Tracking of deformable linear objects (DLOs) is important for many robotic applications. However, achieving robust and accurate tracking is challenging due to the lack of distinctive features or appearance on the DLO, the object's high-dimensional state space, and the presence of occlusion. In this letter, we propose a method for tracking the state of a DLO by applying a particle filter approach within a lower-dimensional state embedding learned by an autoencoder. The dimensionality reduction preserves state variation, while simultaneously enabling a particle filter to accurately track DLO state evolution with a practically feasible number of particles. Compared to previous works, our method requires neither running a high-fidelity physics simulation, nor manual designs of constraints and regularization. Without the assumption of knowing the initial DLO state, our method can achieve accurate tracking even under complex DLO motions and in the presence of severe occlusions. Our implementation is available at https://amm.aass.oru.se/dlo-pf-tracking/.