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Getting started with Least Squares

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(@rcliffwilkie)
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Paul in PA said: ‰ Ô
Least Squares Adjustment does not make observations better, but it does make them different.

I partially disagree. I think any adjustment only "improves" measurements to the extent that the stochastic and mathematical model of the adjustment reflect where the errors are coming from. Another way of putting that is to say that the geometry of the network has to be solid (well-conditioned), and the a priori weighing scheme has to be realistic. In other words, the internal redundancy gives one more overall "measurement" that is applied on top of the internal redundancy already achieved by doing things like repeating angles and distances etc. However there is usually another factor involved that often degrades the actual observations. This is the error already inherent in the positional values of the control points that the measurements are tied to. Least Squares can only spread this error into the actual observations of the survey, and this can seriously degrade original observations especially with contemporary high accuracy equipment that most surveyors use today. It is not unusual to have internal survey accuracies that are better than the accuracy of the control points that are tied into. This was especially noticeable in the past when tying GPS surveys to NAD27 values, but still occurs in other types of surveys today.

 
Posted : 07/10/2015 10:17 am
(@jbrinkworth)
Posts: 195
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For those of you that do not use LS, how do you know (I mean really know) if you are meeting RPA?

Are you performing an independent survey of higher order on your own survey to determine if your survey meets the standards?

 
Posted : 07/10/2015 11:25 am
(@aliquot)
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Paul in PA, post: 339455, member: 236 wrote: I thought I had made it clear, I do not adjust my everyday field work. If it falls within my expectation of erros, I accept it for what it is. Honest measurements with error.

Quote me on his, "Least Squares Adjustment does not make observations better, but it does make them different.
The measurements are not closer to the truth, mathematical perfection is not what surveying is about."

Least squares is much more useful in checking your product than it is in being your product.

What do I prove by adjusting my field angle by 1" or a distance by 0.01', when I use a 5" gun and a bipod on a found pipe that is deformed or a rebar with a not so flat top?

Paul in PA

Paul, least squares used correctly does make your observations better. As you go around a traverse your true position gets further and further from your measured position. Provided that there is no blunder, When you add in redundancy and process it with least squares you get an answer that will be closer to the true value. If you do have a blunder, least squares is great way to locate it.

If you don't adjust your field measurments how do you close your maps?

 
Posted : 08/10/2015 10:01 am
(@norman-oklahoma)
Posts: 7610
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"...I accept it for what it is. Honest measurements with error..."
Without least squares you use only the measurements and ignore the error. With it, you account for the the errors. I ask, which is more honest?

 
Posted : 08/10/2015 2:00 pm
(@edward-reading)
Posts: 559
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JBrinkworth, post: 339622, member: 6179 wrote: For those of you that do not use LS, how do you know (I mean really know) if you are meeting RPA?

Are you performing an independent survey of higher order on your own survey to determine if your survey meets the standards?

I notice that no one has answered this question....

 
Posted : 08/10/2015 2:16 pm
(@bajaor)
Posts: 368
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..and if you want to generate true state plane coordinates, no?

 
Posted : 08/10/2015 2:19 pm
(@norman-oklahoma)
Posts: 7610
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There are 2 reasons for not using least squares:

1. The cost of the program.
2. Stubborness

If someone claims some other reason they are in denial.

 
Posted : 08/10/2015 4:08 pm
(@lmbrls)
Posts: 1066
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3. Unwilling to learn something new.

 
Posted : 09/10/2015 3:08 am
(@paul-d)
Posts: 488
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Agree, the issue (assuming no blunders) is not the small (hopefully) errors in each line, it is the propagation of those errors throughout the traverse. If ìÄAZ n = ‰ö?ìÄAZ 12 + ìÄë± 22 + ìÄë± 32 +.... ìÄë± n2, then ignoring the propagation through a traverse is a folly in my opinion.

 
Posted : 09/10/2015 6:31 am
(@ralph-perez)
Posts: 1262
 

RCliffWilkie, post: 339612, member: 10285 wrote: Paul in PA said: ‰ Ô
Least Squares Adjustment does not make observations better, but it does make them different.

I partially disagree. I think any adjustment only "improves" measurements to the extent that the stochastic and mathematical model of the adjustment reflect where the errors are coming from. Another way of putting that is to say that the geometry of the network has to be solid (well-conditioned), and the a priori weighing scheme has to be realistic. In other words, the internal redundancy gives one more overall "measurement" that is applied on top of the internal redundancy already achieved by doing things like repeating angles and distances etc. However there is usually another factor involved that often degrades the actual observations. This is the error already inherent in the positional values of the control points that the measurements are tied to. Least Squares can only spread this error into the actual observations of the survey, and this can seriously degrade original observations especially with contemporary high accuracy equipment that most surveyors use today. It is not unusual to have internal survey accuracies that are better than the accuracy of the control points that are tied into. This was especially noticeable in the past when tying GPS surveys to NAD27 values, but still occurs in other types of surveys today.

