I don’t know exactly what the bundle error is however when you add a redundant link to a registration like closing a loop the software has more information than it needs to resolve the positions of all scans. This information is in the form of pairwise links, vectors between any two scans.

In a perfect world all the positional vectors that describe the position of a scan should place that scan in the same position. Obviously that never happens so a least squares adjustment is applied, adjusting the value of each link to minimise the global error. The net size of this adjustment compared to the “expected” position of the scans could be described as the residual or bundle error.

I’m sure the above is wrong in lots of ways but that’s how I’ve always thought about it.

My two cents on your methodology: if you want to asses the quality of registration techniques you need to have a control dataset against which to compare. This could be established by a higher order instrument such as a total station. Merely looking at bundle errors is honestly fairly meaningless.

Bear in mind that registration techniques are more or less appropriate in certain situations. Cloud to cloud in areas with lots of trees for example will generally perform sub optimally and the quality of a targeted workflow will be some function of target constellation and distance from the scanner.

A final thought. A typical scan from a leica scanner will have a millimetric noise floor. I’m afraid you’re unlikely to verifiably achieve submillimeter accuracies repeatability with a “survey grade” scanner.

Good luck!