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Correlation between PDOP and precision

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oldpacer
(@oldpacer)
200+ posts Member

@lee-d    Which is why I was wondering if we could bounce the signal somehow. Satellite repeater, internet duplication or just retrieve the data later back at the office.  Would satellite data on the other side of the earth, improve out vertical height here? 

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Posted : May 17, 2022 8:42 am
Norman Oklahoma
(@norman-oklahoma)
5,000+ posts Member
Posted by: @oldpacer

If we could bounce the QSZZ satellite single off something, would our vertical heights improve??

With a local base I'm getting relative verticals with my Leica GS18 that are pretty dang close to as good as total station data. So I'm not sure how much extra effort has to go into this. The main limiting accuracy factor now is the geoid model.   

From an OPUS report, today:

So the accuracy of the ellipsoidal elevation is 7 mm (≈0.02') . But the ortho is 54mm (≈0.18'). Granted, this is for a 4 hour OPUS occupation. But it illustrates how much uncertainty there is in the geoid model. And with all the effort going into the gravity models for NATRF2022 I presume there will be an improvement there. 

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Posted : May 17, 2022 8:58 am
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Bill93
(@bill93)
5,000+ posts Member
Posted by: @oldpacer

@lee-d    Which is why I was wondering if we could bounce the signal somehow. Satellite repeater, internet duplication or just retrieve the data later back at the office.  Would satellite data on the other side of the earth, improve out vertical height here? 

No, because a) it would still be coming at the receiver from a high angle, and b) you need to know the path delay/length (which is what GNSS works on) and that's data you aren't likely to have.

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Posted : May 17, 2022 9:09 am

oldpacer
(@oldpacer)
200+ posts Member

@bill93   What if the repeater satellite had all the same direct data you had and the repeater satellite is included in your direct data. Could a pseudo-pseudo range for the 'beyond the horizon' satellite be calculated and transmitted to you? And could a revised time clock be calculated and transmitted to you? And could Elon Musk's satellite's do this? 

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Posted : May 17, 2022 9:43 am
MathTeacher
(@mathteacher)
1,000+ posts Member

Here's a thought. If all the OP wants is a measure of association (correlation), he can use a function of the form:  PDOP = a +b*(Horizontal Precision) + c*(Vertical Precision). That is, regress PDOP on the two precision measures.

Now, this reverses the intuitive causality, but the correlation measures will be unaffected. His software will split out the single variable correlations along with the joint correlation. The two single ones should be the same as his original runs.

The constant term will absorb as much of the correlation from undefined sources as the math allows, so an overly large constant term goes with a low correlation.

My sense is that the Vertical Precision is linearly related to PDOP while the Horizontal Precision is not. Vertical is one-dimensional; horizontal is two-dimensional. I would look at an inverse quadratic relationship for horizontal, which is another way of saying hyperbolic, but there are other candidates. In general, though, adding variables to a regression improves the fit, so the combined correlation should be greater than either of the single ones.

Consider this: If there's a weak or no correlation between PDOP and precision, then PDOP isn't very useful. 

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Posted : May 18, 2022 8:13 am
RobertUSA
(@robertusa)
200+ posts Member

You are seeing real world results. Typically H precision is 1/2 of V precision, I.E. the 33/66 ration you mentioned 

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Posted : May 18, 2022 6:02 pm

RobertUSA
(@robertusa)
200+ posts Member

You are seeing real world results. Typically H precision is 1/2 of V precision, I.E. the 33/66 ration you mentioned 

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Posted : May 18, 2022 6:02 pm
MathTeacher
(@mathteacher)
1,000+ posts Member

@robertusa 

Problem is, higher correlation coefficients imply better precision.

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Posted : May 19, 2022 6:28 am
Bill93
(@bill93)
5,000+ posts Member
Posted by: @mathteacher

@robertusa 

Problem is, higher correlation coefficients imply better precision.

Higher precision in estimating one variable from another.

But not in estimating that variable relative to its true value (or long term average as a standin for true).

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Posted : May 19, 2022 7:27 am

MathTeacher
(@mathteacher)
1,000+ posts Member

@bill93 

Agreed, to an extent. But the poster was implying that a high correlation value for a typically lower precision value and a lower correlation value for a typically higher precision value is the normal state. It isn't.

The water in this problem is muddied by the comparison of a unit-defined quantity, precision, to a unitless index, PDOP. High precision might be expected when the index value is low. If high precision is defined as the difference between measured position and actual position, or as some variance, then a low number will represent high precision, and the correlation will be positive. If precision is defined so that a high number means high precision, then the correlation will be negative.

In any event, complicated or not, there should be a measurable relationship between PDOP, horizontal position, and vertical position. But it doesn't have to be linear, so the Pearson correlation coefficient might not be the best measure.

