  We examine stochastic dynamical systems where the transition matrix, $\Phi$,
and the system noise, $\bf{\Gamma}\bf{Q}\bf{\Gamma}^T$, covariance are nearly
block diagonal. When $\bf{H}^T \bf{R}^{-1} \bf{H}$ is also nearly block
diagonal, where $\bf{R}$ is the observation noise covariance and $\bf{H}$ is
the observation matrix, our suboptimal filter/smoothers are always positive
semi-definite, and have improved numerical properties. Applications for
distributed dynamical systems with time dependent pixel imaging are discussed.
