With the continual improvement in spatial resolution of Nuclear Medicine (NM) scanners, it has become increasingly important to accurately compensate for patient motion during acquisition. Respiratory motion produced by lung ventilation is a major source of artefacts in NM that can affect large parts of the abdominal-thoracic cavity. As such, a particle filter (PF) is proposed as a powerful method for motion correction in NM imaging. This paper explores a basic PF approach and demonstrates that it is possible to estimate non-stationary motion using a single respiratory cycle as training data. Using the XCAT phantom, 7 test datasets that vary in depth and rate of respiration were generated. The results using these datasets show that the PF has an average Euclidean distance error over all voxels of only 1.7 mm, about half of the typical dimensions of an NM voxel for clinical applications. The conclusion is that use of the PF is promising, and can be adapted to handle more sophisticated data such as those that arise in clinical situations.