State-Space Analysis of Wildlife Telemetry Data

Abstract

Abstract The location of wildlife is frequently determined from telemetry data. Current procedures may inadequately account for time-dependencies in the data and errors in the observations. We propose a nonlinear state-space model that addresses these two shortcomings. Let y t be a vector of angles measured between known antenna locations and unknown animal positions, and let states x t be the rectangular coordinates of animal position at time t. If x t follows a two-dimensional stochastic process and observation errors are additive, independent, and normal, then location estimates and their precisions may be determined recursively using extensions of the Kalman filter-smoother. We outline the application of the iterated extended Kalman filter-smoother to this situation and consider problems of initial conditions, the identification of filter parameters based on maximum likelihood principles, and the treatment of missing data. Using simulated data, we compare state-space and current procedures according to mean errors of location estimates, parameter estimation, and precision estimates. We apply all procedures to field data and conclude that in this application the use of an iterated extended Kalman filter-smoother improves knowledge both of locations and of the precisions of estimates.