deflection of the vertical?

I'm not sure that I understand your question Dane, so maybe I'm headed off on the wrong trail here;

YES (BIG yes), the GPS 'setup' is normal to gravity (the geoid), and therefore may or may NOT be normal to the reference ellipsoid (e.g. IGS08 or NAD83).

And, YES (BIG YES) the computed Latitude, Longitude, AND Ellipsoid Height is based on the reference ellipsoid, NOT the “geoid.”

SO... yes (little yes), there would (or could) be a small (very small) “error” in the computation from the antenna phase center (or ARP) to the monument (GRP) on the ground. HOWEVER, it is pretty unlikely that this “error” would be more than a millimeter in the horizontal (or maybe 2mm in VERY extreme cases), BUT any “error” would certainly be inconsequential in the ellipsoid height.

As far as the question... ”What does the deflection of the vertical for this station look like” goes...I dunno...WHAT Station?

The deflection of the vertical is entirely dependent on WHERE you are, [in that] it is a function of the geometric shape of the ellipsoid, AND the “shape” of the GEOID (gradient, slope, direction of the plumb-line, etc. etc.) unique to that particular point on the Earth. Or more accurately the relationship of these two surfaces to each other (at that point).

That probably isn't stated very well, but hopefully it makes some sense (and is reasonably correct).

You can compute a very good “modeled estimate” of the deflection of the vertical for any point in the US by using DEFLEC09:

NGS Geodetic Tool Kit:
http://www.ngs.noaa.gov/cgi-bin/GEOID_STUFF/deflec09_prompt.prl

Deflect09 Home Page:
http://www.ngs.noaa.gov/GEOID/DEFLEC09/

I hope that helps,
Loyal

> That probably isn't stated very well, but hopefully it makes some sense (and is reasonably correct).

It's one of the better explanations I have heard on the subject.

> it is pretty unlikely that this “error” would be more than a millimeter in the horizontal (or maybe 2mm in VERY extreme cases)

2 mm in a 2 m setup? Does it really get that big?

Loyal the problem is

The problem is, I do not know enough about this stuff to form an intelligent question.
I was puzzling over the paradox or seeming paradox of starting out the measure plumb to the geoid and winding up with a solution referenced to the ellipsoid.

Jim

Those numbers were pretty much off the top of my head, and may very well be too large. The worst case scenario around my neck of the woods would be about .0003 meters on a 2-meter setup, but that probably isn't the worst case in the lower 48.

My “maybe 2mm” (if it exists at all), would probably be along the south slope of the Himalayas, or west slope of the Andes (or something like that).

Loyal

Dane

It DOES appear to be a mixing of apples and oranges, and in fact it IS I suppose. However, the nature of the measurements and computations involved, make it a trivial consideration (unless you are plumbing a shaft, or your “HI” is very large for other reasons).

Loyal

Loyal

Loyal would I be correct in thinking that the deflection will relate to the Laplace correction. It's been a while since I've applied that to traverse angles, but it's something a surveyor should know.

And it seems that it would have the same relationship.

I think I only did those calculations during NAD27 surveys along mountain ranges (large traverse distancess).

Anyway we are discussing a few seconds of correction.

See Winter/Spring 2010 - The Pennsylvania Surveyor article Geodetic Observations by Charles D Gilhani, page 10: https://www.psls.org/wp-content/uploads/2011/01/Surveyor-Final-2010-low-res.pdf

Mighty

Yup.

Here's a cut-n-paste from the DEFLEC09 Home page:

"DEFLEC09 is a companion product derived from the 2009 hybrid geoid model, and represents the deflections of the vertical at the surface of the Earth. These quantities are typically a few arc seconds, but can reach an arc minute of departure.

DEFLEC09 is comprised of both north-south (Meridian component, designated as "Xi") and east-west components (Prime Vertical component, designated as "Eta"). In DEFLEC09, Xi ranges from +41 arcseconds (Bahamas), to -38 arcseconds (Bermuda), while Eta ranges from +45 arcseconds (Rockies) to -43 arcseconds (Bermuda)."

Time for a brewski here in Wyoming,
Loyal

Mighty

> These quantities are typically a few arc seconds, but can reach an arc minute of departure.

That sounds more like it. A minute in 2 meters is only about half a millimeter, which is noise level for my gear, especially since that's worst-case.

Dear Dane,

Yes, you do level your GPS antenna.
But, no, you don't need to consider deflection of the vertical.

(The GPS data are referenced to XYZ, Earth-centered, Earth-fixed,
and are convertable to ellipsoidal-related quantities.)

Here's why --

The GPS antenna is where the various GPS satellite signals come
together. In a rough approximation, it can be considered as a
point in space, and need not be leveled at all. However, one
does want to relate the antenna phase center to the mark on the
ground. So, you place the antenna "over" the mark. This is
where you invoked a "local astronomic horizon coordinate system".
This was done when you leveled the GPS antenna and used an optical
plummet (perhaps) to put it over the mark. The distance from
antenna to mark is about 2 meters. A single arc-second of
deflection of the vertical over 2 meters is 0.0097 millimeters
of lateral displacement -- negligible. So you (or software) can
transfer the GPS antenna coordinate to the ground mark without
worrying about deflection of the vertical.

