An apparatus and method for wirelessly determining position and orientation of a first object relative to a second object in six dimensions, including one or more recording assemblies and one or more identification-coded or orientation-coded optical transponders. The positions of the recording assemblies are fixed relative to the first object and the transponders are fixed relative to the second object. A light source in each recording assembly emits light into space that is received, modulated, and retransmitted back by each transponder to a photodetector assembly in the recording assembly. The identification-coded optical transponder modulates the retransmitted light with a unique fixed code. The orientation-coded optical transponder modulates the retransmitted light with a unique fixed code that depends upon the direction of the incident light. The photodetector assemblies provide one or two independent position parameters for each transponder and two independent orientation parameters for each orientation-coded transponder. The system includes a combination of recording assemblies and transponders that provides at least six independent measured parameters.