The motion of an object (e.g. ship, jet, pedestrian, bird, drone, etc.) is usually governed by premeditated actions as per an underlying intent, for instance reaching a destination. In this paper, we introduce a novel intent-driven dynamical model based on a continuous-time intrinsic coordinate model. By combining this model with particle filtering, a seamless approach for jointly predicting the destination and estimating the state of a highly manoeuvrable object is developed. We examine the proposed inference technique using real data with different measurement models to demonstrate its efficacy. In particular, we show that the introduced approach can be a flexible and competitive alternative, in terms of prediction and estimation performance, to other existing methods for various measurement models including nonlinear ones.