Data assimilation algorithm based on an approximate solution of the optimal nonlinear filtering problem

Abstract

Listen

Translate article

In the ensemble Kalman filter, a currently popular data assimilation algorithm, it is assumed that the density of the estimation error distribution is a Gauss function, which is not fulfilled in the general case of a nonlinear model and a nonlinear observation operator. Statement of the optimal filtering problem in the general case is based on the Bayesian approach. One way to approximate the nonlinear optimal filtration problem is to represent the distribution density as a sum of Gaussian distributions with given mean values and covariance matrices. Then the optimal estimate is the weighted sum of estimates obtained in the Kalman filter for the corresponding parameters of the Gaussian distribution in this sum. The paper considers the algorithm for implementing this approach, which uses the previously developed effective local ensemble data assimilation algorithm (ensemble pi-algorithm). The results of numerical experiments to evaluate the properties of the proposed algorithm with the 1-dimensional nonlinear model are presented.