For the Internet of Things to be people-centered, things need to identify when people and their things are nearby. In this article, we present the design, implementation, and deployment of a positioning system based on mobile and fixed inexpensive proximity sensors that we use to track when individuals are close to an instrumented object or placed at certain points of interest. To overcome loss of data between mobile and fixed sensors due to crowd density, traditional approaches are extended with mobile-to-mobile proximity information. We tested our system in a museum crowded with thousands of visitors, showing that measurement accuracy increases in the presence of more individuals wearing a proximity sensor. Furthermore, we show that density information can be leveraged to study the behavior of the visitors, for example, to track the popularity of points of interest, and the flow and distribution of visitors across floors.