Unveiling a System's State through Data: Estimating Unknown Governing Equations

Researchers have developed a method for state estimation that can handle model-structure uncertainty, allowing for the estimation of unknown governing equations. By simultaneously learning the motion model and state estimate using a set of symbolic differential equations, this approach enables state estimation in situations with substantial modeling errors or completely unknown dynamics. The method utilizes a reparametrization trick for Markov Gaussian processes and outperforms standard state-estimation techniques in the presence of modeling errors. It also allows for the discovery of missing terms in the governing equations using indirect observations.