Correlation between PDOP and precision

You didn't say anything about VDOP.?ÿ PDOP is a combination of HDOP and VDOP. ie/PDOP at least has a VDOP component. HDOP has no such component. When the satellite geometry is such that you are maximizing (lower) HDOP it is natural that VDOP would suffer.?ÿ

I understand. However, I'm unable to determine what VDOP en HDOP I have, because my raw data only contains PDOP. I assume I can't make valid conclusions based on my data?

In simple terms position dilution of precision considers 3 dimensions. Because you are combining 2 and separating 1 it will naturally be stronger. I'm sure there are more scientific explanations. If you separate all three you could see less difference.?ÿ

Also when taking observations in obstructed conditions PDOP can give the user a delusional sense of precision.?ÿ

@norm?ÿ

OMG delusion of precision,,,,,,,,,Genius!!!!!

Posted by: @norm

IAlso when taking observations in obstructed conditions PDOP can give the user a delusional sense of precision.?ÿ

To emphasize Norm's statement, I believe all the DOP values are computed from satellite positions, so depend only on how many satellites are received and how well they are spread around your sky view.?ÿ They do not take into account interference or any propagation effects, such as iono/tropo effects, local multipath, etc.

The way I learned it MANY years ago is that PDOP is sort of an inverse measure of the volume of the polygon formed by the satellites in the sky and the observers position on the ground (or on a ship, etc). If the satellites being received are all bunched together in one area, then the volume will be small and the PDOP will be high.?ÿ

It is a simplification but I found that useful when I was giving classes and workshops...

Perhaps the relationship is not linear. Look carefully at your scatterplot. You may have something like the graph below, where the actual relationship is hyperbolic but it's modeled with a straight line:

If a curve fits better than a straight line, then you won't be able to use a simple correlation coefficient to judge the strength of the relationship. You'll need R^2, the coefficient of variation, which is the ratio of the variance of the predicted values (model values) to the variance of the actual values. Sometimes you can get some flak from a professor about the truth of that definition of R^2. Ask them if R^2 in words is coefficient of variation and ask them why they think it has that name.

As PDOP falls, accuracy goes up, so it's an inverse relationship. Try some different shapes and see if your fit?ÿ improves.

?ÿ

Posted by: @thidmey

Hi all,

I'm a final year student Survey Engineering and the correlation between PDOP and vertical precision is much stronger than between PDOP and horizontal precision (64 versus 38%)

The discussion has given some good information, but doesn't directly address this question.

GNSS vertical error usually is 2 to 3 times horizontal error, rms. Thus the vertical component of PDOP (the VDOP you don't have data for) is driving the vertical position error.?ÿ

The horizontal component HDOP is usually the smaller component of PDOP and the horizontal error is smaller, so they don't drive the correlation.

I am not sure about your use of the term 'precision'. All of your measurements are probably expressed to the same precision, i.e.?ÿ number of digits.

You are probably looking at repeatability of measurements,?ÿ which in the long term average is a measurement of accuracy if constant or biased errors are insignificant.

Perhaps you could use theoretical PDOP, HDOP, and VDOP calculations from a planning tool, verify that your collected data matches well enough, and then calculate correlations with the theoretical values?

https://www.gnssplanning.com/#/settings

The differences between the planning tool and what you collected should be small if you are receiving mostly the same satellites, but could differ more if part of your sky was blocked or you had a limited number of channels (old receiver).

@norm?ÿ

The prior to editing version was the best version.?ÿ

The reason the VDOP is higher than the HDOP (and therefore the vertical precision is typically 2- 3 times the horizontal) is really very simple. The satellites are some 20,000Km up, so even when they're relatively spread out (good HDOP) the area of vertical intersection is still relatively large (higher VDOP). Think of it as a resection problem; if all of your control points are between azimuth 10 degrees and azimuth 170 degrees, your east - west precision is naturally going to suffer. In order for the vertical to be as strong (or even stronger) than the horizontal, there would need to be signals coming from beneath the receiver.

As others have stated, the PDOP is the product of the HDOP and VDOP. DOP (Dilution Of Precision) isn't really directly quantifiable in terms of positional error (i.e. if my PDOP is x then my error is y). It's an expression of the strength of the satellite geometry as regards the ability of the GNSS receiver to calculate a precise position.

Interestingly, everyone I've spoken with about the Trimble R12i has said that in an RTK survey the vertical actually tends to be as good as or even better than the horizontal; presumably because of the IMUs.

Horizontal GNSS positions are better than the vertical because their are no satellites received from below.?ÿ?ÿ

@norman-oklahoma?ÿ ?ÿIf we could bounce the QSZZ satellite single off something, would our vertical heights improve?? Is QSZZ satellite data available for PPP? Would that help vertical heights??ÿ ?ÿI am not trying to be funny or negative.

@oldpacer The QZSS satellite (or maybe there's more than one?) is/are geostationary and are made to enhance the precision in Japan and the region, similar to WAAS in the US. Other than probably in Hawaii and possibly on the Pacific coast they can't be seen from the US.

@lee-d?ÿ ?ÿ 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.?ÿ Would satellite data on the other side of the earth, improve out vertical height here??ÿ

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.?ÿ ?ÿ

From an OPUS report, today:

So the accuracy of the ellipsoidal elevation is 7 mm (ƒ??0.02') . But the ortho is 54mm (ƒ??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.?ÿ

Posted by: @oldpacer

@lee-d?ÿ ?ÿ 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.?ÿ Would satellite data on the other side of the earth, improve out vertical height here??ÿ

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.

@bill93?ÿ ?ÿWhat 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??ÿ

Here's a thought. If all the OP wants is a measure of association (correlation), he can use a function of the form:?ÿ 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.?ÿ