A new arrangement of interferometers allows to measure the movement of a retroreflector in space with high precision. Applications are the testing of the position accuracy of three dimensional coordinate machines, industrial mbots, tooling machines etc. This system uses four Michelson interferometers with deflector units, controlled by a servo system. For the position of the retro-reflector and the position of the deflector units are unknown at start-up, a at least ten point calibration cycle is necessary. A mathematical algorithm, using the signals of the four Michelson interferometers, allows to determine the position of the retroreflector and the deflector units in a given coordinate system.