Calculating your own GPS accuracy
In my post on GPS accuracy I made some claims about the accuracy of GPS devices and used a graphic that was created by a third party that may have confused the issue for some people, as it appeared to show a different level of accuracy that I was writing about.
Here is how to determine the accuracy of your own GPS, based on an experiment I did last week on two of my own units.
Set up the GPS
The GPS I am using is the Garmin GPSMAP 62st (pictured right).
Turn on the GPS and let it “settle” or calculate your position. If it hasn’t been on in a while this might take as long as 15 minutes. While you’re at it, configure the GPS to record the position regardless of how far it believes it has moves since the last calculation. Some GPS units “filter” positions so they don’t introduce distances that haven’t been travelled. This is important to athletes who are using it to track how far they run. If you don’t do this step, the results are going to be very strange, as the GPS will only record wide swings in position.
It’s probably a good idea to make sure the batteries are fresh.
Choose a location where the GPS can be put, safely, for several hours and where it has a reasonable view of the sky, similar to what you might expect under the conditions you regularly use it.
Start gathering data
Delete the current track. This important step “zeros” the current recording of the track file so we start with data that’s current, and “stable” — the GPS has had the time to refine the position. We’re only interested in the current position as long as the GPS is not moving.
Let the GPS gather data for several hours. Do not move it. This is where we let the little unit do it’s work gathering data.
Save the track, and download it to your computer. In my case the data is in a GPX file. I took the file and converted the latitude/longitude into UTM, because I want to express the position and error in terms of meters. I then import the data into a spreadsheet.
Analyse the data
Find the mean of the UTM coordinates (which is in meters), and use that to calculate the “delta X” and “delta Y” positions by subtracting the mean X and mean Y to create two new columns in the spreadsheet.
Calculate the standard deviation of the delta X and Y columns.
Use the standard deviation to calculate the CEP ( 50%) radius using the following formula:
where $latex \sigma_x$ is the standard deviation of the easting value, and $latex \sigma_y$ is the standard deviation of the northing. In this case, the radius is 6.06 meters.
Then calculate the 2DRMS (95%) radius using the formula:
That radius is 14.86 meters.
Finally, plot the delta X and delta Y columns, and the CEP and 2DRMS rings to help you visualize the accuracy. I present the results of my experiment, ebedded below.
The spreadsheet of the data that produced this chart is available here.
Code to create the chart is available here.
Read about a comparison between a wilderness GPS and a Smartphone GPS
Anyone having trouble reproducing these results feel free to email me a GPX file and I’ll send you a quick analysis of the accuracy using this method.