A few new questions. First, it appears that the lamp is at a fixed position in space and that you want to find the location directly below it, on the ground?
1) Are the observation points (a,b,c,d) movable?
From the drawing, each point appears to know it's separation from two other points.
2) Do points a-d know where they are, relative to some fixed coordinate system?
3) or do they just know relative distances between each other?
4) For the distance measured to the lamp, is that distance the line-of-sight distance from the observation points (a,b,c,d) on the ground directly up to the lamp? (i.e. do you know the lengths of the dashed green lines? or do you know the length of the blue lines?)
(FYI, this adds a level of complexity, because the previous thread solutions worked in a 2-D plane, but this is now likely to be a 3-D problem, which would mean at least 3 simultaneous linear equations to solve, which is a much, much more complex algorithm)
5) What scenario is this for? Do you have 4 linked robots that are running around, trying to find the location of the lamp and then get underneath it?