Computational Movement Analysis Using Brownian Bridges

Widespread availability of location tracking devices leads to a rapidly increasing amount of movement data and to the need to analyse these data. These data typically consist of location measurements taken at discrete times, often with a non-negligible error margin in the measured locations. A low sampling rate leads to high uncertainty of the locations between the times at which these measurements were obtained. So far this uncertainty is usually ignored in the computational analysis of movement data. In this thesis we investigate how to incorporate this uncertainty into the analysis by the use of movement models that model the movement as a random process. Specifically we consider the Brownian bridge movement model, which assumes that an entity performs Brownian motion that is conditioned on the measured locations. In previous work this model was used only to derive a probability distribution of space use or to visualize movement data. In this thesis we contribute to the computational analysis of movement data in the following ways. Firstly, we provide algorithmic tools for analysing movement data using the Brownian bridge movement model. We develop a framework for detecting movement patterns from movement data in this model. Many patterns are composed from basic building blocks like position, distance, speed and direction. We derive their distributions in the Brownian bridge movement model. Using these building blocks, we show how to detect the patterns encounter, regular visit and following. Secondly, we combine our algorithmic tools with the movement ecology paradigm by Nathan et al., which models influences on the movement path from the environment and the internal state of an entity. We demonstrate how these influences can be integrated into our algorithmic framework by the example of two studies on the speed of animals. In one study, we integrate external factors a priori through the parameters of the movement model. In the other we use the external variables in the analysis after obtaining the results from the model. Thirdly, we show how to refine the Brownian bridge movement model using information on the behavioural state of the entity being studied. We demonstrate a new method to estimate the parameter of the model. In order to obtain this behaviour information from accelerometer data, we discuss approaches to augment existing classifiers for data that have dependencies between consecutive observations. Finally, we present a tool with easy to use implementations of many of the methods discussed in this thesis. We provide this tool as a package for the R environment for statistical computing, which is commonly used in movement ecology. Many of the tasks allow efficient parallelization using graphics processors and therefore we have implemented some functions using OpenCL, a standard for parallel programming on various hardware platforms.