In my last post I reviewed the D302-RTK receiver from DataGNSS.

Since the unit is designed for surveying, I thought it would be fun to use it to actually try and measure an actual survey marker, something I’ve never done before.

So, to find an official marker I went to the NGSDataExplorer website from the U.S. National Geodetic Survey group and brought up an easy-to-use interactive map of the local area with different types of survey markers marked. Here’s a zoom in of the map showing a nearby marker I found with easy access and a decent sky view.

Clicking on “Datasheet” brings up the following information about the marker.

About halfway down, you can see that the NAD83 (2011) coordinates for this site are:

latitude = 40 05 14.86880 N

longitude = 105 09 01.68689 W

ellipsoidal height = 1613.737 meters

So let’s see how close we get to these numbers with the D302-RTK. The D302-RTK uses a u-blox M8T receiver and a version of the demo5 RTKLIB code, so any results from this experiment should be valid not just for the D302-RTK, but for any M8T/RTKLIB based solution.

The survey marker is just over 1 km from my house and so I will use the antenna mounted on my roof connected to another M8T receiver as the base station. The base observations are then broadcast to the internet with an RTK2GO.com NTRIP caster as I described in this post. Using an M8T receiver for the base station allows me to enable GLONASS ambiguity resolution in the solution since both receivers are using identical hardware.

Since I am doing a real-time solution, I need internet service at the site of the measurement to get the base observations. I got this by enabling a hot spot on my cell phone and connecting the D302-RTK to that. I have surveyed the base station antenna with both RTK solutions from nearby CORS stations as well as online PPP solutions so I have a fairly good idea of it’s location, maybe within a cm or so.

The clamp and surveying pole in the top photo look nice but I don’t own anything like that, so instead I used a $20 camera tripod, a piece of wood, two rubber bands, a wood clamp, a piece of string, and a carriage bolt. Here is the resulting setup aligned over the survey marker. Note that I am using the optional helix antenna which was included with the receiver that was sent to me rather than an external antenna.

Here’s a close-up of the marker itself with the carriage bolt and string aligned over the top of the marker pin. The other end of the string is fastened directly underneath the D302-RTK, making it easy to align the receiver directly over the marker and measure the vertical distance between the two. If you’re wondering about the film canister at the bottom of the well, it seems that the marker is also serving as a local geocache location.

At this point everything is ready to go. I powered on the receiver, enabled the RTK service for a static solution, waited five minutes and then recorded the position. I did this three times to get three different measurements. Here are some not-so-good photos from the screen of the D302-RTK for the three runs. It is possible to store these values to the unit using an additional Android app, then uploading with a USB cable later, but in my case I just copied the values manually to my computer.

The numbers are a little hard to read but are very consistent between results so I’ll just use the middle values. The indicated height is the height of the base of the antenna, not the survey marker so I need to subtract the difference which I got by adding the length of string and bolt to the height of the receiver, in this case 1.49 meters.

latitude = 40 05 14.8870 N

longitude = 105 09 01.7374 W

ellipsoidal height = 1614.393 – 1.49 = 1612.903 meters

Comparing to the published survey numbers, we are not very close. It’s a little less intuitive to compare degrees of latitude and longitude but the height is obviously off by almost a meter, so something is wrong.

Usually this kind of large error suggests there may be a mismatch between coordinates. Sure enough, when I double-checked the base location that I had entered into the D302-RTK, I realized that I had used WGS84 coordinates, not NAD83. As I mentioned earlier I had computed the base position using both RTK solutions from nearby CORS stations as well as online PPP solutions. RTK solutions are always relative to the base station so will be in the same coordinate system as the base. CORS stations locations in the U.S are normally specified in NAD 83 so using those coordinates would have been fine, but instead I had used coordinates from the online PPP solution which were in WGS-84 coordinates. Since the RTK solution will be in the units of the base station, my results are in WGS-84 coordinates, and the published survey coordinates are in NAD83.

Fortunately there is another easy-to-use tool from the U.S. National Geodetic Survey that will translate from one coordinate system to another. Entering the WGS84 coordinates from the measurement and translating to NAD83 gave the following:

You can see the WGS-84 coordinates on the left and the NAD83 translations on the right. The translated coordinates from above are:

latitude = 40 05 14.86828 N

longitude = 105 09 01.68627 W

ellipsoidal height = 1614.393 – 1.49 = 1613.759 meters

Compare these to the marker coordinates we got from the NGS website earlier:

latitude = 40 05 14.86880 N

longitude = 105 09 01.68689 W

ellipsoidal height = 1613.737 meters

That’s looking much better. The heights now differ by only about 2 cm, well within the expected vertical accuracy given the fact that my base station location was not exact, both antennas were uncalibrated, and my tripod setup was a little imprecise.

How about latitude and longitude? The error in latitude is 0.00052 arc seconds and in longitude is 0.00062 arc seconds. Those seem small, but unless you are a professional surveyor these numbers are probably not very meaningful to you, they certainly are not to me.

Meters would be much easier to interpret. I usually use a free matlab geodetic toolbox, available on the Matlab file exchange to do these sorts of translations, but this time, let’s do it by hand.

At the equator, one arc second of longitude or latitude is approximately equal to the circumference of the earth divided by 360 degrees, then by 60 min/degree, then 60 sec/min. A quick google search finds that the equatorial circumference of the earth is about 40.07 million meters. Divide that by 360*60*60 gives 30.92 meters per arc second. This is not exact but good enough for our exercise. Arc-seconds of latitude remain nearly constant with location but arc-seconds of longitude will get smaller as we approach the poles of the earth by the cosine of the latitude. I am located at approximately 40 degrees latitude, so 30.92*cos(40 degrees)=23.68 meters per arc second of longitude.

The error in latitude in our measurement from above was 0.0052 arc seconds. Multiply this by 30.92 meters/arcsec gives an error in meters of 0.016 or 1.6 cm. For longitude, multiplying 0.000062*23.68 meters/arcsec gives 0.0015 meters or 0.15 cm.

So total error in this exercise was 2.2 cm of vertical error and 1.6 cm of combined horizontal error. Not too bad for two rubber bands, a piece of string, a bolt, and a wood clamp (as well as a nice low-cost receiver)!

Although I used the D302-RTK for this experiment, I believe the results would be very similar for any solution using a pair of M8T receivers and RTKLIB.