-aware computing systems demand an accurate and up-to-date world model which computationally represents the environment they oversee. Systems to date tend to have small-scale implementations with hand-programmed world models. In real environments, manual creation and maintenance of such models is infeasible. This paper presents a novel method of using signals propagating in a multilateration positioning system to assist in creating and maintaining models of a dynamic world. It builds on a previous method for discovering objects in static environments. The methods are implemented and evaluated using a real positioning system. They are shown to build three-dimensional occupancy grids of indoor volumes, and have the capability of modifying those grids as time proceeds and the environment is reconfigured.