  Global Navigation Satellite Systems (GNSS), such as the Global Positioning
System (GPS), are among the most important sensors for movement analysis. GPS
is widely used to record the trajectories of vehicles, animals and human
beings. However, all GPS movement data are affected by both measurement and
interpolation error. In this article we show that measurement error causes a
systematic bias in distances recorded with a GPS: the distance between two
points recorded with a GPS is -- on average -- bigger than the true distance
between these points. This systematic `overestimation of distance' becomes
relevant if the influence of interpolation error can be neglected, which is the
case for movement sampled at high frequencies. We provide a mathematical
explanation of this phenomenon and we illustrate that it functionally depends
on the autocorrelation of GPS measurement error ($C$). We argue that $C$ can be
interpreted as a quality measure for movement data recorded with a GPS. If
there is strong autocorrelation any two consecutive position estimates have
very similar error. This error cancels out when average speed, distance or
direction are calculated along the trajectory.
  Based on our theoretical findings we introduce a novel approach to determine
$C$ in real-world GPS movement data sampled at high frequencies. We apply our
approach to a set of pedestrian and a set of car trajectories. We find that the
measurement error in the data is strongly spatially and temporally
autocorrelated and give a quality estimate of the data. Finally, we want to
emphasize that all our findings are not limited to GPS alone. The systematic
bias and all its implications are bound to occur in any movement data collected
with absolute positioning if interpolation error can be neglected.
