What are the ramifications of localizing to a site using a set of known points down the middle versus a set of points surrounding the site. We are talking 10 acres or less here.
In theory that project could have some tilt and you wouldn't know it. In cases like this I just set up a total station and set a couple of points further out at the ends of the project to get a stronger figure.
A lot this also depends on how you localize, if you held one point for elevation and used a geoid model it would be less of a problem using points down the middle of a project.
Hopefully, I am not showcasing my ignorance...but I am only interested in the x and y.
I am both confused and curious - what theory/algorithms/equations are you quoting with regard to "tilt" in the project?
I applaud you for testing your work and congratulate you for publishing reliable results that others can use when they follow your work.
The problem with points in a line only manifests itself when you are solving for tilts, i.e. trying to fit Z.
It's been my experience that as you move away from the center your error increases exponentially. People I've talked to who do road construction say they always had points on each side that were well outside the right of way.
What algorithims? To be honest, I'm not sure what my data collector uses. I understand it to be some kind of least squares adjustment.
The tilt would be a problem in a extreme case. Take a two point adjustment where you hold both points for elevation and location. If you shot additional points that fall along the line of the two points in theory the shots would be good. Now try to take a shot that is 5 miles away from this line, you can see your localization could easily have a tilted plane, there is no third point to anchor it. I know my data collector would allow this but it would give some warnings when doing so.
I use the N, E, Elevation on one point only, then only the N, E, on the remaining points.
For a bit more detail, If I have control points 1 thru 6, I set up and shoot all six points storing G1 thru G6. I can then key in my calibration connecting 1 to G1, 2 to G2, ect. I pick one to use for elevation and then I can inverse 1 to G1, ect to see how much elevation difference I get. If all five of the horizontal only don't match close on elevation then I may select a different point to use for vertical.
James
I have experienced tilt when localizing to control on construction projects more than once. It has shown up when holding two points for elevation and then checking other control during the process of localizing on additional points. Tenths have shown up in a relatively short distance - 1500’ and my data collector has never warned me of this problem.
Seven parameter transformation rotates x y and z axis.
You must also consider the difference between a rigid body transformation and an overdetermined transformation. Overdetermined scales the observed difference between your measurements and calculation. So if a short distance measures 99.95 and should have been 100.00 this results in a scale factor of 1.0005. On a thousand foot line this 0.05 foot difference becomes half a foot. For this reason it is best to interpolate rather than extrapolate. If you can force a rigid body transformation this is less of an issue.
John, I don't mean to hijack, and I normally don't throw off on a feller's livestock, but you is ridin' the ugliest mule that I ever did see.
Bit like balancing a sheet of paper on the edge of a knife.
Just because I'm paranoid, doesn't mean they aren't out to get me.
Yea, and he spits too!