This will be the third time I've rewritten this article trying to make it less confusing, and still I haven't succeeded.
First, a GPSr uses the satellite information to "estimate" where it's located (and where you're located, if you're holding it) -- that is, it makes an educated guess about where on the planet it is. It's notion about where the the coordinates (of a cache or waypoint) are is based on, and no better than, it's guess about where it is. EPE (Estimated Position Error) is an estimate of how close (how good) its guess about its location is -- i.e., EPE is a estimate of how far off its location guess may be. For example, if your GPSr reports you're 20 feet from the target coordinates and shows an EPE of 10, it means the 20 feet can be off by as much as 10 feet. So, you're really 20 ± 10 feet from the coordinates. The real location of the coordinates could be as close as 10 feet or as far away as 30 feet.
Imagine you are at the service station where you buy gas (petrol for the Brits). The owner asks, "How far away do you live?" You make a educated guess how far it is. Let's say you guess 5 miles. Even though it's just a guess you know about the most you could be off. You might know your guess isn't likely to be more than 2 miles off. You can think of the 2 miles as your EPE -- the amount your guess could be off.
Now that you've got that idea, it’s not really true, because the EPE itself is an estimate and has error. So, how accurate is the EPE? How “confident” can you be in the gadget's guess about its own error? I’ve read things that say a Garmin EPE is 50-50 – or, a confidence level of 50%. That is, with an EPE of 10, half the time the error in the coordinates will be less than 10 feet and half the time it will be more than 10. So, in the illustration above, half the time you will be between 10 and 30 feet from the coordinates and half the time you’ll be either closer than 10 feet or further away than 30.
A big problem is there's no standard for this among manufacturers. Garmin says their Accuracy (EPE) calculations are proprietary/secret. Different GPSr manufacturers use different confidence values. Some may have a confidence level of 75%, so only 25% of the time (one time in four) would the example coordinates be closer than 10 feet or further than 30 feet. Without an industry standard you can’t know what a particular manufacturer’s EPE really means. And, since people will tend to judge the performance of a GPSr based partly on how small it’s errors (EPEs) are, manufacturers are motivated to use low confidence numbers that produce low EPEs. This way Johnny can say to Sue, “You should buy my Brand X GPSr, because it’s always more accurate than yours. Every time we go geocaching together I get smaller errors (EPE numbers) than you, so my unit's more accurate than yours.”
But, for a given GPSr the lower the EPE the more confidence you can have
in the location it's giving you and, over time you'll develop a feel for
what your unit's EPE means. If you can find a surveyor's benchmark near
you with accurate coordinates (Benchmarks labeled Adjusted are measured precisely,
others are only guessed at.) you can get a feel for this fairly quickly by
going to it repeatedly on different days and at different times of the
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