Systems and methods for location representation using a discrete global grid system

A navigation system, comprising:

• a position receiver situated to detect a plurality of location signals;
• a processor coupled to the position receiver to:
• establish a location based on the detected location signal;
• assign the established location to a cell in an array of cells, wherein the array of cells includes cells situated on a path defined by an embedding of at least a portion of an icosahedral surface corresponding to an associated portion of a spherical surface and the array of cells is based on at least one set of great circles;
• and
• estimate a distance from the established location to a destination location based on the cell associated with the established location and a destination cell associated with the destination.

A navigation system, comprising:

• a position receiver situated to detect a plurality of location signals;
• a processor coupled to the position receiver to:
• establish a location based on the detected location signal;
• assign the established location to a cell in an array of cells, wherein the array of cells includes cells situated on a path defined by an embedding of at least a portion of an icosahedral surface corresponding to an associated portion of a spherical surface;
• and
• estimate a distance from the established location to a destination location based on the cell associated with the established location and a destination cell associated with the destination, wherein the cell associated with the established location is situated in a selected least common denominator triangle.

A method, comprising, in a navigation system that includes

• a processor:
• receiving a first location;
• identifying at least one cell in a cellular grid associated with the first location, wherein the cell is on a path defined by embedding at least a portion of a spherical surface onto a plane based on a selected set of great circle paths on the spherical surface and a selected ordering of cells with respect to the selected set of great circle paths;
• and
• identifying at least one cell in the cellular grid associated with a second location;
• and
• determining a distance between the first location and the second location based on the associated identified cells, wherein the cells are hexagonal, a plurality of cells are identified as corresponding to the second location, and the distance between the first location and the second location is determined as a minimum of the distances between the cell associated with the first location and each of the cells associated with the second location, and wherein the cellular grid is defined based on a selection of one or more of Type I, Type II, and/or Type III Great Circles on the spherical surface, or combinations thereof, and the cells are oriented as Class I, Class II, Class I/III, or Class II/III cells.