The Observability in Unobservable Systems

In this paper, we introduce the concept of observability of selected state variables for systems that may not be fully observable. For their estimation, we introduce and exemplify a deep filter, which is a neural network specifically designed for the estimation of selected state variables without computing the trajectory of the entire system. The observability definition is quantitative rather than a yes or no answer so that one can compare the level of observability between different sensor locations.