Tracking and determining orientation of object using coordinate transformation means, system and process

An object tracking system for tracking the position and angular orientation of an object free to translate and orient in three dimensions, said system comprising:

• means for generatng a series of three primary reference signals, said primary reference signals being a DC signal, a first AC signal and a second AC signal in phase quadrature with said first AC signal and said primary reference signals being aligned along the axes of a pointing coordinate frame, the DC signal being aligned with the x-axis, the first AC signal being aligned with the y-axis and the second AC signal being aligned with the z-axis;
• first means for transforming said primary reference signals in accordance with a first transformation representing a presumed pointing angle so the signals defined in the pointing frame are now defined in an orthogonal reference coordinate frame;
• means including three orthogonal radiators coincident with the axes of the reference frame for radiating said transformed primary reference signals;
• means including three orthogonal sensors defining a sense coordinate frame for sensing the transformed primary reference signals to produce sense signals, said sensing means being rigidly affixed to the object;
• second means for transforming said sense signals in accordance with a second transformation which is the inverse of a presumed set of orientation angles of the sense frame with respect to the reference frame;
• third means for transforming said sense signals in accordance with a third transformation which is the inverse of said first transformation, said third means receiving as inputs the outputs from the second means;
• means for deriving from the sense signals so transformed by the second and third means the deviation of the position and orientation of the sense frame from the presumed pointing and orientation angles as expressed with respect to the pointing coordinate frame;
• a decoupling matrix to receive and decouple the signals representing the translation and orientation displacements of the sense frame with respect to the pointing frame so that each signal represents only one translation or orientation displacement with respect to the pointing frame;
• a translation coordinate transformer apparatus having as inputs two signals representing the translation displacement of the sense frame from the x-axis of the pointing frame and having as outputs two signals representing the translation displacement of the sense frame from the pointing vector defined in the reference frame;
• an orientation coordinate transformer apparatus having as inputs three signals representing the orientation displacement of the sense frame from the pointing frame and having as outputs three signals representing the difference between the actual Euler angles which define the sense frame with respect to the reference frame and presumed Euler angles defining the sense frame with respect to the reference frame;
• and
• means for altering the presumed pointing and orientation angles as defined in the reference frame in accordance with errors in the presumed pointing and orientation angles as defined in the reference frame.

A process for tracking an object free to translate and to orient in three dimensions relative to a reference frame defined by a radiator grouping the process comprising:

• radiating a nutating field describing a conical motion about a pointing vector which defines the x-axis of a pointing coordinate frame, the y-axis of the pointing frame being in the x-y plane of the reference frame;
• sensing the radiated field in three orthogonal axes of a sense coordinate frame attached to the object, to produce an output signal for each axis;
• determining the position and orientation error as defined in the pointing frame with respect to a presumed angular position of the object and a presumed angular orientation of the object by comparing said sensed output signals in each of said three orthogonal axes due to said sensed radiation field with presumed output signals that would be sensed in said three orthogonal axes in said presumed angular position and orientation, and determining the difference between said sensed output signals and said presumed output signals;
• transforming the errors of the angular position and angular orientation of the object from the pointing frame to the reference frame;
• and
• altering, if said difference between said sensed output signals and said presumed output signals is not zero, the presumed angular position and orientation as defined in the reference frame in accordance with the generated errors of the presumed angular position and orientation as defined in the reference frame.