Best Fit As-Staked Data

I would use a helmert solution.

There are autocad lsp routines out there

Perfect! Thank you for the information. Trimble Business Center does a least squares analysis when using Transform Survey Points. I had never thought to try to use that solution, until you mentioned it.

I'd go with the TBC solution myself; I find it easier to work with and I really like the automated reports generated from the Transform tool.

I'm curious if this is a client-driven thing, or if you are having to stake from multiple setups? Usually once the as-staked deltas are below a certain threshold, if it's all from a single setup, we don't analyze things further unless someone throws a red flag.

Its not client driven. I wanted some metrics to prove the reliability of the staked locations.

I've never heard of such a thing. Doesn't anyone check their staked points from another setup anymore? I once checked the positions of building corners set by another surveyor. I assumed that he set them radially, and I taped between them to check them. The distances didn't check well at all. Maybe we're too dependent on adjustment methods, and we're losing sight of good surveying techniques.

We do always check them from another setup. That is the idea to "fit" those check as-staked points shot from another setup to the design points. The least squares allows you to "fit" the as-staked points to the design point without any of manual iterations. I was trying to find away to simplify this task.

I might check from another setup if I think there is a problem, or if it's really high-pressure work, but if I know my gear is in adjustment and I am paying attention to best practices I'm going to stake it and if my inverses are good, then I'm satisfied. If we made it SOP to check EVERYTHING from another setup, we'd never get anything done.

For the vast majority of stakeout work, including building layout, if they need guarantees of better than 0.01-0.2', or someone's getting bent out of shape over 5-10-second angle "bust" over a 300 foot line (which is about 0.01-0.02'), it's time to switch to a more precise staking method. Break out the tape and plumb bob, or the level, or get a HP instrument or a laser tracker. That's getting into monitoring-level precision there, which means a lot more time and money. Most of the time they can't even build to those tolerances anyways.

Beyond that, simply transforming an observed building envelope to a design envelope will not capture those random errors - it will only demonstrate that we staked what we intended to stake.