The motion of a tracked object often has long term underlying dependencies due to premeditated actions dictated by intent, such as destination. Revealing this intent, as early as possible, can enable advanced intelligent system functionalities for conflict/opportunity detection and automated decision making, for instance in surveillance and human computer interaction. This paper presents a novel Bayesian intent inference framework that utilises sequential Monte Carlo (SMC) methods to determine the destination of a tracked object exhibiting unknown jump behaviour. The latter can arise from the object undertaking fast maneuvers (e.g. for obstacle avoidance) and/or due to external uncontrollable environmental perturbations. Suitable intent-driven stochastic models and inference routines are introduced. The effectiveness of the proposed approach is demonstrated using synthetic and real data.