  State observation is necessary for feedback control but often challenging for
nonlinear systems. While Kazantzis-Kravaris/Luenberger (KKL) observer gives a
generic design, its model-based numerical solution is difficult. In this paper,
we propose a simple method to determine a data-driven KKL observer, namely to
(i) transform the measured output signals by a linear time-invariant dynamics,
and (ii) reduce the dimensionality to principal components. This approach is
especially suitable for systems with rich measurements and low-dimensional
state space, for example, when videos can be obtained in real time. We present
an application to a video of the well-known Belousov-Zhabotinsky (B-Z) reaction
system with severe nonlinearity, where the data-driven KKL observer recovers an
oscillatory state orbit with slow damping.
