论文标题
布朗运动插值位置数据
Interpolating Location Data with Brownian Motion
论文作者
论文摘要
2018年，荷兰统计局开始了2018年的“ Nederland Onderweg”（翻译：荷兰旅行调查）项目，在那里要求参与者使用应用程序跟踪其位置，并检查数据是否正确。发生的问题是在位置数据中所谓的“差距”，其中缺少整个数据点。填补这种空白的最简单方法是直线，但这会导致系统的错误，例如低估了行进的距离。填补这一空白的一种更现实的方法是使用随机过程。我们使用布朗桥对旅行者的运动进行建模，因为这些桥梁在生态研究中已成功使用。我们找到了可以从数据中获得的某些参数来传播的距离的明确表达式。为了测试该方法是否对行进距离进行准确估计，我们使用多个不同的过程模拟旅行数据。
In 2018 the ''Onderweg in Nederland'' (translation: the Dutch Travel Survey) project by Statistics Netherlands was commenced, where participants were asked to track their location using an app, and check if the data is correct. An issue that occurs is so-called 'gaps' in the location data, where a whole sequence of data points is missing. The easiest way to fill such a gap is with a straight line, but this leads to systematic errors such as an underestimation of the distance travelled. A more realistic way to fill this gap is with a stochastic process. We use a Brownian bridge to model the movement of a traveller, as these have been used before successfully in ecological research. We find an explicit expression for the distance travelled in terms of some parameters that can be obtained from the data. To test whether this method gives an accurate estimation of the distance travelled, we simulate travel data using multiple different processes.
