Geostatistical Analysis of GPS Trajectory Data: Space-Time Densities

Tomislav Hengl+, E. Emiel van Loon, Judy Shamoun-Baranes and Willem Bouten
Computational Geo-Ecology (CGE), Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, Netherlands 
Abstract. Creation  of  density maps  and  estimation  of  home  range  is  problematic  for  observations  of animal  movement  at  irregular  intervals.  We  propose  a  technique  to  estimate  space-time  densities  by separately modeling animal movement paths and velocities, both as continuous  fields. First  the  length of trajectories for a given grid is derived; then the velocity of individual birds is interpolated using 3D kriging; finally  the space-time density is calculated by dividing the density of trajectories (total length of lines per grid cell) by the aggregated velocity at that grid cell. The resulting map shows density of a species in both space  and  time,  expressed  in  s/m2   units. This  length-by-velocity  (LV)  technique  is  illustrated  using  two case studies:  (1) a synthetically generated dataset using  the Lorenz model; and  (2) GPS  recordings of 14 individual  birds  of  lesser  black-backed  gull  (Larus  Fuscus).  The  proposed  technique  is  compared  with kernel  smoother –  a  technique  commonly  used  to derive home  range  for  species. The  results of using  a synthetic dataset proved that the LV method produces different outputs than kernel smoothing, especially if irregular  observation  intervals  are  used.  The main  advantages  of  the  proposed  technique  over  a  kernel smoother  are:  (1)  it  is  not  sensitive  to missing  observations;  (2)  it  is  suited  to  analyze  fly  paths  (e.g.  it preserves  information about velocities and directions), and  (3)  it allows  the movement of birds  (velocity, trajectory)  to  be  modeled  separately  e.g.  as  function  of  environmental  conditions,  wind,  day  time  and similar. The remaining research  issues are development of methodology for selection of optimal grid size and optimal time interval between recordings.

Keywords: animal movement, 3D kriging, velocity, home range, space-time cube.


In: Wan, Y. et al. (eds) Proceeding of the 8th international symposium on spatial accuracy assessment in natural resources and environmental sciences, World Academic Union (Press).

Hengl2008accuracy.pdf1.73 MB