 

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Posted : May 19, 2022 12:42 pm
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Norm Miller
(@norm)
1,000+ posts Member

Last time I was observing, the least birds I had was 30+.  PDOP was < 2 on everything. With multi-constellations we might be spinning our wheels analyzing PDOP stats. In the 90's with 4 or 5 birds a different story. In my experience the two or three major horiz and vert error sources are pole errors. Out of plumb or bad phase center height above the mark. And those locations where it takes longer than normal to fix for whatever reason. 

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Posted : May 20, 2022 7:39 am
MightyMoe
(@mightymoe)
5,000+ posts Supporter

@norm 

I'm with you there.

It's gotten to be very rare when the unit won't fix, either deep woods or some type of communication glitch.

My 4-wheeler sitting next to me running will interfere with the radio, turn it off and I fix instantly.

But tracking down the "error" in the R-10 unit locations would be exhausting.

Set up control points on a site with the R-10, occupy them with the S6 and there is .02' of error, mostly vertical, over .04' and we start looking for a problem.

This is repeated over and over.

Rod plumb, tribrach, GPS "errors", PDOP, distance meter, scale factors.

A big bucket of mini teeny-tiny errors that add up to nothing. Interesting in an academic sense, but working in the field pfttt!!!

I recently finished a boundary locating a 1/4 corner that was surveyed by the state in 1996. On the state plat the surveyor noted that the monument is a recovered set stone and there is a northing, easting in state plane shown on a table on the plat. In 2001 the state re-monumented the stone with an Aluminum cap, no coordinates for that survey. My new survey is .07' N, .04' E. of the 1996 coordinate. Good times we live in. 

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Posted : May 20, 2022 8:21 am

Norman Oklahoma
(@norman-oklahoma)
5,000+ posts Member
Posted by: @norm

Last time I was observing, the least birds I had was 30+.  PDOP was < 2 on everything. With multi-constellations we might be spinning our wheels analyzing PDOP stats. In the 90's with 4 or 5 birds a different story. In my experience the two or three major horiz and vert error sources are pole errors. Out of plumb or bad phase center height above the mark. And those locations where it takes longer than normal to fix for whatever reason. 

In the wide open spaces, sure. I'm using RTK in an urban environment where

  1.  real estate is priced by the square foot, and
  2.  there is a lot of sky obstruction 

I'm lucky to get 12 or 13 satellites at the rover and often am down to 8 or 9. And it matters which ones I'm getting. In these conditions the PDOP numbers are important. Granted, without all these extra constellations RTK is just not an option at all. 

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Posted : May 20, 2022 9:33 am
lukenz
(@lukenz)
200+ posts Member

@norman-oklahoma 

Will preface this with a disclaimer that I expect you do technology independent checks and are working within necessary error budget for your projects; the following is more a caution to those who treat GNSS as a magic stick.

 

If the sky visibly is that bad then is rtk the tool for job? Once I'm down to those satellite levels (with all four constellations) I'm looking at CQ readouts of 7-10mm HZ and 15-20mm V which you at least need to double to 95% CI. For urban control I'm wanting <=10mm in HZ repeatiblity so RTK isn't there.  Plus once it's not wide open you get the problem of biased GNSS when multiple control shots at different times agree but when you shoot it with total station you find it's ~20mm out. The more I use RTK GNSS the less I trust it (or the more I try to avoid pushing it's limits).

 

Govt. auditing surveyor here tells a story of following a surveyor who called the middle of three stable control points that were placed on a line disturbed based on GNSS alone. Auditing surveyor set up his GNSS (different brand to first guy) and got pretty much the same result. He then set up total station at one end, shot the other, and checked the middle; what do you know all three marks were still in terms. The middle mark only had a mid sized tree to one side, not a poor site for GNSS at all but enough to bias the solution. I've had a similar experience next to a standard street powerpole, double tied with 10mm HZ repeatiblity by GNSS but was 20mm out when shot with total station.

 

Used Lecia, Trimble and even the fabled Javad but find the total station hasn't been superseded for ~10mm HZ positioning in urban environment yet. Sure at ~20mm HZ the GNSS ups the production but thats typically not urban spec for control/boundary where you are signing on the plan where I work.

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Posted : May 20, 2022 6:28 pm
Norman Oklahoma
(@norman-oklahoma)
5,000+ posts Member
Posted by: @lukenz

If the sky visibly is that bad then is RTK the tool for job?

We RTK what we can but traverse (almost) everything. In rare cases we double RTK tie things - different bases - if traversing is impractical. StarNet adjust everything.  But, yes. RTK is not 100%. 

The RTK'ing serves the purpose of putting the control on the grid, and also provides blunder detection.    

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Posted : May 20, 2022 7:25 pm

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