Partial Observability and Its Consistency for Linear PDEs

In this paper, a quantitative measure of partial observability is de_ned for PDEs. The quantity is proved to be consistent in well-posed approximation schemes. A first order approximation of an unobservability index using empirical gramian is introduced. For linear systems with full state observability, the empirical gramian is equivalent to the observability gramian in control theory. The consistency theorem is exemplified using a Burgers' equation.