Joint state and dynamics estimation with high-gain observers and Gaussian process models

With the rising complexity of dynamical systems generating ever more data, learning dynamics models appears as a promising alternative to physics-based modeling. However, the data available from physical platforms may be noisy and not cover all state variables. Hence, it is necessary to jointly perform state and dynamics estimation. In this paper, we propose interconnecting a high-gain observer and a dynamics learning framework, specifically a Gaussian process state-space model. The observer provides state estimates, which serve as the data for training the dynamics model. The updated model, in turn, is used to improve the observer. Joint convergence of the observer and the dynamics model is proved for high enough gain, up to the measurement and process perturbations. Simultaneous dynamics learning and state estimation are demonstrated on simulations of a mass-spring-mass system.