Noise-aided nonlinear Bayesian estimation.

Estimation on a noisy signal observed by a nonlinear sensor taking the form of a threshold quantizer is considered. The optimal Bayesian estimator with minimal error is derived in this nonlinear setting. The existence of conditions where the performance of this estimator can be improved by raising the level of noise is established, both theoretically and numerically. These results constitute a different instance of the nonlinear phenomenon of stochastic resonance for signal enhancement by noise.