Noise Enhanced Parameter Estimation

This paper investigates the phenomenon of noise enhanced systems for a general parameter estimation problem. When the estimator is fixed and known, the estimation performance before and after the addition of noise are evaluated. Performance comparisons are made between the original estimators and noise enhanced estimators based on different criteria. The form of the optimal noise probability density function (pdf) is determined. The results are further extended to the general case where the noise is introduced to the system via a transformation. For the case where the estimator is fixed and unknown, approaches are also proposed to find the optimum noise. Finally, two illustrative examples are presented where the performance comparison is made between the optimal noise modified estimator and Gaussian noise modified estimator.