title: Why GPS makes distances bigger than they are.
abstract: Global navigation satellite systems such as the Global Positioning System (GPS) is one of 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 errors. 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 in practice is the case for movement sampled at high frequencies. We provide a mathematical explanation of this phenomenon and illustrate that it functionally depends on the autocorrelation of GPS measurement error (C). We argue thatCcan be interpreted as a quality measure for movement data recorded with a GPS. If there is a strong autocorrelation between any two consecutive position estimates, they have very similar error. This error cancels out when average speed, distance or direction is calculated along the trajectory. Based on our theoretical findings we introduce a novel approach to determineCin real-world GPS movement data sampled at high frequencies. We apply our approach to pedestrian trajectories and car trajectories. We found that the measurement error in the data was strongly spatially and temporally autocorrelated and give a quality estimate of the data. Most importantly, our findings are not limited to GPS alone. The systematic bias and its implications are bound to occur in any movement data collected with absolute positioning if interpolation error can be neglected.
authors.affiliation: Department of Geoinformatics - Z_GIS, University of Salzburg , Salzburg , Austria.
authors.forename: Peter
authors.initials: P
authors.lastname: Ranacher
authors.affiliation: Salzburg Research Forschungsgesellschaft mbH , Salzburg , Austria.
authors.forename: Richard
authors.initials: R
authors.lastname: Brunauer
authors.affiliation: Department of Mathematics, University of Salzburg , Salzburg , Austria.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Trutschnig
authors.affiliation: Faculty of Architecture, Department of Urbanism, Delft University of Technology , Delft , The Netherlands.
authors.forename: Stefan
authors.initials: S
authors.lastname: Van der Spek
authors.affiliation: Salzburg Research Forschungsgesellschaft mbH , Salzburg , Austria.
authors.forename: Siegfried
authors.initials: S
authors.lastname: Reich
keywords: GPS measurement error; autocorrelation; car movement; movement analysis; pedestrian movement; quadratic forms; trajectories