This invention is a system that tracks the 3-dimensional position and orientation of one or more bodies (20) in a volume by a light based as well as at least one non-light based mensuration sub-system. This overcomes the limitation of light based mensuration systems to the necessity of the bodies (20) to be in constant line-of-sight of its light based position sensors (26). The invention possesses most of the accuracy and stability of its light based position measurement sub-system (24, 26, 72), but can also work without direct line of sight either for short periods of time or within certain parts of the volume. It does so by incorporating other sensors (31, 34), such as inertial or magnetic, which are frequently recalibrated against the light based sub-system (24, 26, 72) while the bodies (20) are visible by the light based sub-system (24, 26, 72).