What does the term "Best Fit" mean to you?

I was thought not to use least squares when dealing with boundary resolution. What do you guys think about this opinion?

Jim:

Only pertains to socks and gloves. 😛

Can't imagine anytime you would use it for that.

> Over the years, I have ran across the term "Best Fit" on surveys by others with no apparent quantification describing how the best fit was determined or what method was used.
>
> I have used Least Squares, Linear Regression and coordinate transformation for shift and rotation.
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> How have you used "Best Fit" in your survey adjustments?

It sounds to me as if the surveyor was saying that he or she calculated the coordinates of various boundary corners in some arbitrary coordinate system (System 1), surveyed the coordinates of survey markers in some subset of boundary corners in another coordinate system (System 2) and used a Helmert transformation to calculate the translation, rotation, and scale factor that would need to be applied to System 1 to minimize the sum of squares of the residuals of the coordinates of nominally the same points in Systems 1 and 2.

In practice, that is seldom a really excellent way of reconstructing boundaries that were actually laid out by conventional survey. I mean, if a line was actually run, the fact that the markers were laid out on nominally one line is more important in the reconstruction than their relationship to some markers a half mile away on the extreme other side of the project. However, a Helmert transformation but may be a fairly good approach for reconstructing an RTK effort where the random positional errors of marks set tend to be independent of those of adjacent markers.

Where a line is claimed to be a "best fit" to a series of markers that aren't exactly on one straight line, I'd assume that the surveyor means the best fitting line was computed by linear regression or was chosen by eye using a double-scale map (a map showing the offsets of the markers to a baseline that is a good approximation of the line they nearly lie upon, but with the offset distances plotted at exaggerated scale for clarity. This is a very useful technique for fences that zig and zag a bit.

[sarcasm]I eyeballed it[/sarcasm]

Kinda like balancing out the error in a deed description. Nothing wrong with that. Right?????

> I was thought not to use least squares when dealing with boundary resolution. What do you guys think about this opinion?
Let's say you have a line of half a dozen or so front subdivision lot corners, nominally making a line. But the monuments are a little this way and that way of a straight line. In this circumstance, I think, it is sometimes appropriate to determine a single straight line by best fit, and then apply the virtual hammer to adjust those pins the 0.04', more or less, it takes to put those pins on an exact line.

The alternatives are to hold 2 of them and call the others off, hold two of them and swing that virtual hammer a lot harder on the others, or jiggle the line this way and that as it goes down the block.

I'll use the best fit.

Your client wants to use a barbed wire fence as a boundary, you locate a number of point on lines then do a "best fit" along the basically straight fence to make one long line where the line is within a few tenths of a foot from each location? Do the same thing for locations along the centerline of a dirt road to be used as a centerline of an easement, these are some situations to use a "best fit" line.

> How have you used "Best Fit" in your survey adjustments?

One special problem encountered in resurveys in parts of Central Texas with a highly expansive clay soil is that it is almost impossible to establish boundary markers that will be perfectly stable over time. When the clay develops cracks more than two inches wide that you can drop a 48-inch lath into, you are in just such a soil condition.

The end result is that markers move around significantly, migrating generally downslope over wet-and-dry cycles, and figuring out how to reconstruct their original positions requires some attention. Helmert transformations are an excellent tool to use as a first approximation to identify the markers that have moved the most and to identify markers that have probably been closest to stable.

The idea that monuments control boundaries is fine as long as the monuments remain in the positions they were placed when the boundaries were created. In an unstable soil, that just is an unlikely event if the marker was driven into ground with a significant slope and the first task is to identify which markers have wandered so much from their original positions that they do not fall into the category of original, undisturbed monuments.

If no other details are given to define "best" then that's about all you can assume.

I think Norman Oklahoma has it. Some survey cogo's have a feature called "best fit" to do just as he said. Works on line points and circles.
BTW I like the virtual hammer tag!

> Some survey cogo's have a feature called "best fit" to do just as he said. Works on line points and circles.

Yes, that's certainly true, but when you have recovered markers that don't supposedly fall either on a line or a circle, the best fit option is a Helmert transformation to find the best fit relationship between the coordinates of various boundary points calculated from record data (in some coordinate system) and the coordinates as found (in some other coordinate system). What you end up with in optimal conditions is similar to the line and arc best fit routines in that it generates a description of the theoretical figure that best fits on the whole what has been found on the ground while possibly exactly matching nothing other than the theoretical figure described in the record.

Blue jeans, 33 x 32, relaxed fit do the trick for me.

That's how I'd use it. A linear regression routine, probably least squares. You want the "best fit" of a series of measurements about along a straight line (but not) that is a straight line. Of course it depends on the shots taken. The routines usually produce a report of the points showing how far and to which side of the line each point is from the solution. It's nice to check just how straight something is. Say you take shots along a half mile of fence and the "best fit" report says that all fall within a 0.5 foot strip. Might indicate the fence was built off a survey or other precise measurement (how else did it end up that straight?). On the other hand if it's zig zaging all over the place it's more likely no survey was involved. Of course if you don't have a direct record that a survey was done it's left to judgement.

I'm a bad boy. I was thinking in a more X-rated way than that.

I would not use least squares to resolve boundary issues (boundary geometry). I would only use those types of adjustments to account for measurement error. I think that is the reason for least squares. As far as points not fitting on a line, there is, most likely, a decision to be made about two of these points holding more clout than the others. I would not adjust the line to conform to the averaged position of the monuments (in most cases). Again, I'm speaking in general terms and from a colonial metes and bounds state perspective. I know there are cases where the PLSS rules may tend to lead you to do the opposite of what I'm describing.

Yeah, I've got my Mighty version of least squares. I set an error budget and in autocad I display my shots with a circle having a radius equal to my error budget; if my line touches the circle, I'm good, I've met my least square confidence level.

AutoCad "feature" http://docs.autodesk.com/CIV3D/2013/ENU/index.html?url=filesCUG/GUID-168E7230-C428-43A5-8A69-3F7DECB18970.htm,topicNumber=CUGd30e117087

Never heard the term before Cad...

PS: don't remember if I ever used that tool for a final analysis, but I have seen Many Surveyors push that button and call it "done!"

I've seen it used often, not by me, but it will produce a report....:-P