21. Dilution of Precision

The arrangement of satellites in the sky also affects the accuracy of GPS positioning. The ideal arrangement (of the minimum four satellites) is one satellite directly overhead, three others equally spaced near the horizon (above the mask angle). Imagine a vast umbrella that encompasses most of the sky, where the satellites form the tip and the ends of the umbrella spines.

GPS coordinates calculated when satellites are clustered close together in the sky suffer from dilution of precision (DOP), a factor that multiplies the uncertainty associated with User Equivalent Range Errors (UERE - errors associated with satellite and receiver clocks, the atmosphere, satellite orbits, and the environmental conditions that lead to multipath errors). The DOP associated with an ideal arrangement of the satellite constellation equals approximately 1, which does not magnify UERE. According to Van Sickle (2001), the lowest DOP encountered in practice is about 2, which doubles the uncertainty associated with UERE.

GPS receivers report several components of DOP, including Horizontal Dilution of Precision (HDOP) and Vertical Dilution of Precision (VDOP). The combination of these two components of the three-dimensional position is called PDOP - position dilution of precision. A key element of GPS mission planning is to identify the time of day when PDOP is minimized. Since satellite orbits are known, PDOP can be predicted for a given time and location. Various software products allow you to determine when conditions are best for GPS work.

MGIS student Jason Setzer (Winter 2006) offers the following illustrative anecdote:

I have had a chance to use GPS survey technology for gathering ground control data in my region and the biggest challenge is often the PDOP (position dilution of precision) issue. The problem in my mountainous area is the way the terrain really occludes the receiver from accessing enough satellite signals.

During one survey in Colorado Springs I encountered a pretty extreme example of this. Geographically, Colorado Springs is nestled right against the Rocky Mountain front ranges, with 14,000 foot Pike's Peak just west of the city. My GPS unit was easily able to 'see' five, six or even seven satellites while I was on the eastern half of the city. However, the further west I traveled, I began to see progressively less of the constellation, to the point where my receiver was only able to find one or two satellites. If a 180 degree horizon-to-horizon view of the sky is ideal, then in certain places I could see maybe 110 degrees.

There was no real work around, other than patience. I was able to adjust my survey points enough to maximize my view of the sky. From there it was just a matter of time... Each GPS bird has an orbit time of around twelve hours, so in a couple of instances I had to wait up to two hours at a particular location for enough of them to become visible. My GPS unit automatically calculates PDOP and displays the number of available satellites. So the PDOP value was never as low as I would have liked, but it did drop enough to finally be within acceptable limits. Next time I might send a vendor out for such a project!

Students who register for this Penn State course gain access to assignments and instructor feedback, and earn academic credit. Information about Penn State's Online Geospatial Education programs is available at http://gis.e-education.psu.edu.