Estimation and forecasting of dynamic state are fundamental to the design of autonomous systems such as intelligent robots. State-of-the-art algorithms, such as the particle filter, face computational limitations when needing to maintain beliefs over a hypothesis space that is made large by the dynamic nature of the environment. We propose an algorithm that utilises a hierarchy of such filters, exploiting a filtration arising from the geometry of the underlying hypothesis space. In addition to computational savings, such a method can accommodate the availability of evidence at varying degrees of coarseness. We show, using synthetic trajectory datasets, that our method achieves a better normalised error in prediction and better time to convergence to a true class when compared against baselines that do not similarly exploit geometric structure.