In signal estimation, an optimal estimator is frequently unachievable, because its closed form may not be analytically tractable or is too complex to implement. Alternatively, one can turn to suboptimal yet easily implementable estimators for practical signal estimation tasks. In this paper, a general noise-boosted estimator is designed and the adaptive stochastic resonance method is implemented to simultaneously exploit the beneficial role of the injected noise as well as the learning ability of the estimator parameter. Aiming to effectively improve the estimation performance, we use the kernel function method to find an approximate solution for the probability density function (PDF) of the optimal injected noise. During this process, the noise PDF and the estimator parameter establish a finite dimensional non-convex optimization space for maximizing the estimation performance, which is adaptively searched by the sequential quadratic programming algorithm at each iteration.
Two representative signal estimation problems are explored, consisting in estimating a random signal from low-resolution observations, or a deterministic parameter in a heavy-tailed noisy environment. The obtained results demonstrate that this adaptive stochastic resonance method can improve the performance of the suboptimal estimators and bring it very close to that of the optimal estimator.