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 ( @math ). We argue that @math 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 @math 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.
@cite_7: The Georgia Institute of Technology is evaluating the feasibility and effectiveness of mileage-based pricing programs as transportation control measures. Incentives were provided to study participants who change driving behavior in response to cent per mile pricing (fixed pricing and pricing as a function of congestion level). In-vehicle Global Positioning System (GPS) devices were used to estimate distance traveled and driver behavior (e.g., speed and acceleration profiles). The accuracy of estimated mileage accrual speeds by road classification, and acceleration rates used in pricing algorithms, is paramount. Various data-smoothing techniques were applied to the instrumented vehicle GPS speed data, and performance of the algorithms was evaluated in minimizing the impact of GPS random error on speed, acceleration, and distance estimates. The conventional discrete Kalman filter algorithm was modified to enhance its ability to control GPS random errors. Each smoothing method produces different second-by-se...
@cite_2: Focus on movement data has increased as a consequence of the larger availability of such data due to current GPS, GSM, RFID, and sensors techniques. In parallel, interest in movement has shifted from raw movement data analysis to more application-oriented ways of analyzing segments of movement suitable for the specific purposes of the application. This trend has promoted semantically rich trajectories, rather than raw movement, as the core object of interest in mobility studies. This survey provides the definitions of the basic concepts about mobility data, an analysis of the issues in mobility data management, and a survey of the approaches and techniques for: (i) constructing trajectories from movement tracks, (ii) enriching trajectories with semantic information to enable the desired interpretations of movements, and (iii) using data mining to analyze semantic trajectories and extract knowledge about their characteristics, in particular the behavioral patterns of the moving objects. Last but not least, the article surveys the new privacy issues that arise due to the semantic aspects of trajectories.
The above-mentioned research has mainly focused on describing and understanding GPS measurement error. In addition to this, filtering and smoothing approaches have been proposed for recording movement data, in order to reduce the influence of errors on movement trajectories. A concise summary of these approaches can be found in @cite_2 . @cite_7 tested smoothing methods that best preserve travelled distance, speed, and acceleration. The authors found that Kalman filtering resulted in the least difference between the true movement and its representation.