Abstract
A theoretical nonlinear filtering method that can estimate a weak signal buried in strong non-Gaussian noise has been proposed in previous studies. This method is attractive because it maximizes the signal-to-noise ratio at the filter output. A mathematical expression for the probability density function (PDF) of the noise is necessary to determine the characteristics of the filter in this method. To enhance the usability of this filtering method, the present study proposes an estimation method for the PDF. Kernel density estimation is considered, and the design framework of two key parameters, the kernel function and bandwidth, is introduced. Employing the Epanechnikov kernel reduces the computational complexity, and the proposed bandwidth achieves a filtering performance close to the theoretical limit. A well-known optimal bandwidth, which minimizes the estimation error, is expected to achieve the best filtering performance, but our proposed method improves upon this performance. In a numerical evaluation, several typical examples of noise types are considered, and the effectiveness of the proposed method is confirmed.
