A positioning system, in particular, positioning in six dimensions of a sensor with respect to an assembly composed of a multitude of LEDs, is provided. The sensor is a shadow sensor and has a mask and a 2D imager. By recording the shadow of the mask cast by each LED on the imager, and by properly multiplexing the LEDs, the system can compute the 6D position of the LED assembly with respect to the shadow sensor. This computation is based, in part, on treating the shadow of the mask cast on the imager as the equivalent of the projection of light in a pinhole camera.