Rate distortion lower bound for a special class of nonlinear estimation problems

Abstract

A rate distortion lower bound of minimum mean square error is presented for a special class of discrete time nonlinear filtering problems which have measurements that can be expressed as a memoryless nonlinear function of a Gaussian distributed space process with additive Gaussian noise. The lower bound is exactly and practically computable for a large class of nonlinearities and is proved to be asymtotically tighter than Cramer-Rao type bounds in the limit of low signal-to-noise ratio.