Collective cell movement affects vital biological processes in the human organism such as wound healing, immune response, and cancer metastasis. A better understanding of the mechanisms driving cell movement is then essential for the advancement of medical treatments. In this paper, we demonstrate how the unscented Kalman filter, a technique used extensively in engineering in the context of filtering, can be applied to estimate random or directed cell movement. Our proposed model, formulated using stochastic differential equations, is fitted on data describing the movement of Dictyostelium cells, an amoeba routinely used as a proxy for eukaryotic cell movement.