Stochastic Resonance in Bayesian Estimation and CRLB for Nonlinear System

In this work, noise enhanced parameter estimation problems are investigated for a general nonlinear system, where an additive noise is added to the nonlinear system input and a Bayesian estimator is developed based on the noise modified output. The optimal probability distribution of the additive noises is formulated successively for minimizing the mean square error (MSE) of the optimal Bayesian estimation and the Cramer–Rao lower bound (CRLB). Then the optimal additive noises for the two different noise enhanced optimization problems are explicitly derived as constant vectors, which implies the randomization of constant vectors is not beneficial to these optimizations. Finally, numerical results are presented to illustrate the theoretical results.