A Bayesian inference approach for batch trajectory estimation

A curve fitting algorithm for batch ship trajectory estimation that employs Bayesian statistical inference for non-parametric regression is presented. It assumes no knowledge about the ship motion model while only assuming standard ship maneuvers. The trajectory is thought to be well represented by a cubic spline with an unknown number of knots in two-dimensional Euclidean plane. The function estimate is determined from positional measurements which are assumed to be received in batches at irregular time intervals. As the measurements are often delivered by different sensors the measurement errors are assumed to be heteroscedastic and correlated. A fully Bayesian approach is adopted by defining the prior distributions on all unknown parameters: the spline coefficients as well as the number and the locations of knots. The quality of the estimator algorithm is evaluated statistically using several simulated scenarios. The results suggest that the algorithm represents efficient methodology for trajectory estimation in maritime surveillance, especially in the absence of prior knowledge of the motion model.