# Orthogonal Distance Fit of a Pyramid (Geodäsie/Vermessung)

Hi,

Can I ask, if you could summarize or describe the algorithm "pyramid" in a logical steps, in order to understand it. Because, some steps still I couldn't understand it.

You are referred to the listed publications for details to the least-squares algorithm.

To fit the pyramid, the algorithm estimates the parameters of the 4 planes. The planes are parametrized as Hesse normal form:

with the secondary condition

For each plane the unknowns are , , and . In your case, the algorithm estimates 4×4 = 16 plane-parameters. Up to this point, the algorithm produces the same results as a single fit of each plane.

To estimate the intersection, the number of unknowns increased by 3 - the coordinates of the intersection-point. To force a intersection of the 4 planes, 4 additional conditions are introduced. If is the intersection-point, each plane has to contain , or similar:

This is the whole mathematic model, which can be used in a common orthogonal distance fit algorithm - see listed publications to get formulas of Gauß-Helmert model.