Target tracking is a challenging problem with a wide range of applications such as surveillance, robotics, and autonomous vehicles. Recent years have seen significant progress in the field of object tracking; nonetheless, there are still numerous challenges that need to be addressed in modern tracking systems. These difficulties include the development of scalable and robust tracking algorithms that can perform reliably under extreme conditions such as heavy clutter, closely-spaced targets, occlusion, and high target density. Modern tracking algorithms also face new demands in learning information about tracking scenes, interpreting target behaviour and detecting anomalies in real time.

The objective of this thesis is to analyse state-of-the-art object tracking problems and present statistical tools for the design of efficient tracking systems with the help of Bayesian computational methods. The target tracking problem is typically divided into two sub-tasks: data association and state estimation. Data association involves identifying which measurements correspond to which object, while state estimation involves estimating the position, velocity, and other properties of each object. The major challenge of data association lies in its fast-growing combinatorial complexity due to the growth of the measurement and target number. On the other hand, an accurate state estimation relies on a good model of the target's motion and interaction, including the ability to capture the dynamic interaction structure as well as the manoeuvre behaviours.

This thesis will present solutions for several tracking applications based on the efficient design of Monte Carlo sampling methods, which sets us apart from the existing techniques that are based on the Kalman filter or other recursive closed-form Gaussian mixture filter implementations with approximations and heuristic design. The Monte Carlo sampling methods, despite being theoretically optimal and having superior tracking performance, are considered of less practical interest due to their computational burden. Therefore, our goal is to investigate real-time sampling-based solutions for modern tracking problems by exploring modelling and inference strategies to speed up and scale the sampling structures. A highlight of this thesis is the application of Rao-Blackwellisation strategies for different inference and tracking tasks, which could be a good case study for learning the performance of Rao-Blackwellisation strategies in sequential Bayesian estimation problems.