Smooth pursuit eye movements provide meaningful insights and information on subject's behavior and health and may, in particular situations, disturb the performance of typical fixation/saccade classification algorithms. Thus, an automatic and efficient algorithm to identify these eye movements is paramount for eye-tracking research involving dynamic stimuli. In this paper, we propose the Bayesian Decision Theory Identification (I-BDT) algorithm, a novel algorithm for ternary classification of eye movements that is able to reliably separate fixations, saccades, and smooth pursuits in an online fashion, even for low-resolution eye trackers. The proposed algorithm is evaluated on four datasets with distinct mixtures of eye movements, including fixations, saccades, as well as straight and circular smooth pursuits; data was collected with a sample rate of 30 Hz from six subjects, totaling 24 evaluation datasets. The algorithm exhibits high and consistent performance across all datasets and movements relative to a manual annotation by a domain expert (recall: μ = 91.42%, σ = 9.52%; precision: μ = 95.60%, σ = 5.29%; specificity μ = 95.41%, σ = 7.02%) and displays a significant improvement when compared to I-VDT, an state-of-the-art algorithm (recall: μ = 87.67%, σ = 14.73%; precision: μ = 89.57%, σ = 8.05%; specificity μ = 92.10%, σ = 11.21%). Algorithm implementation and annotated datasets are openly available at www.ti.uni-tuebingen.de/perception