Using the picard method to calculate covariance matrices in the discrete Kalman filters

Abstract

A new method of calculating covariance matrices for transition from a system of continuous linear stochastic differential equations to its discrete multidimensional stochastic analog has been developed. The proposed method is based on the use of the Picard iterative process. The comparison of the proposed method with more widespread analogs has shown a significant computational advantage of the new method when applied to the Kalman algorithms.