Beyond Brownian bridges: Time-series Kriging of autocorrelated animal tracking data
We introduce a rigorous statistical approach to estimating the locations and confidence regions of tracked animals. This method is the time-series analogue of Kriging, and is based on a continuous-time movement model that significantly improves location and region estimates when the relocation data is gappy or imprecise. Kriging provides the best linear unbiased estimate of animal movement trajectories as inferred from tracking data. We show that both the Brownian bridge and the correlated random walk library (CRAWL) are special cases of time-series Kriging that assume particular autocorrelated movement models. Estimation methods that assume a model a priori will only provide statistically rigorous location estimates if that model happens to be appropriate for the focal dataset. Currently, such assumptions are rarely tested in practice. In contrast, our approach proceeds by first identifying an appropriate movement model for the data, and then Kriging based on the selected model.
We demonstrate the superiority of Kriging with a selected model over the widely used Brownian bridge on a case study with Mongolian gazelles, where motion is Brownian on some spatio-temporal scales but not on others. Most critically, the Krige provides substantially more reliable confidence regions, making it better posed as a space-use estimator. In the case of the gazelles, the Brownian bridge overestimated confidence regions by 50%, even though the gazelle movement was predominantly Brownian over the sampled scales.