Two-antenna positioning system for surface-mine equipment

A method for determining the spatial location and orientation of a work machine having a known geometry, comprising the following steps:

• (a) determining spatial coordinates of a first point on the work machine corresponding to a position along a trajectory traveled by said first point in three-dimensional space;
• (b) determining spatial coordinates of a second point on the work machine corresponding to a position along a trajectory traveled by said second point in three-dimensional space;
• (c) repeating steps (a) and (b) a predetermined number of times to produce a plurality of said coordinates of the first and second points on the work machine corresponding to successive positions along said trajectories traveled in three-dimensional space;
• (d) fitting a surface equation through said plurality of coordinates and determining orientation parameters for the surface equation so produced;
• and
• (e) calculating a spatial location and orientation parameters of the work machine utilizing current spatial coordinates for said first and second points on the work machine, the orientation parameters of the surface equation calculated in step (d), and the known geometry of the work machine;
• wherein said step (d) is carried out using linear regression.

A method for determining the spatial location and orientation of a work machine having a known geometry, comprising:

• (a) determining a plurality of coordinates of a first point on the work machine corresponding to successive positions along a trajectory traveled by said first point in three-dimensional space;
• (b) determining a plurality of coordinates of a second point on the work machine corresponding to successive positions along a trajectory traveled by said second point in three-dimensional space;
• (c) fitting a surface equation through said plurality of coordinates determined in steps (a) and (b);
• and
• (d) calculating a spatial location and orientation parameters of the work machine on the basis of current coordinates of said first and second points on the work machine, orientation parameters of said surface equation, and said known geometry of the work machine.

A method for determining the spatial location and orientation of a work machine having a known geometry, comprising:

• (a) determining a plurality of coordinates of a first point on the work machine corresponding to successive positions along a trajectory traveled by said first point in three-dimensional space;
• (b) determining a plurality of coordinates of a second point on the work machine corresponding to successive positions along a trajectory traveled by said second point in three-dimensional space;
• (c) fitting a surface equation through said plurality of coordinates determined in steps (a) and (b);
• and
• (d) calculating a spatial location and orientation parameters of the work machine on the basis of current coordinates of said first and second points on the work machine, orientation parameters of said surface equation, and said known geometry of the work machine;
• wherein said step (c) is carried out using linear regression.

An apparatus for determining the spatial location and orientation of a work machine having a known geometry, comprising:

• first means for determining position coordinates of a first point on the work machine in three-dimensional space at successive times corresponding to successive positions along a travel trajectory of said first point;
• second means for determining position coordinates of a second point on the work machine in three-dimensional space at successive times corresponding to successive positions along a travel trajectory of said second point;
• means for storing a plurality of said position coordinates of the first and second points on the work machine;
• means for fitting a surface equation through said plurality of position coordinates of the first and second points on the work machine and for determining orientation parameters for said surface equation;
• and
• means for calculating a spatial location and orientation of the work machine utilizing a current set of position coordinates for said first and second points on the work machine, the orientation parameters corresponding to a current surface equation, and the known geometry of the work machine.

An apparatus for determining the spatial location and orientation of a work machine having a known geometry, comprising:

• first means for determining position coordinates of a first point on the work machine in three-dimensional space at successive times corresponding to successive positions along a travel trajectory of said first point;
• second means for determining position coordinates of a second point on the work machine in three-dimensional space at successive times corresponding to susccessive positions along a travel trajectory of said second point;
• means for storing a plurality of said position coordinates of the first and second points on the work machine;
• means for fitting a surface equation through said plurality of position coordinates of the first and second points on the work machine and for determining orientation parameters for said surface equation;
• and
• means for calculating a spatial location and orientation of the work machine utilizing a current set of position coordinates for said first and second points on the work machine, the orientation parameters corresponding to a current surface equation, and the known geometry of the work machine;
• wherein said means for fitting a surface equation includes means for implementing linear regression on said plurality of position coordinates.