Ubiquitous computing is rapidly emerging as a framework for deploying mobile and context-aware applications. This paper focuses on a new approach, and the resulting architecture, for implementing positioning services over ubiquitous infrastructures. Our driving idea is to estimate zones where mobile devices operate measuring the power level of wireless communications for locating them. The proposed architecture is largely independent from the devices used and from the wireless communication technologies. We experiment the approach over a Bluetooth and Wi-Fi infrastructure.