Can a least squares adjustment be used on a level run starting on old BM 'A' and closing on old BM 'B?' In between BM 'A' and BM 'B' would be five traverse points to be used for a topo. I'm guessing an adjustment can be done only if loop 'A' and loop 'B' are run through a new BM. The new BM 'C' is then adjusted.
You can absolutely do that, mathematically speaking. Whether you want to is another story. Hold BM "A" and BM "B" and naturally any error in the relative record elevations of the 2 BM will warp the adjustment.?ÿ So running a full loop is preferred.
As a trial, hold one BM and free the other in the adjustment. That will create what is called a "minimally constrained adjustment" It will tell you how for off you are on the record elevation of the freed BM. If you are satisfied with the results you can then hold the 2nd BM elevation and warp away.
Another option is to hold neither BM fixed, but to give both a small standard error value. Then your measurements will be fixed and best fit to the BM elevations.?ÿ?ÿ
Without redundancy, least squares is a waste of time. You have to have observations to compare. That requires a loop, ties to other control or cutoff loops to analyze and adjust.
With digital levels there is virtually no adjustment needed, and standard balancing is fine. If have a large adjustment,?ÿ then something went wrong.
A 1-way run between two good benchmarks is a better check than a loop on one, because, as well as checking your work, it can indicate whether one of them has moved.
Without the redundancy of either a loop or two control points, you have no check on your work.
Without redundancy, least squares is a waste of time. You have to have observations to compare. That requires a loop, ties to other control or cutoff loops to analyze and adjust.
That's the bottom line. Nothing to analyze by least squares if you only have a single set of observations.
Personally, I add digital level files to my control networks, which also contain total station or GNSS observations, or both. It's easy to import and that way I have all my data in the same project.
But as others have said, with a calibrated (and recently pegged) digital level, unless you have a complex network of points, just adjusted by turns and leave it at that, it won't make much difference. Certainly not enough for 95% of survey work.
Which reminds me, I need to send in our quarks and gluons in for calibration.?ÿ?ÿ
If you start from "Old A", run through five traverse points, then to "Old B".
Then run from "Old A", through "New C", to "Old B". you should have a complete loop... ?
I use LSA for my level runs. But I always have redundancies... i.e. run through GPS points as a check for busts. Ensure I run my levels in a loop. It gives me confidence that my level runs are accurate.?ÿ
Mathematically its a loop regardless of the direction or order the legs are run.
John Hamilton and Chris Mills in their work may consider subtle effects depending on direction, perhaps having to do with environmental effects vs time, and geoid gradients, but for most work I don't think it matters a lot.
I think that you will find that most high order leveling procedures require that you run a loop between two known bench marks before you start running a new line.?ÿ As others have said, unless you have a web of interconnected loops or are combining the level data with terrestrial or GNSS observations in a single adjustment then LSA will not give you any better information than a good old loop closure.?ÿ
It will be a mute point is a couple of years since passive BMs will be obsolete.?ÿ Beat the rush to clean you office and send my you LS15 now. ????ÿ
Closing on a second known benchmark is redundancy (minimal). By weighting the observations by either distance (I prefer) or number of turns, any misclosure will be distributed systematically.?ÿ
It will be a mute point is a couple of years since passive BMs will be obsolete.?ÿ Beat the rush to clean you office and send my you LS15 now.
Do you have any literature to back up this statement? Who makes the LS15? Were you joking?
Whether you want to is another story
I have no experience using a least squares adjustment (LSA) in any aspect of surveying. I can read about in a textbook, but I don't know how it's used in the real world. It seems to me that the key words in its use are "redundant observations." I conclude that topo traverse points elevated in a straight level run between two published benchmarks don't warrant the use of LSA because the traverse points have only been observed once. I further conclude that running at least two looped or straight level runs between two published benchmarks, in each case, through a new benchmark warrants a LSA on the new benchmark.
Obsolete is perhaps too strong a word, because there will remain uses for them.
But Google NATRF2022. The official definition of new elevation data will be based on GNSS and a geoid model, rather than physical monuments.
