Bounds on the Accuracy in Causal Filtering for Nonlinear Observations with Some Implications on Asymptotic Separation in Stochastic Control

摘要

A bound is derived on the accuracy in causally estimating a Gaussian process from nonlinear observations. Both additive Gaussian noise and Poisson observations are included. The bound is used to study the control of a stochastic linear dynamical system with nonlinear observations and an average quadratic cost. An asymptotic separation theorem is established showing that a linear feedback control law, involving a state estimate, is asymptotically optimum as the accuracy of the state estimate approaches the bound. (Author)