In the present work a new concept of satellite-based navigation system, which does not require on-board atomic references, is presented. This novel concept consists of a constellation of compact low-earth orbit positioning satellites that are equipped with on-board steerable clocks, i.e. voltage controlled crystal oscillator (VCXO). An appropriate ground-satellite synchronization network is responsible for keeping in lock step clocks on-board visible satellites with a master atomic reference located on the ground. Regional/local clock synchronization, low-weight satellites and low manufacturing cost are some of the peculiar aspects of this novel system. Key issues such as number and spatial location of required synchronization stations, clock de-synchronization issues and positioning accuracy are extensively discussed. A software simulator specifically developed for studying its feasibility is also presented together with a plan to develop a micro-satellite payload to demonstrate the feasibility of such system.