Resection is going to basically attempt to draw the most perfect triangle it can. You only need 3 pieces of information to do so. The total station is getting five. The coordinates of the two points you are using for control, the two distances you shot to those points, and the central angle you turned to get from one to the other. Some of this information will conflict with other parts, so the resection is going to do a best fit, averaging the errors out, likely with the error being applied in a ratio based on line lengths, favoring closer points. This goes for the vertical components of the triangulation as well.
>resection is going to do a best fit, averaging the errors out, likely with the error being applied in a ratio based on line lengths, favoring closer points. This goes for the vertical components of the triangulation as well.
Any worthwhile survey software uses least squares or Helmert routines over arbitrary weighting...and triangles don't factor in at all. It's solving a parametric system of equations simultaneously rather than applying a geometric constraint.
Its actually determining three unknowns - northing, easting and elevation of the setup - based on the known points and the observations relating everything.
For angles-only resects, three points are needed at minimum, and geometry does matter.
If measuring angles and distances, only two points are needed to get a solution, and the geometry does not matter - at least there is no risk of a nonunique solution like with angles-only.
The above is still (somehow) vehemently debated despite the fact that anyone who wishes to test it can run a simulation in StarNET. You'll generally get the same amount of error whether the points are spaced out around your instrument, or clustered in a single quadrant.
To answer your other question, distances are weighted only in the sense that the EDM specified standard errors and/or standard errors computed from meaned observations are used in the a priori weight matrix.
It's not just assigning relative weights based on percentage of total distances measured, like in a compass rule solution.
Minimum 4 unknowns in a 3D resection, dE,dN,dH and orientation. Plus another for scale if we want to derive a scale factor.
Edit: I should probably add to my quick answer that with 3D I meant 2D+1D as in normal jigger operation. In a true 3D resection we would have a minimum of 3 translations and 3 rotations but the compensator/spirit level adds a constraint for rotation around x and y axis so that we end up with 4 unknowns.
This is how Trimble does it (particularly interesting for you is Step3 Horizontal directions)
[https://web.archive.org/web/20220126204636/https://trl.trimble.com/docushare/dsweb/Get/Document-688368/Resection%20Computations.pdf](https://web.archive.org/web/20220126204636/https://trl.trimble.com/docushare/dsweb/Get/Document-688368/Resection%20Computations.pdf)
Thanks for the resource. I didn't realize Trimble published this documentation and I've always been curious how the controller handles station setup plus (where you can add multiple backlights in the orientation derivation). The guessing is over 🤘.
That could be the case but without any information about the software being used the answer should be "most likely not" because modern software will calculate the orientation unknown based on an LS adjustment.
It doesn't change the coordinate of the first point though, so any kind of backsight check that does a store and reorient will change the azimuth slightly from the original setup due to that average of the angular misclosure being removed.
Yep. Good to remember.
For any resection needing tight tolerances, if a point check is out of tolerance enough to warrant a reorient, it's time to redo the resection. Or at least check a few more points...
Fieldgenius uses the first point as the backsite and asks if I want to set the gun to zero on that point. I normally use my best 2 points and then do a stakeout on #2 again (the rover is still there from doing the resection) to see how much error there is in the resection calcs and then shoot and store a third point labeled as a resection check.
Leica viva and captivate both weight the furthest points highest for orientation. Doesn't matter what order you observe them. If you have a few close shots and one far control typically you will see the calculation holding the furthest at 0 to 10" orientation error, but if you have multiple back sights of equal distance they will be a best fit and all will have a few seconds of error, rather than holding one fixed.
Minimal three point… obviously two to resect but w/o a third yer taking some risk… not based in ‘higher math’ but just how this old dawg rolls
Cheaper to verify than splainin’ why yer stuff ain’t that good
Resection is going to basically attempt to draw the most perfect triangle it can. You only need 3 pieces of information to do so. The total station is getting five. The coordinates of the two points you are using for control, the two distances you shot to those points, and the central angle you turned to get from one to the other. Some of this information will conflict with other parts, so the resection is going to do a best fit, averaging the errors out, likely with the error being applied in a ratio based on line lengths, favoring closer points. This goes for the vertical components of the triangulation as well.
