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Using GPS Data to Calculate Position,
Calculate Distance, and Draw Maps

GPS Data

My trail distances differ from the distances shown on some official maps. My distances are based on the global positioning system (GPS). Originally designed for the military to determine position on the ground, the GPS system now is available to civilians. The GPS system is based on about 30 satellites that circle the earth every 12 hours in nearly circular orbits about 11,000 nautical miles above the planet. These satellites broadcast time and position data, and GPS receivers (GPS units) pick up broadcasts from at least three satellites and use software to calculate the on-the-ground longitude-latitude position of the receiver. With four or more satellites, GPS units can also calculate elevation.

While the system is good, it is not perfect. Originally, the military introduced error (called selective availability) into the satellite data to throw off GPS units, but that no longer is the case. Still, there are sources of error in the satellite data. For example, satellite transmissions can bounce off of buildings or cliffs and confuse the receiver, tree cover can partially block the transmissions, and the satellites sometimes are arranged poorly in the sky (sometimes even turned off). Even under the best of conditions, the system has an expected position error about about 10 meters (about 30 feet) horizontally; a GPS unit gives you position information that is within about 30 horizontal-feet of the true position. With a WAAS-enabled GPS unit, the system might be able to correct for some of the error, reducing it to about 3 meters (10 feet). Elevation is the most difficult calculation for GPS units, and vertical position error still is about 100 meters (300 feet).

I record GPS coordinates by walking trails with a Garmin handheld GPS unit and using the tracks feature (sometimes called bread crumbs) to record where I went. The GPS unit records my position in three dimensions: north-south and east-west (Figure 1), plus elevation (Figure 2). All GPS units can convert between longitude-latitude and universal transverse Mercator (UTM). For this exercise, I used the NAD27 Map Datum, but that is another story.

For this discussion, I illustrate my methods using tracks that I recorded on the Fire Ecology and Pine Creek trails in the Red Rock National Conservation Area. The 1-mile-long Fire Ecology loop trail (Figure 3) starts on a hill, drops into a wash, follows an old road, does a figure-8 loop out on the flats in the wash, and then returns over the road and trail to the trailhead. The Pine Creek Trail starts at the same place, but it continues past the Fire Ecology Trail to the west.

I hiked without intending to use these tracks for this example, so I did not give the GPS unit time to find my position and settle in after I turned it on (it takes GPS units a few minutes to accurately determine where it is). Thus, at the start, I didn't have a precise estimate of my horizontal location, and in particular, I had a bad estimate of my vertical location (elevation). Elevation is the most difficult position for a GPS unit to calculate and errors can be quite large. It can take several minutes for a GPS unit to settle in on the correct elevation.

The UTM coordinate system is based on the metric system (1 meter = about 1 yard; or more exactly 1 meter = 3.2808 feet). The "northing" coordinate is the number of meters north of the equator, and just like latitude, this measurement is straightforward. However, just like longitude, the "easting" coordinate is more complicated because it converges to zero at the poles. The earth is divided into 120 UTM Zones that make 3-degree-wide, north-south longitude bands. The center of each zone is defined as 500000 east, so it is important to record the UTM Zone where the measurements were taken (for example, Red Rocks is in UTM Zone 11, while the Grand Canyon is in UTM Zone 12.

After the hike, I downloaded the tracks to a PC, and then used Microsoft Excel to plot the points. I plotted the UTM Northing and Easting on a 100-m grid in two dimensions (Figure 1) and the sequence of elevations versus total distance (in feet, Figure 2).

Figure 1. Horizontal tracks from the Fire Ecology Trail plotted on a 100-m UTM grid.

Figure 2. Vertical tracks (elevation) versus total distance for the Fire Ecology Trail.

On the horizontal plot (Figure 1), the outgoing and return tracks (double line in the upper right portion) do not match exactly. I turned on the GPS unit in the parking lot and took a short cut across the viewpoint area to the trail on the way out, but I walked on the trail to the trailhead sign on the way back, so the start and end points should not exactly match. However, I walked the same exact trail going and coming, and the differences in the parallel track lines in the upper right portion of the figure show an estimate of error in the horizontal measurements (not much). On the ground, this error is about equal to the width of a one-lane dirt road.

Similarly, the start and end points on the vertical plot (Figure 2) do not exactly match, again an example of measurement error because the trailhead area is flat. Elevation is the most difficult position for a GPS unit to calculate accurately, and this difference (about 30 feet) is actually pretty good. The figure-8 section of the trail is fairly level, so it appears that the GPS unit was slowly adjusting the elevation upwards while I was out there (distances from 1,575 ft to 3,570 ft).

Overlaying the horizontal tracks on an aerial image of the area (Figure 3), we see that overall, the tracks fairly represent the actual on-the-ground positions along the old road and the trail. These positions are close enough for finding places (e.g., trailheads or trail junctions) where a few meters of error are not important. These positions also are close enough for marking a trail on a map where the width of the lines on my maps is more than the measurement error). This amount of error, however, does add a tiny bit of challenge to finding GeoCaches.

Figure 3. Aerial image of the Fire Ecology and Pine Creek trails with tracks plotted on
the image. Differences between the tracks and the actual trail and road indicate
the degree of error in using tracks to calculate distances and draw trails on maps.

Assuming, then, that the positions are accurate enough, I clean the dataset to remove instances where I might have walked back and forth chasing birds, or stepped off the trail to get a picture (the GPS unit records these movements too). Using the clean dataset, I use the 3-dimensional tracks to calculate Point-to-Point Distance between successive points (distance = square root [(a1-a2)^2+(b1-b2)^2+(c1-c2)^2], and then I sum the distances over the desired interval to estimate the total distance. In this example, my 111 points on the Fire Ecology Trail resulted in 110 Point-to-Point Distances that ranged from 0 to 41-m apart, averaged 14.7 m apart, and summed to 1,635 m (1.02 miles).

In this example, the average distance between points was 14.7 m (48 feet). On a very crooked trail, recording one point every 48 feet would underestimate the actual on-the-ground distance, but in most cases, the underestimate would be slight. Although there is error in this method, when checked against highway distances on winding roads, this method actually is pretty accurate and much better than using a ruler and a map.

To make my maps, I get digital USGS topo maps off the Internet and use Photoshop to overlay the tracks onto the map. I also have software for drawing maps using GPS data, but the original USGS DRGs make for better maps.

Happy hiking! All distances, elevations, and other facts are approximate.
copyright; Last updated 120824

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