Fourier-Hermite Rauch-Tung-Striebel smoother

In this article, we introduce the Fourier-Hermite Rauch-Tung-Striebel smoother which is based on expansion of nonlinear functions in a Fourier-Hermite series in same way as the traditional extended Rauch-Tung-Striebel smoother is based on the Taylor series. The first order truncation of the Fourier-Hermite series gives the previously known statistically linearized smoother.