Grid to Ground Coordinates

what part of the world are you in

I am in Vermont

It totally depends on what software you use and what its capabilities are.

I have Carlson and use the NGS website.
What is your procedure, regardless of software.

I setup a low distortion projection and run everything in that..no conversion necessary

How do you add you GPS points to your low distortion projection?

GPS does not work in "Grid coordinates". This is a misconception. GPS works in ECEF (Earth Centered Earth Fixed). This is then projected onto an ellipsoid to produce latitude and longitude, which is then projected onto a conic surface (such as a cylinder or a cone for State Plane) by your data collector.

This is a common misconception among surveyors, and one I held in my early understanding of GPS. This is probably due to State Plane being the most functional, largely accepted, largely supported and documented projections available to US surveyors. As a result, most of us start of with GPS using State Plane and arrive at the conclusion that this is what GPS operates in. Nothing could be further from the truth.

To answer your question, there are two factors that distort any projection distance: the distance between the ellipsoid and the projection surface, and the distance from the ellipsoid to the surface. The distance between the ellipsoid and projection surface produces the Grid factor while the distance between the ellipsoid and the surface produces the Elevation factor. Note that the elevation factor is determined from the ellipsoid height, NOT the orthometric (sea level) height. The distance between the projection surface (the cone or cylinder) and the ellipsoid changes as the distance from the Central Meridian (for Transverse Mercator) or the Standard Parallel changes.

Generally for small projects with relatively little elevation change a single Grid Factor and Elevation Factor can be used project wide. These can be multiplied together to form the Combined Factor. The most technically correct method requires determining the Grid Factor and Elevation factor (and subsequently the Combined Factor) for each point. Then an inverse is solved by averaging the unique Combined Factor for each endpoint and multiplying the reciprocal of the average to the Grid inverse distance. NOTE this is for inverse distances and not to be applied to coordinates to develop a modified or scaled Grid coordinate system. Modified systems should ONLY USE ONE CF.

For State Plane reduction to "Ground" Distances, there are three practical options:

Keep your coordinates in true State Plane Grid and apply the proper, unique Combined Factor to each inverse. The problem with this will be that in areas of substantial relief, the factors will scale to different elevations and your bearings and distances won't close (the chain will be longer for higher elevations and shorter on lower elevations).

Keep your coordinates in true State Plane Grid and apply an average, project wide, Combined Factor to each inverse. The problem with this is that in areas of substantial relief, your measured distances will vary from the scaled inverse - not as much as from the true Grid inverse, but there is distortion that can be observed.

Scale your true State Plane Grid coordinates by an average, project wide, Combined Factor. This does the same thing as option 2, but does the multiplication once, instead of with each inverse. It has the same limitations as option 2, but also adds the issue of the coordinates being similar in appearance to true State Plane, but no longer actually being State Plane. Careful attention to metadata should be taken, and it is recommended to subtract off a significant value (such as the millions) from the coordinates to reduce the possibility of future confusion.

The Low Distortion Projection starts at the beginning of this post. Rather than project the Latitude and Longitude onto the State Plane Projection, we create a projection in the software that have less distortion (all projects include distortion). While an LDP has a Grid Factor and an Elevation Factor, just like State Plane, the Grid Factor is specifically designed to produce a Combined Factor that is so close to 1 that it can be ignored without significant injury to the reported distances.

> I have Carlson and use the NGS website.
> What is your procedure, regardless of software.
Least Squares simultaneous adjustment of the OPUS positions and the terrestrial observations. I use StarNet for that, but you have SurvNet as part of your Carlson Survey which will do the job.

Scaling of grid coordinates can be done using Excel. You should consider translating them as well.

depends on what type of GPS points they are, network rtk, I set up the LDP on the data collector and just import the points directly, static points I process in Trimble Business center using whatever datum the control is in and then switch to the LDP projection. TBC allows you to switch projections easily.

What Shawn said. My understanding is all any GPS receiver does is measure lat, long, & height (on the elipsoid). Everything else is software of your choosing. I'm Trimble and they are turning into a PIA and I just want to retire.

Getting to ground is pretty basic stuff (combined scale factor), but lots of guys here prefer to stay on grid and have a way better understanding of it all than me. I suspect many are close to sea level or match the geoid separation so the differences are minor. My robot likes ground, but I'm up around 4,000 ft elev so I just adjust things to accommodate my needs. It all kind of goes hand in hand with many prior posts on calibration/localization preferences.

And as mentioned above, are you utilizing a local RTN, OPUS, or just winging it and hit the "here" key every time. Makes a difference.

well delineated posts like these are what keep me tuned in. thank you, Shawn

> How do you add you GPS points to your low distortion projection?
You reference the geographic coordinates (lats/longs). Grid coordinates are a mathematical product of the projection parameters in use. Typically you use a Least Squares adjustment software to do this math. Input the geographic coordinates of the point you want to hold, the raw data, and the projection parameters. Output grid coordinates, residuals, and other statistics.

Low distortion system

I used Carlson (scale points) to scale from grid to ground.

The combined scale factor used is .999987558589

The points are about 8000' apart so the difference in distance from grid to ground is 0.10'.

When scaling the cords from grid to ground Carlson multiplies the Northing and the Easting cords for each point

The resulting Cords are about 20' away from the grid (original) cords.

So now the cord. system is basically a local system.

If a client wants Grid cords would you leave the 0.10' of slop between grid and ground in the control? or scale the points and tell them they cant use GPS without localizing?

Not sure what the next step is.

> If a client wants Grid cords would you leave the 0.10' of slop between grid and ground in the control? or scale the points and tell them they cant use GPS without localizing?
That's not slop. It's projection. If the client the project on the grid, you put the project on the grid. Just make sure that you note that it is on the grid.

When scaling from grid to ground, I would hope that Carlson would divide by a combined factor. In scaling from ground to grid, hopefully the software would multiply.

And therein lies one big problem with the method: Do I multiply or do I divide?

Thanks for the kind words, Eddie. People taking the time to explain GNSS and geodesy on the old RPLS board was the genesis to much of the knowledge I have today. It's rewarding to pay it forward.