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 that C can 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 determine C in 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.

中文翻译：

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为什么 GPS 使距离大于实际距离

摘要 全球导航卫星系统，例如全球定位系统 (GPS)，是用于运动分析的最重要的传感器之一。GPS被广泛用于记录车辆、动物和人类的轨迹。然而，所有的 GPS 运动数据都会受到测量误差和插值误差的影响。在本文中，我们表明测量误差会导致 GPS 记录的距离出现系统偏差；GPS 记录的两点之间的距离——平均而言——大于这些点之间的真实距离。如果可以忽略插值误差的影响，这种系统性的“距离高估”就变得重要了，这实际上是在高频率采样的运动的情况下。我们提供了这种现象的数学解释，并说明它在功能上取决于 GPS 测量误差 (C) 的自相关性。我们认为 C 可以被解释为用 GPS 记录的运动数据的质量度量。如果任意两个连续位置估计之间存在强自相关，则它们具有非常相似的误差。当沿轨迹计算平均速度、距离或方向时，此误差会抵消。基于我们的理论发现，我们引入了一种新方法来确定高频采样的真实世界 GPS 运动数据中的 C。我们将我们的方法应用于行人轨迹和汽车轨迹。我们发现数据中的测量误差在空间和时间上具有很强的自相关性，并给出了数据的质量估计。最重要的是，我们的发现不仅限于 GPS。如果可以忽略插值误差，那么系统偏差及其影响必然会出现在使用绝对定位收集的任何运动数据中。