Filtering and control performance bounds with implications on asymptotic separation

A bound is derived on the accuray in causally estimating a Gaussian process from nonlinear observations. Both additive Gaussian noiac and Poisson observations are included. The bound is used to study the control of a stochastic linear dynamical system with nonlinear observations of either type and an average quadratic cost. An asymptotic Separation Theorem is established showing that a linear feedback cootrol law. involving a state estimate. is asymptotically optimum as the accuracy of the state estimate approaches the bound.