Data fusion via intrinsic dynamic variables: An application of data-driven Koopman spectral analysis

¹ Program in Applied and Computational Mathematics (PACM), Princeton University - Princeton, NJ 08544, USA
² Department of Mechanical and Aerospace Engineering, Princeton University - Princeton, NJ 08544, USA
³ Department of Mechanical Engineering, University of California, Santa Barbara - Santa Barbara, CA 93106, USA
⁴ Department of Chemical and Biological Engineering & PACM, Princeton University - Princeton, NJ 08544, USA

Received: 10 December 2014
Accepted: 4 February 2015

Abstract

We demonstrate that the Koopman eigenfunctions and eigenvalues define a set of intrinsic coordinates, which serve as a natural framework for fusing measurements obtained from heterogeneous collections of sensors in systems governed by nonlinear evolution laws. These measurements can be nonlinear, but must, in principle, be rich enough to allow the state to be reconstructed. We approximate the associated Koopman operator using extended dynamic mode decomposition, so the method only requires time series of data for each set of measurements, and a single set of “joint” measurements, which are known to correspond to the same underlying state. We apply this procedure to the FitzHugh-Nagumo PDE, and fuse measurements taken at a single point with principal-component measurements.