Diffusion Maps Kalman Filter

In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems. We combine diffusion maps, a manifold learning technique, with a linear Kalman filter and with concepts from Koopman operator theory. More concretely, using diffusion maps, we construct data-driven virtual state coordinates, which linearize the system model. Based on these coordinates, we devise a data-driven framework for state estimation using the Kalman filter. We demonstrate the strengths of our method with respect to both parametric and non-parametric algorithms in two object tracking problems. We show that the proposed method outperforms the competing non-parametric algorithms in the examined stochastic problem formulations. Additionally, we obtain results comparable to common parametric algorithms, which, in contrast to our method, are equipped with the hidden model knowledge.