Next level of detail.

We are (likely) talking dual-frequency carrier phase. This means
there are two antenna phase centers, L1 and L2. Their relative
relationships are in a coordinate system that is aligned with
the GPS antenna body. The phase center locations are coded up
in antenna files, cataloged by IGS, NGS, and GPS manufacturers.
However, when the GPS reduction software invokes those files,
it assumes (a good assumption) that the antenna is leveled
(and not laying on its side, for example). Hence the antenna
body coordinate system is taken to be aligned with the local
geodetic horizon system. However, since the GPS antenna was
leveled, the alignment is relative to the local *astronomic*
frame. The difference is the DoV. But, the distance between
the L1 and L2 phase centers is small. Call it 2 cm. This
means one arc-second of DoV causes 0.000097 millimeters lateral.
100 times *less* than what we saw above. Negligible.

Last level of detail.

Assume we are talking about a 5+ km line. This is very roughly
where one needs to consider troposphere in GPS data reduction.
The issue in question is the refraction along a ray path from
the GPS antenna to the GPS satellite. This can be a simple
model based on vertical angle (and a solvable tropo parameter),
or it can be somewhat more elaborate with a mapping function
that captures curvature in the ray path. Either way, you get
the wrong answer for tropo delay if there are systematic
tilts in figuring the ray path. Same deal for iono refraction.

Well, this really does happen. It was found that there is
antenna phase center variation, and that antenna radomes also
affect the path. These small displacements are tabulated in
the antenna files discussed above. The fitting process needs
to filter through a lot of phase noise. But the results are
tabulated every 5 degrees of zenith distance. In GPS reduction
software, the tables are linearly interpolated to obtain
the small PCV corrections. One can look at a favorite antenna
file and see that a few arc seconds of DoV in a 5 degree linear
interpolant range will also be negligible.

To summarize, DoV corrections should be considered for
optical technology where the instrument is leveled. But, for
GPS, the requirement that the antenna be leveled is solely
to make sure the antenna is more or less vertical.
One would never take a Wild T-4 hanging level and try to attach
it to a GPS antenna. That would be overkill.

Hope this helps ...

Dennis

> In GPS reduction software, the tables are linearly interpolated to obtain the small PCV corrections.

It's never been clear to me whether anything other than the mean north, east and up values are used by a particular baseline processor. I'm sure there are some that do the elevation angle interpolations, but I'll bet there are others than just use the means and call it good enough.

Good question Jim

It is my understanding that only the REALLY high-end processors (PAGES, BERNESE, GAMIT etc.) support the full blown antenna calibration data in the IGS ANTEX file (robot calibrations that include “elevation angle” data in different azimuths as well).

The WAVE processor in GPSurvey and TGO certainly supported the “elevation angle” data, and you could chose Trimble's version, or the NGS (relative) version. The Trimble files were ASCII text files, so one could update to the new ABSOLUTE calibrations without too much hassle. I don't have a clue about TBC, but I would assume that it has this capability as well.

The Novatel/Waypoint GrafNav program also supports the [simple] “elevation angle” data for the terrestrial antenna, as well as the calibration data on the SV (space vehicle) antennas! This is the ONLY commercial processor that I have played with that supports the SV calibrations. There may very well be others though.

For all but the most exacting work, I seriously doubt that this is an significant issue. But then again, there is a LOT more about this stuff that I DON'T know, than there is that I do know (or think I know).

Maybe Dr. Milbert will jump back in and give us the straight scoop.

Loyal

Good question Jim

> The WAVE processor in GPSurvey and TGO certainly supported the “elevation angle” data, and you could chose Trimble's version, or the NGS (relative) version.

I have no doubt that these applications use the mean offsets given in the antex and antinfo files, but I haven't seen anything definitively stating that they use the elevation- and/or azimuth-dependent variables give in the files. Without some serious testing (which would take more time that I'm prepared to devote for the foreseeable future), the user wouldn't be able to tell whether the software was using only the mean values or the more sophisticated position-dependent variations.

In the end it's probably not a big deal. There are so many other error sources in GPS measurements that these may not amount to much for all but the most stringent applications. However, it's something I've long been curious about.

Good question Jim

My take on the subject is pretty the same Jim.

I have heard that the "elevation dependent" corrections don't really make much difference until the baselines get REALLY long.

Of course the mix of antenna types/models on a given baseline might factor into things too.

Loyal

For those who might be interested...the NGS GEOID Team released a new "deflec" program recently:

http://www.ngs.noaa.gov/cgi-bin/GEOID_STUFF/deflec12A_prompt.prl

This new version is based on GEOID12a, so it is the latest greatest!

Loyal

Wow, thanks for going in the wayback machine and posting that Loyal.

Tom,

DEFLEC12a was released just a week or so ago, but I figured this thread would be a good place to "announce" it....

🙂
Loyal