Abstract
In this paper, a quantitative measure of partial observability is defined for PDEs. The quantity is proved to be consistent if the PDE is approximated using well-posed approximation schemes. A first order approximation of an unobservability index using an empirical Gramian is introduced. Several examples are presented to illustrate the concept of partial observability. The theory is developed for the estimation of initial value. However, the concept can be extended to the observability of state variables at final time or any fixed time moment.
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