Linear-grammetry and calibration by simultaneous multilateration using only edge distance estimates through two-way ranging

A computer implemented method for relatively locating a plurality of objects in a space having a plurality of dimensions, using one-dimensional distance estimates between selected pairs of objects, said method comprising:

• by the computer:
• identifying a set of objects (clique) for which a distance estimate between pairs of individual objects in the set is known;
• relatively localizing the objects within the clique by their respective coordinates;
• unifying the coordinate systems among the clique;
• wherein the unifying coordinate system between two cliques comprises finding two cliques that have a common clique of size equal to the dimension of the space plus one;
• wherein unifying the coordinate system between cliques performed successively by initializing every clique to be a union clique and generate a set of all union cliques;
• unifying the coordinate system between two union cliques to generate a combined union clique with a unified coordinate system;
• replacing the two union cliques with their combined union clique in the set of all union cliques;
• and
• outputting an indicia of the locations of the objects.