Least squares, what to hold as fixed?

GeomÌÁgico, post: 367264, member: 11554 wrote: Let's say I am going to do a property survey, it's a new job, local coordinate system, and I have no previous job (point data) around the area. After collecting all the data needed, I need to perform the least squares adjustments. Lets say I set a nail and 2 cut crosses as control for my network, but I also found some iron bars. When performing the adjustments, should I hold the nail or the cut crosses as fixed points?

Okay, the premise is that you are going to use a coordinate system with an arbitrarily chosen origin, i.e. some control point can be assigned a value of 5000, 5000 or 500000, 500000. It doesn't matter because there are no other boundary markers or data to be combined with the data from your survey. This is increasingly a rare case in the real world, but in the case you describe, you will choose one point to assign coordnates to and hold those values fixed in the adjustment.

Then you have to determine how to orient your arbitrary coordinate system, i.e. what direction does the Y axis parallel? Is it a real world direction like geodetic North at some specific point, grid North of some standard mapping projection like the SPCS, or the "North" direction to which some prior survey of the land referred? If one of the former two, then it is usually most convenient to fix the coordinates of some point from which you know the direction of a line passing through the point to which your survey will be tied. If it is merely "North" as based upon some prior survey, then you'll choose two markers positioned by your survey that have a specific bearing in relation to your "North" as assumed from some other surveyor's prior work and you'll hold that bearing fixed as a constraint.

Kent McMillan, post: 367280, member: 3 wrote: Okay, the premise is that you are going to use a coordinate system with an arbitrarily chosen origin, i.e. some control point can be assigned a value of 5000, 5000 or 500000, 500000. It doesn't matter because there are no other boundary markers or data to be combined with the data from your survey. This is increasingly a rare case in the real world, but in the case you describe, you will choose one point to assign coordnates to and hold those values fixed in the adjustment.

Then you have to determine how to orient your arbitrary coordinate system, i.e. what direction does the Y axis parallel? Is it a real world direction like geodetic North at some specific point, grid North of some standard mapping projection like the SPCS, or the "North" direction to which some prior survey of the land referred? If one of the former two, then it is usually most convenient to fix the coordinates of some point from which you know the direction of a line passing through the point to which your survey will be tied. If it is merely "North" as based upon some prior survey, then you'll choose two markers positioned by your survey that have a specific bearing in relation to your "North" as assumed from some other surveyor's prior work and you'll hold that bearing fixed as a constraint.

Thanks for the fast response, I actually meant to ask if I should hold the nail/cut cross or the bar? Because what I am thinking is, if the bar is not on the right place and I adjust my coordinates based on that, then my coordinates will get messed up

GeomÌÁgico, post: 367284, member: 11554 wrote: Thanks for the fast response, I actually meant to ask if I should hold the nail/cut cross or the bar? Because what I am thinking is, if the bar is not on the right place and I adjust my coordinates based on that, then my coordinates will get messed up

But your coordinate system is purely arbitrary, right? What does it matter whether the coordinates of any point changes in the adjustment since the relative positions will remain (presumably) correct? If you are wondering how land surveyors deal with the problem of boundary monuments ending up placed in different positions from the target coordinates, the answer is somewhat different, but generally the best practice is to set out boundary monuments from a fully adjusted control network, not set out as you go and then discover later that you wished you'd waited until the basic network was adjusted.

Kent McMillan, post: 367286, member: 3 wrote: But your coordinate system is purely arbitrary, right? What does it matter whether the coordinates of any point changes in the adjustment since the relative positions will remain (presumably) correct? If you are wondering how land surveyors deal with the problem of boundary monuments ending up placed in different positions from the target coordinates, the answer is somewhat different, but generally the best practice is to set out boundary monuments from a fully adjusted control network, not set out as you go and then discover later that you wished you'd waited until the basic network was adjusted.

Thanks, that's actually what I was planning on asking next!

I know that different locations have different standards, but lets say you measured a line of 100.020m or 100.030m, and a supporting plan shows it as 100.000m, would you consider this line to be plan & measured?

GeomÌÁgico, post: 367289, member: 11554 wrote: Thanks, that's actually what I was planning on asking next!

I know that different locations have different standards, but lets say you measured a line of 100.020m or 100.030m, and a supporting plan shows it as 100.000m, would you consider this line to be plan & measured?

It would depend upon the jurisdiction, but ordinarily (in Texas) I would report the adjusted distance between the markers as my survey result and note the prior measurement(s) for comparison. What you would not want to do for any reason I can think of, is fix the plan distance of 100.000m as a condition of the adjustment between two markers that are actually 100.025m +/-2mm apart since the object of most surveys is to report the actual conditions as found.

Great, much appreciated!

Cheers

Why do you assume you have to adjust before you even understand your data?

Assuming you have a 4 corner lot and only have the relative 4 corners markers, not that that is a good idea, because you have not in fact done a survey worthy of the name. You look for point to point conformity, one side or cross corners for the closest fit. Holding your deed you translate and rotate your field work and see how your other corners fit. You may redo that several times more. If you have to adjust a 3 legged traverse your equipment is probably out of whack.

No one else can really tell you what to hold, but you may decide to be held by certain data over other data.

Paul in PA

GeomÌÁgico, post: 367289, member: 11554 wrote: Thanks, that's actually what I was planning on asking next!

I know that different locations have different standards, but lets say you measured a line of 100.020m or 100.030m, and a supporting plan shows it as 100.000m, would you consider this line to be plan & measured?

Let's say you are consistantly long by the same proportion on the sides then you need to get on that surveyor's chain when retracing and looking for corners.

One point that Kent made, that I will restate differently, is that LSA works best with the minimum number of constraints, if your purpose is to define your accuracy withing a certain confidence level.

Boundary surveying is an evidence based process. Boundary determination is not based upon a least squares adjustment. By this I mean that a boundary resolution is not based upon which measurements have the smallest error ellipse, in order to determine what to hold as controlling. Measurement is important boundary determination evidence but it must be placed in the proper context with respect to the duty the surveyor has to properly retrace a boundary. State law, statute and case, is a very important part of what boundary surveyors concern themselves with, following the footsteps of the previous surveyor or original surveyor, intent of the parties, junior/ senior rights, evidence of various boundary establishing doctrines.

Thanks everyone, much appreciated your input!