  Compressed Estimation approaches, such as the Generalised Compressed Kalman
Filter (GCKF), reduce the computational cost and complexity of high dimensional
and high frequency data assimilation problems; usually without sacrificing
optimality. Configured using adequate cores, such as the Unscented Kalman
Filter (UKF), the GCKF could also treat certain non-linear cases. However, the
application of a compressed estimation process is limited to a class of
problems which inherently allow the estimation process to be divided, at
certain intervals of time, in a subset of lower dimensional problems. This
limitation prohibits applying the compressing techniques for estimating densely
coupled high dimensional processes. However, those limitations can be overcome
by applying proper techniques. In this paper, the concept of subsystem
switching, and information exchange architecture, namely Exploiting Local
Statistical Dependency (ELSD), has been derived and explored, for allowing
compressed estimators to mimic optimal full Gaussian estimators. The
performances of the methods have been verified through its application in
solving usual types of linear Stochastic Partial Differential Equations
(SPDEs). The computational advantages of using the proposed techniques have
also been highlighted with recommendation of its usage over the full filter
when dealing with high dimensional and high frequency data assimilation.
