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

This paper studies a rate distortion lower bound of the mean square error for a special class of non-linear estimation problems which have measurements that can be expressed as a memoryless nonlinear function of a Gaussian distributed state plus Gaussian distributed measurement noise. This bound is computable in closed form for a large class of nonlinearities and it is asymptotically tighter than Cramer-Rao type bounds in the limit of low signal-to-noise ratio. Practical computability and tightness of the bound are discussed, and several illustrative examples are given, including the cubic sensor problem.