Abstract In applications involving large scale systems such as discretized partial differential equations, it is often of interest to use data to estimate state variables associated with a subregion of the spatial domain. In this paper we derive an extension of the classical Kalman filter in which data injection is confined to a subspace of the system states. Acknowledgements This research was supported by the National Science Foundation Information Technology Research Initiative, through Grant ATM-0325332 to the University of Michigan, Ann Arbor, USA.