This thesis presents work on the development of model-based Bayesian approaches to object tracking and intent prediction. Successful navigation/positioning applications rely fundamentally on the choice of appropriate dynamic model and the design of effective tracking algorithms capable of maximising the use of the structure of the dynamic system and the information from sensors. While the tracking problem with frequent and accurate position data has been well studied, we push back the frontiers of current technology where an object can undergo fast manoeuvres and position fixes are limited. On the other hand, intent prediction techniques which extract higher level information such as the intended destination of a moving object can be designed, given the ability to perform successful tracking. Such techniques can play important roles in various application areas, including traffic monitoring, intelligent human computer interaction systems and autonomous route planning.

In the first part of this thesis Bayesian tracking methods are designed based on a standard fix-rate setting in which the dynamic system is formulated into a Markovian state space form. We show that the combination of an intrinsic coordinate dynamic model and sensors in the object's body frame leads to novel state space models according to which efficient proposal kernels can be designed and implemented by the sequential Monte Carlo (SMC) methods. Also, sequential Markov chain Monte Carlo schemes are considered for the first time to tackle the sequential batch inference problems due to the presence of infrequent position data. Performance evaluation on both synthetic and real-world data shows that the proposed algorithms are superior to simpler particle filters, implying that they can be favourable alternatives to tracking problems with inertial sensors.

The modelling assumption that leads to Markovian state space models can be restrictive for real-world systems as it stipulates that the state sequence has to be synchronised with the observations. In the second major part of this thesis we relax this assumption and work with a more natural class of models, termed variable rate models. We generalise the existing variable rate intrinsic model to incorporate acceleration, speed, distance and position data and introduce new variable rate particle filtering methods tailored to the derived model to accommodate multi-sensor multi-rate tracking scenarios. The proposed algorithms can achieve substantial improvements in terms of tracking accuracy and robustness over a bootstrap variable rate particle filter. Moreover, full Bayesian inference schemes for the learning of both the hidden state and system parameters are presented, with numerical results illustrating their effectiveness.

The last part of the thesis is about designing efficient intent prediction algorithms within a Bayesian framework. A pseudo-observation based approach to the incorporation of destination knowledge is introduced, making the mathematics of the dynamical model and the observation process consistent with the Markov state process. Based on the new interpretation, two algorithms are proposed to sequentially estimate the probability of all possible endpoints. Whilst the synthetic maritime surveillance data demonstrate that the proposed methods can achieve comparable prediction performance with reduced computational cost in comparison to the existing bridging distribution based methods, the results on an extensive freehand pointing database, which contains 95 three-dimensional pointing trajectories, show that the new algorithms can outperform other state-of-the-art techniques. Some sensitivity tests are also performed, confirming the good robustness of the introduced methods against model mismatches.