On the construction of a second order Gaussian Recursive Filter

Gaussian recursive filters (RFs) are frequently used in several research fields with th aim to approximate in an efficient way Gaussian filters and Gaussian-based convolutions. Among them, the first-order Gaussian RF, also in its K-iterated form, has been recently used in data assimilation. However, a recent study has proved that in the base case (K = 1) this method is not able to well approximate the Gaussian convolution for all values of the standard deviation. Here we propose a new way to construct a second order RF whose smoothing coefficients are chosen in order to enhance the accuracy of the approximation.