Empirically Informed Random Trajectory Generator in 3-D
Switch branches/tags
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Failed to load latest commit information.


GitHub version License: GPL v3

Empirically Informed Random Trajectory Generation in 3-D

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. 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.

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 startet from a 2-D version of the eRTG algorithm by Technitis et al. (2016).

Functionality - 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


Prerequisites - Software needed:

  • R - R is a free software environment for statistical computing and graphics.
  • RStudio - Open source and enterprise-ready professional software for R.

Install Package - Get development version from github:



  • Merlin Unterfinger - eRTG3D and R Package - munterfinger
  • George Technitis - 2-D eRTG - nnneogeorge
  • Dr. Kamran Safi - 2-D eRTG - MPIO
  • Prof. Dr. Robert Weibel - 2-D eRTG - GIUZ


This R package is licensed under the GPL (>= 3) License - see the LICENSE file for details.


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

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