Deep-Koopman-ehnanced Kalman Filter for multibody systems

State estimation is a key requirement for the control of multibody systems, yet full state measurements are rarely available in practice. This necessitates the use of observers. While extended Kalman filters (eKFs) are widely used for nonlinear systems, their reliance on local linearizations often results in approximation errors. The Koopman operator framework offers an alternative by transforming nonlinear dynamics into a higher-dimensional linear representation, theoretically valid over the entire state space. In this work, we propose a Koopman-based observer that integrates a Kalman filter for state estimation in nonlinear multibody systems. The Koopman operator is approximated using a deep neural network trained on system trajectories. We evaluate the method in simulation on two representative systems: a cable-driven parallel robot and a planar parallel robot. Results show that our Koopman-based observer consistently achieves lower estimation errors than a conventional eKF, demonstrating its potential for accurate and robust state estimation in nonlinear control applications.