Why GPS Almost Always Overestimates Distances

You might not notice it on a car trip for several miles, but runners and hikers and those that routinely get around courtesy of their own two feet have likely experienced the phenomenon of GPS distance overestimation.

For example, four laps around a standard track makes up 1,600 meters or .994 miles, but a GPS device recording a runner's actual physical movements around that track may come up with something more like 1,722 meters or 1.07 miles. Google Maps may offer a distance of x miles from here to there, but taking a GPS track of the same trip will reveal a distance of x plus some extra amount. This will occur reliably, and, for most, it will likely go unnoticed. We're jogging, not targeting ICBMs.

Why does this error occur? The answer(s), as described in a recent paper by GIS researcher Peter Ranacher and others from the University of Salzburg, turn out to be pretty interesting, even intuitive. It's a matter of statistics.

One might imagine the problem to be interpolation. The GPS system is not constantly tracking you, and instead takes samples of your position at regularly spaced intervals. It's analogous to how analog signals are translated to digital signals, and, as in ADC (analog to digital conversion), the system at some point needs to make some estimates for all of the stuff in between points that gets left out. This is interpolation and it's a potential source of error.

But the error of interpolation is more likely to result in an underestimate, as in the case of linear interpolation where a simple straight line is drawn between sampling points. (This is the easiest way to interpolate, computationally speaking.) It might not matter too much either way, as Ranacher and co. note that GPS data is very often collected at such high frequencies that the interpolation error winds up being pretty small. So, we need to look beyond interpolation in cases where positions are sampled frequently. (An earlier study analyzed fishing boat tracks and found that for low rates of positional sampling, distances were underestimated, but for high rates, they were overestimated.)

This leaves measurement error. The GPS system will get your position a bit wrong almost all of the time. Even the FAA's most top-notch GPS receivers will wind up with a measurement error of a few meters. Many factors are just uncontrollable, such as atmospheric effects and "sky blockages."

To get the average sampling error for a given device and conditions, we can just imagine walking back and forth between two points and taking GPS readings every time we return to a position. We mark every reading down and, over time, we wind up with a cloud of points representing the likely measurement error for that set of points. This is illustrated above.

Maybe you can see it already. Just start taking combinations of points while noting if they're resulting in a larger path than actual (a straight line between the two "real" points) or a shorter path. Almost all of them are longer for the simple reason that there are many more possibilities for adding length to the path than subtracting it. The only way you're going to get a shorter than actual distance is if the two selected points (from the error clouds) both lie directly on the actual straight-line path, which is unlikely.

CORRECTION: As a reader pointed out, it is possible to get a shorter (underestimated) path by connecting error-points some distance above and below the straight line, but the chances of underestimation remain poorer than overestimation.

Ranacher and his group go on to prove this mathematically, and if that's your thing, the paper (linked above) happens to be open-access.

How significant is this particular bias? The group tested out their theory via some real-world experiments, which involved participants pacing around a 10 meter square. A intervals of 1 meter, the average measurement was 1.2 meters, while for 5 meter intervals the average was 5.6 meters (data abstracted by Mike James at I Programmer). That's a lot of error—up to 20 percent.

Finally, Ranacher and his group conclude, "Our findings are not only relevant for GPS. The overestimation of distance is bound to occur in any type of movement data where distances are deduced from imprecise position estimates, of course only if interpolation error can be neglected."

Correction: An earlier version of this story said four laps around a standard track make up exactly a mile; this is incorrect. A standard track is 400 meters making four laps 1,600 meters precisely. A mile is slightly longer at 1,609.34 meters. (Hat tip Jason A. Evans)