I then test all 126 unique permutations (no repetition) of 4 star groups which return x,y,z coordinates which will fit in a 1/32 grid. I then run a count of the number of matching coordinates on each axis. The coordinate with the highest count is the one selected.
Typically there are 120+ matching positions for each axis (many times the full 126). I'd like to think a 95%+ agreement on position on each axis is pretty good result.
Are you counting on each axis independently? If so, then I think you could end up choosing coordinates that were never generated by any set of references. E.g if your generated coordinates were this:
X Y Z
1 1 1
1 1 1
1 1 1
1 3 2
2 2 2
2 2 3
2 2 3
3 2 3
3 3 3
Would your algorithm pick [1, 2, 3] for the final coordinates? Or would it pick [1, 1, 1]? If it's [1, 2, 3] that would seem counter-intuitive to me, though I doubt it would happen with real data.
I'm doing something similar. I also test all the combinations of the reference stars, though I only select groups of 3 stars. Each 3 star combination gives me 2 candidate coordinates. I then pick the single set of coordinates from all the candidates that gives the lowest error when comparing the supplied distances and the calculated distances.
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