Mobile tracking technologies are facilitating the collection of increasingly large and detailed data sets on object movement. Movement data are collected by recording an object’s location at discrete time intervals. Often, of interest is to estimate the unknown position of the object at unrecorded time points to increase the temporal resolution of the data, to correct erroneous or missing data points, or to match the recorded times between multiple data sets. Estimating an object’s unknown location between known locations is termed path interpolation. This paper introduces a new method for path interpolation termed kinematic interpolation. Kinematic interpolation incorporates object kinematics (i.e. velocity and acceleration) into the interpolation process. Six empirical data sets (two types of correlated random walks, caribou, cyclist, hurricane and athlete tracking data) are used to compare kinematic interpolation to other interpolation algorithms. Results showed kinematic interpolation to be a suitable interpolation method with fast-moving objects (e.g. the cyclist, hurricane and athlete tracking data), while other algorithms performed best with the correlated random walk and caribou data. Several issues associated with path interpolation tasks are discussed along with potential applications where kinematic interpolation can be useful. Finally, code for performing path interpolation is provided (for each method compared within) using the statistical software R.

Movement analysis has become an integral part of many disciplines, yet with relatively little overlap. A foresight paper in this journal entitled “Towards an integrated science of movement: converging research on animal movement ecology and human mobility science” argued for a better integration of concepts across the divide of animal and human movement, which would lead to the Integrated Science of Movement, but did so from a top-down perspective based on a series of expert workshops. We argue that for a solid establishment of the Integrated Science of Movement, a bottom-up approach is necessary, one based on existing literature which identifies similarities and differences across disciplines. We therefore review, compare, and contrast movement analysis methodologies from GIScience, movement ecology, geography, transportation, public health, computer science, and physics. We structure our review along the dichotomy of individual versus population-based movement or, using terminology from wildlife ecology, between the Lagrangian and Eulerian perspectives. We further introduce a new unifying framework for movement research that is sufficiently general to cover any type of movement study in any discipline and that spans the Lagrangian/Eulerian divide, with the ambitious goal to bridge the gap between disciplines and lay a solid foundation for a new Integrated Science of Movement.

The analysis of interaction between movement trajectories is of interest for various domains when movement of multiple objects is concerned. Interaction often includes a delayed response, making it difficult to detect interaction with current methods that compare movement at specific time intervals. We propose analyses and visualizations, on a local and global scale, of delayed movement responses, where an action is followed by a reaction over time, on trajectories recorded simultaneously. We developed a novel approach to compute the global delay in subquadratic time using a fast Fourier transform (FFT). Central to our local analysis of delays is the computation of a matching between the trajectories in a so-called delay space. It encodes the similarities between all pairs of points of the trajectories. In the visualization, the edges of the matching are bundled into patches, such that shape and color of a patch help to encode changes in an interaction pattern. To evaluate our approach experimentally, we have implemented it as a prototype visual analytics tool and have applied the tool on three bidimensional data sets. For this we used various measures to compute the delay space, including the directional distance, a new similarity measure, which captures more complex interactions by combining directional and spatial characteristics. We compare matchings of various methods computing similarity between trajectories. We also compare various procedures to compute the matching in the delay space, specifically the Fréchet distance, dynamic time warping (DTW), and edit distance (ED). Finally, we demonstrate how to validate the consistency of pairwise matchings by computing matchings between more than two trajectories.