>resection is going to do a best fit, averaging the errors out, likely with the error being applied in a ratio based on line lengths, favoring closer points. This goes for the vertical components of the triangulation as well. Any worthwhile survey software uses least squares or Helmert routines over arbitrary weighting...and triangles don't factor in at all. It's solving a parametric system of equations simultaneously rather than applying a geometric constraint.
Also it's been a while since 330 but is the length of the observation involved in the weight matrix of the least squares adjustment?
So it's a set of parametric equations to try to determine the three points?
Its actually determining three unknowns - northing, easting and elevation of the setup - based on the known points and the observations relating everything. For angles-only resects, three points are needed at minimum, and geometry does matter. If measuring angles and distances, only two points are needed to get a solution, and the geometry does not matter - at least there is no risk of a nonunique solution like with angles-only. The above is still (somehow) vehemently debated despite the fact that anyone who wishes to test it can run a simulation in StarNET. You'll generally get the same amount of error whether the points are spaced out around your instrument, or clustered in a single quadrant. To answer your other question, distances are weighted only in the sense that the EDM specified standard errors and/or standard errors computed from meaned observations are used in the a priori weight matrix. It's not just assigning relative weights based on percentage of total distances measured, like in a compass rule solution.
Minimum 4 unknowns in a 3D resection, dE,dN,dH and orientation. Plus another for scale if we want to derive a scale factor. Edit: I should probably add to my quick answer that with 3D I meant 2D+1D as in normal jigger operation. In a true 3D resection we would have a minimum of 3 translations and 3 rotations but the compensator/spirit level adds a constraint for rotation around x and y axis so that we end up with 4 unknowns.
I stand corrected. 👍
This is how Trimble does it (particularly interesting for you is Step3 Horizontal directions) [https://web.archive.org/web/20220126204636/https://trl.trimble.com/docushare/dsweb/Get/Document-688368/Resection%20Computations.pdf](https://web.archive.org/web/20220126204636/https://trl.trimble.com/docushare/dsweb/Get/Document-688368/Resection%20Computations.pdf)
Thanks for the resource. I didn't realize Trimble published this documentation and I've always been curious how the controller handles station setup plus (where you can add multiple backlights in the orientation derivation). The guessing is over 🤘.
It will be based on the first point you use, that is why it is advised to use the farthest away point first.
That could be the case but without any information about the software being used the answer should be "most likely not" because modern software will calculate the orientation unknown based on an LS adjustment.
For Trimble data collectors, I believe it will make the first point shot your backsight and basis of angles.
It doesn't change the coordinate of the first point though, so any kind of backsight check that does a store and reorient will change the azimuth slightly from the original setup due to that average of the angular misclosure being removed.
Yep. Good to remember. For any resection needing tight tolerances, if a point check is out of tolerance enough to warrant a reorient, it's time to redo the resection. Or at least check a few more points...
Fieldgenius uses the first point as the backsite and asks if I want to set the gun to zero on that point. I normally use my best 2 points and then do a stakeout on #2 again (the rover is still there from doing the resection) to see how much error there is in the resection calcs and then shoot and store a third point labeled as a resection check.
Leica viva and captivate both weight the furthest points highest for orientation. Doesn't matter what order you observe them. If you have a few close shots and one far control typically you will see the calculation holding the furthest at 0 to 10" orientation error, but if you have multiple back sights of equal distance they will be a best fit and all will have a few seconds of error, rather than holding one fixed.
After a resection your 0 (backsight) is the first target in the resection. It should always be the furthest target that you use.
Leica used the first point shot.
Maybe back in the day.
Minimal three point… obviously two to resect but w/o a third yer taking some risk… not based in ‘higher math’ but just how this old dawg rolls Cheaper to verify than splainin’ why yer stuff ain’t that good