The empirically informed Random Trajectory Generator in three dimensions (eRTG3D) is an algorithm to generate realistic random trajectories in a 3-D space between two given fix points, so-called Conditional Empirical Random Walks. The trajectory generation is based on empirical distribution functions extracted from observed trajectories (training data) and thus reflects the geometrical movement characteristics of the mover. A digital elevation model (DEM), representing the Earth’s surface, and a background layer of probabilities (e.g. food sources, uplift potential, waterbodies, etc.) can be used to influence the trajectories.

The eRTG3D algorithm was developed and implemented as an R package within the scope of a Master’s thesis (Unterfinger, 2018) at the Department of Geography, University of Zurich. The development started from a 2-D version of the eRTG algorithm by Technitis et al. (2016).

Getting started

# Install release version from CRAN

# Install development version from GitHub


The eRTG3D package contains functions to:

  • calculate movement parameters of 3-D GPS tracking data, turning angle, lift angle and step length
  • extract distributions from movement parameters;
    1. P probability - The mover’s behavior from its perspective
    2. Q probability - The pull towards the target
  • simulate Unconditional Empirical Random Walks (UERW)
  • simulate Conditional Empirical Random Walks (CERW)
  • simulate conditional gliding and soaring behavior of birds between two given points
  • statistically test the simulated tracks against the original input
  • visualize tracks, simulations and distributions in 3-D and 2-D
  • conduct a basic point cloud analysis; extract 3-D Utilization Distributions (UDs) from observed or simulated tracking data by means of voxel counting
  • project 3-D tracking data into different Coordinate Reference Systems (CRSs)
  • export data to sf package objects; ‘sf, data.frames’
  • manipulate extent of raster layers


Unterfinger M (2018). 3-D Trajectory Simulation in Movement Ecology: Conditional Empirical Random Walk. Master’s thesis, University of Zurich.

Technitis G, Weibel R, Kranstauber B, Safi K (2016). “An algorithm for empirically informed random trajectory generation between two endpoints.” GIScience 2016: Ninth International Conference on Geographic Information Science, 9, online. doi: 10.5167/uzh-130652.