A New Approach for Nonlinear Transformation of Means and Covariances in Direct Statistical Analysis of Nonlinear Systems

Abstract

Covariance analysis describing function technique is a conventional method to solve the performance analysis of the nonlinear missile guidance system. Aiming at the faultiness of covariance analysis describing function technique and its improved method, this paper proposes a new method to solve the mean and covariance transfer issue by using the high-degree spherical-radial cubature rule. In terms of simulation models, the nonlinear missile guidance system contains the saturation link to limit the lateral acceleration command and the initial heading error is introduced. In addition, the zero-mean target evasive maneuver with exponentially-decaying autocorrelation function is chosen as the input of the missile guidance system. Furthermore, compared with the existing methods, the proposed method has higher computational efficiency, accuracy and better applicability in high-dimensional nonlinear systems by theoretical derivation and simulation results from the mean and covariance values of relative lateral separation. Finally, the presented analysis method can be used as a general method for the design and statistical analysis of multidimensional nonlinear systems.