3d Helmert 7 Parameter Transformation

[ChuckTurlington]

Hello,

I am using ArcMap 10.4.1.

My question does not pertain directly to ArcMap, but to an excel 3d similarity transformation calculator I am attempting to develop.  I am using a decent text reference (Datums and Map Projections, by JC Iliffe) that gives me 4 of the matrix (vector) relationships but, beyond setting the provisional values to zero as a first approximation, I am unclear what additional assumptions are being made to solve all the variables such as rotations about each axis, lambda, etc..  My example is not a 3d Helmert 7 parameter type, which I would actually prefer.  So I have to ask, does anyone have a 3d Helmert 7 parameter transformation example that has a little more detail beyond the first assumption to assist in solving?

[MelitaKennedy]

I may be misunderstanding. You need several points and then you need to do a least squares fit to derive the transformation parameters.

[ChuckTurlington]

Thanks for your response Melita.  Your understanding is correct.  I have been studying the concepts and trying to follow the math derivations to better understand.  Some of the variables I can see performing a separate least squares calculation, such as variance and covariance in a weight matrix.  But there appears to be several variables, not enough equations, and no clear correlation to variables in least squares, or which variables of least squares are represented in the Transformation mathematics.  In using the Helmert method, there are several iterations, to start by setting provisional values to zero as a valid assumption.  But it is not clear how to progress the iterations, and which variables are strictly least squares and which are isolated by transformation algebra.  I was hoping you may know a text reference or similar that would explain these details more clearly.  Thanks again for your expertise on these subjects.

[MelitaKennedy · Accepted solution]

If I still had my least squares textbook from grad school, I'd send it to you! 

I follow a surveyor's forum and they've discussed least squares a few times. I think you can access the threads without having a login. It's not a big deal if you do decide to create a login. It's a personally run website, and they won't spam you. For instance,

Least squares spreadsheet

Getting Started with Least Squares

They're not doing the same problem as they're solving for traverses, etc. but you certainly may find some references to code or good textbooks.

Melita