Adaptive-Velocity Time-Geographic Density Estimation for Mapping the Potential and Probable Locations of Mobile Objects

Time-geographic density estimation (TGDE) provides a method for generating probability density surfaces for mobile objects. The technique operates by fitting distance-weighted geo-ellipses to each pair of points in a tracking dataset and combining them to create a final density surface. The sizes of the geo-ellipses, and thus the amount of smoothing, are determined by a velocity parameter which specifies how fast the object can travel. In prior formulations of TGDE this maximum-velocity parameter was treated as constant or fixed. This can be problematic if an object displays variable movement patterns, such as alternating between movements and stops. In this research we develop a more robust formulation of time-geographic density estimation, termed adaptive-velocity TGDE, which allows the maximum-velocity parameter to vary for each segment of the space-time path. First, the new mathematical formulation is demonstrated and compared with fixed-TGDE through an application to synthetic pedestrian tracking data. Second, both methods are evaluated in the context of accurately mapping the movement patterns of a homing pigeon tracked by GPS. The results of both applications demonstrate that adaptive-velocity TGDE has the potential to more accurately delineate the trajectories of mobile objects than the fixed-velocity version. Implications of these results in the context of developing a probabilistic time geography for general mobile objects are also discussed.