Diffusion Maps Particle Filter

In this paper, we propose a new nonparametric filtering framework combining manifold learning and particle filtering. Diffusion maps, a nonparametric manifold learning method, is applied to obtain a parametric state-space model, inferring the state coordinates, their dynamics, as well as the function that links the state to the noisy observations, in a purely data-driven manner. Then, based on the inferred parametric model, a particle filter is devised, facilitating the processing of high-dimensional noisy observations without rigid prior model assumptions. We demonstrate the performance of the proposed approach in a simulation of a challenging tracking problem with noisy observations and a hidden model.