  The purpose of this paper is to explore the concept of the regional boundary
asymptotic gradient full order observer (RBAGFO-observer) in connection with
the characterizations of sensors structures. Then, we present various results
related to different types of measurements, domains and boundary conditions for
distributed parameter systems (DPSS) in parabolic systems problem. The
considered approach of this work is derived from Luenberger observer theory
which is enable to estimate asymptotically the state gradient of the original
system on a sub-region of the domain boundary Omega in order that the
RBAGFO-observability notion to be achieved. We also show that there exists a
dynamical system for the considered system is not BAGFO-observer in the usual
sense, but it may be regional RBAGFO-observer.
