Joint State and Boundary Condition Estimation in Linear Data Assimilation using Basis Function Expansion

S. Gillijns and B. De Moor (Belgium)


Boundary condition estimation, Kalman filtering, unknown input estimation, data assimilation.


This paper addresses the problem of joint state and bound ary condition estimation in linear data assimilation. By ap proximating the equations of an optimal estimator for linear discrete-time state space systems with unknown inputs, an efficient recursive filtering technique is developed. Unlike existing boundary condition estimation techniques, the fil ter makes no assumption about the initial value or the time evolution of the boundary conditions. However, the deriva tion is based on the assumption that measurements at the boundary are available. Furthermore, it is assumed that the spatial form of the boundary condition can be expanded as a linear combination of a limited number of predefined basis vectors. A simulation example on a linear heat con duction model shows the effectiveness of the method.

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