Spatially localized Kalman filtering for data assimilation

In data assimilation applications involving large scale systems, it is often of interest to estimate a subset the of the system states. For example, for systems arising from discretized partial differential equations, the chosen subset of states can represent the desire to estimate state variables associated with a subregion of the spatial domain. The use of a spatially localized Kalman filter is motivated by computing constraints arising from a multi-processor implementation of the Kalman filter as well as a lack of global observability in a nonlinear system with an extended Kalman filter implementation. In this paper we derive an extension of the classical output injection Kalman filter in which data is locally injected into a specified subset of the system states.