In accordance with various embodiments of the invention, a user-borne computer input device is disclosed including a 5D or greater “mouse” or other tool or object containing or consisting of one or more permanent magnetic presenting permanent magnetic dipoles. The position and orientation of the device are determined by magnetic field strength measurements derived from at least two vector-magnetometers fixed in a reference frame connected to the computing device. The system allows a user to interact with the computing device in at least 5 dimensions by manipulating the position and orientation of the device within a measurement volume, which may be a few cubic meters.