Diffusion Maps Kalman Filter for a Class of Systems with Gradient Flows
Name
1711.09598.pdf
Description
Submitted version
Size
2.57 MB
Format
Adobe PDF
Checksum (MD5)
0209af65a3c857f141b416bc73a75e99
Author(s)
Shnitzer, Tal
Talmon, Ronen
Slotine, Jean-Jacques
Date Issued
2020
Journal
IEEE Transactions on Signal Processing
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Original manuscript
Abstract
© 1991-2012 IEEE. In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. 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 three tracking problems. In particular, applying the approach to actual recordings of hippocampal neural activity in rodents directly yields a representation of the position of the animals. We show that the proposed method outperforms competing non-parametric algorithms in the examined stochastic problem formulations. Additionally, we obtain results comparable to classical parametric algorithms, which, in contrast to our method, are equipped with model knowledge.
MIT Department
Massachusetts Institute of Technology. Nonlinear Systems Laboratory
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/TSP.2020.2987750