Interesting you should mention this because one of the things that I like about Move3 (LSA software) is the report of the quality of your controls upon performing a "Free" (unconstrained or minimally constrained adjustment. You really get to see the slop you're inheriting from some of these agencies.

 
Posted : 11/10/2015 4:48 am
(@paul-in-pa)
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JBrinkworth, post: 339622, member: 6179 wrote: For those of you that do not use LS, how do you know (I mean really know) if you are meeting RPA?

Are you performing an independent survey of higher order on your own survey to determine if your survey meets the standards?

"RPA"? I assume you mean Relative Positional Accuracy, which cannot be done as you infer.

Least Squares Adjustment however can give an "estimate" of Relative Positional Precision, but as per Minimum Standard Detail Requirements for ALTA/ACSM Land Title Surveys, 3.E.iii.

"Relative Positional Precision is a measure of how precisely the surveyor is able to monument and report those positions; it is not a substitute for the application of proper boundary law principles. A boundary corner or line may have a small Relative Positional Precision because the survey measurements were precise, yet still be in the wrong position (i.e. inaccurate) if it was established or retraced using faulty or improper application of boundary law principles."

Paul in PA

 
Posted : 11/10/2015 5:56 am
(@jbrinkworth)
Posts: 195
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IN and KY standards refer to RPA, not RPP. I had this in mind when posting my questions above. It seems there may be a semantics issue here. A bit odd considering Gary Kent advises on the ALTA standards...you would think IN and ALTA would be more consistent with one another.

I agree that RPP is a better descriptor of the quantitative elements of a survey and RPA is more representative of a qualitative approach. Both important, nonetheless. Thanks for pointing that out.

Back to the question...How do you ensure that you are meeting the quantitative elements (RPP as you describe) required by the state or ALTA?

You said...

"I thought I had made it clear, I do not adjust my everyday field work. If it falls within my expectation of erros, I accept it for what it is. Honest measurements with error."

I get this, and from what I've read in your posts, you seem to be a prudent and more than competent surveyor. I am not convinced that a savvy attorney and/or competent judge would accept that statement, however.

In my parts, there are guys who slap the "this survey meets the minimum state standards ....of an urban survey .07 +/- 50 ppm..." who have never ran LS and most certainly have never performed an independent survey of higher order.

I am concerned about the surveyor, not so prudent. That's why the question arose.

 
Posted : 11/10/2015 4:11 pm
(@jbrinkworth)
Posts: 195
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IN and KY standards refer to RPA, not RPP. I had this in mind when posting my questions above. It seems there may be a semantics issue here. A bit odd considering Gary Kent advises on the ALTA standards...you would think IN and ALTA would be more consistent with one another.

I agree that RPP is a better descriptor of the quantitative elements of a survey and RPA is more representative of a qualitative approach. Both important, nonetheless. Thanks for pointing that out.

Back to the question...How do you ensure that you are meeting the quantitative elements (RPP as you describe) required by the state or ALTA?

You said...

"I thought I had made it clear, I do not adjust my everyday field work. If it falls within my expectation of erros, I accept it for what it is. Honest measurements with error."

I get this, and from what I've read in your posts, you seem to be a prudent and more than competent surveyor. I am not convinced that a savvy attorney and/or competent judge would accept that statement, however.

In my parts, there are guys who slap the "this survey meets the minimum state standards ....of an urban survey .07 +/- 50 ppm..." who have never ran LS and most certainly have never performed an independent survey of higher order.

I am concerned about the surveyor, not so prudent. That's why the question arose.

 
Posted : 11/10/2015 4:11 pm
(@exbert)
Posts: 215
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JBrinkworth, post: 340068, member: 6179 wrote: IN and KY standards refer to RPA, not RPP. I had this in mind when posting my questions above. It seems there may be a semantics issue here. A bit odd considering Gary Kent advises on the ALTA standards...you would think IN and ALTA would be more consistent with one another.

I agree that RPP is a better descriptor of the quantitative elements of a survey and RPA is more representative of a qualitative approach. Both important, nonetheless. Thanks for pointing that out.

Back to the question...How do you ensure that you are meeting the quantitative elements (RPP as you describe) required by the state or ALTA?

You said...

"I thought I had made it clear, I do not adjust my everyday field work. If it falls within my expectation of erros, I accept it for what it is. Honest measurements with error."

I get this, and from what I've read in your posts, you seem to be a prudent and more than competent surveyor. I am not convinced that a savvy attorney and/or competent judge would accept that statement, however.

In my parts, there are guys who slap the "this survey meets the minimum state standards ....of an urban survey .07 +/- 50 ppm..." who have never ran LS and most certainly have never performed an independent survey of higher order.

I am concerned about the surveyor, not so prudent. That's why the question arose.

I'll say this... I use LS. I keep up with about a dozen other licensed surveyors in town. None of them use least squares, all of them do ALTA surveys, most of them don't adjust their control. These folks range from 10 years to 40 years of professional experience.

 
Posted : 01/11/2015 5:01 pm
 adam
(@adam)
Posts: 1163
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You are spot on.

 
Posted : 02/11/2015 5:03 am
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