Bayesian Approaches to Trajectory Estimation in Maritime Surveillance

In maritime surveillance, multisensor data differ to a great extent in their temporal resolution. Additionally, due to multi-level security and information management processing, many contact reports arrive hours after observations. This makes the contact report data usually available for batch processing. The dissimilar multi-source information environment results in contact reports with heteroscedastic and correlated errors (i.e. measurement errors characterized by normal probability distributions with non-constant and nondiagonal covariance matrices), while the obtained measurement errors may be relatively large. Hence, the appropriate choice of a trajectory estimation algorithm, which addresses the aforementioned issues of the surveillance data, will significantly contribute to increased awareness in the maritime domain.;The quality of the estimated trajectories obtained by both algorithms is assessed using several simulated scenarios and evaluated statistically. The positional measurements, received at irregular time intervals are assumed to have heteroscedastic and correlated errors and available in batches. The performance evaluation includes the performance comparison of both algorithms with another batch stochastic optimization algorithm for trajectory estimation, i.e. the genetic algorithm (GA). The sensitivity analysis is carried out with respect to perturbations in parameters of the algorithms. The results show similar performance between the linear stochastic filtering algorithm and the Bayesian spline regression algorithm, while both algorithms show superiority over the GA-based trajectory fitting with respect to tracking accuracy, due to complete account for uncertainty. Batch data processing approach is confirmed to be more suitable in maritime surveillance than standard recursive approaches. The thesis demonstrates that for the accurate trajectory estimation it is crucial to completely account for uncertainty of measurements, especially if the measurements are characterized by heteroscedastic and correlated errors. The results of this thesis are useful as they facilitate selecting the appropriate approach to data processing in maritime surveillance applications, hence contribute to increased maritime domain awareness. These can also serve for selecting appropriate methods for data processing in dissimilar sensor and other environments in which data have large and heteroscedastic measurement errors.;This thesis presents two novel batch single ship trajectory estimation algorithms employing Bayesian approaches to estimation: (1) a stochastic linear filtering algorithm and (2) a curve fitting algorithm which employs Bayesian statistical inference for nonparametric regression. The stochastic linear filtering algorithm employs a combination of two stochastic processes, namely the Integrated Ornstein-Uhlenbeck process (IOU) and the random walk (RW), process to describe the ship's motion. The assumptions on linear modeling and bivariate Gaussian distribution of measurement errors allow for the use of Kalman filtering and Rauch-Tung-Striebel optimal smoothing. In the curve fitting algorithm, the trajectory is considered to be in the form of a cubic spline with an unknown number of knots in two-dimensional Euclidean plane of longitude and latitude. The function estimate is determined from the data which are assumed Gaussian distributed. A fully Bayesian approach is adopted by defining the prior distributions on all unknown parameters: the spline coefficients, the number and the locations of knots. The calculation of the posterior distributions is performed using Markov Chain Monte Carlo (MCMC) and reversible jump Markov sampling due to the varying dimensions of subspaces where the searches are performed. Both algorithms assume no knowledge about the ship motion model, however assuming standard ship maneuvers.