Extended object tracking (EOT) have numerous applications and can be integrated in autonomous systems like self-driving cars or autonomous surface vehicles. These systems can be improved by using robust tracking algorithms that accurately estimate the position, velocity and extent of surrounding targets from sensor data. EOT is relevant for many different sensors, and the methods developed are based on which sensor that is used. In this thesis LIDAR is used to track a single target in a maritime environment that have a shape which can be approximated by an ellipse. The sensor detections of the target will often be noisy, and it is crucial to model the measurement uncertainties in a proper way. Both measurements from target and other objects (clutter) need to be included in the probabilistic modelling, where the data association problem is important to solve. In this thesis we present and implement two different methods designed for tracking a single target from LIDAR data. To model clutter measurements the generalized probabilistic data association (GPDA) filter is used together with the filter methods. Through simulations of a single elliptical target with and without clutter measurements, it is found that the method using contour measurement modelling is performing considerably better than the random matrix method. This result is obtained by considering both absolute error and covariance consistency of the two methods. The contour measurement method is also superior when testing the methods on real LIDAR data of the Munkholm boat taken from Ravnkloa in Trondheim, by looking at track plots, extent estimation errors and innovation statistics. i EOT Extended object tracking LIDAR Light detection and ranging IR Infrared pdf Probability density function EKF Extended Kalman filter CEKF Contour EKF PHD Probability hypothesis density RFS Random finite sets PDA Probabilistic data association GPDA Generalized PDA C-GPDA Contour GPDA JPDA Joint PDA RMSE Root mean square error NEES Normalized estimation error squared NIS Normalized innovation squared vii d Chi-squared distribution with d degrees of freedom W d (•) Wishart pdf of matrix with dimension d IW d (•) Inverse Wishart of matrix with dimension d C (•) Constant (•) k|k−1 Predicted quantity arctan2(•, •) Arctan-function based on the argument signs diag[•] Diagonal matrix with arguments along the main diagonal max (•) , min (•) Maximum and minimum with respect to the argument tr(•)