Ever thought your GPS system said youād gone further than you expected? A new study dives into the statistics behind the satellite-based positioning serviceāand finds that overestimates in distance are inevitable based on the way measurements are currently made.

A team of researchers from the University of Salzburg in Austria have been looking at how GPS systems calculate distances between two points. Their findings suggest that on average the predicted distances are bigger than the true distance between the points.

The math that supports GPS is complex, but the finding is pretty easy to explain. A GPS system calculates total distance by calculating short distances between points along the route that can be reasonably approximated by a straight line. These distances are pretty small, so the curvature of the Earthāwhich would mean that GPS could actually underestimate distance using this straight line approachāis fine to ignore.

The problems comes from how errors in position accumulate over time. There is, obviously, random noise in the position data from GPS, with the system getting your location wrong by anything from millimeters to meters at any given moment. Youād expect those random errors to cancel out over a large number points, because theyāre random: theyād be small as frequently as they are big, and in one direction as often as another. Over enough points, their effects should melt away.

Turns out, though, thatās not quite what happens with GPS. I Programmer explains the problem neatly:

Consider the two points and the straight line between them. This straight line is the shortest distance between the two points. Now consider random displacements of the two points. The only displacements that reduce the distance are those that move the two points closer together, for example displacements along the line towards each other. The majority of random displacements end up increasing the distance.