The Cell-ID positioning technique is usually implemented on cellular networks to locate mobile phones according to the cell identification code forwarded by the Base Transceiver Station (BTS). The user is then assumed to be located at the same coordinate position as the BTS. However, this simple positioning method, also used in indoor location systems with WiFi or RFID technologies, suffers from a lack of accuracy due to the size and the density of cells. In this paper we propose an indoor positioning system in underground mine tunnels based on the cell-ID method and the innovative Visible Light Communications (VLC) technology. Unlike previous technologies, it is possible to increase the position accuracy in controlling the number of light sources, i.e. the distribution of overlapping cells. As a result, self-adaptive positioning systems could be developed, where the switch on (or off) of the individual LEDs is determined according to the precision required by the application. We present an analytical model for such systems, based on Euclidean geometry equations. It is shown that the maximum position error in each cell may be fixed to obtain a positioning system with a constant accuracy. Finally, an application of this system is given to locate people or machinery in underground mine tunnels.