An Analysis of Stochastic Disturbances on Nonlinear Missile-Target Engagements Based on the Adjoint Method

A stochastic adjoint analysis tool that can capture the dominant nonlinearities of a typical missile-target engagement scenario, in addition to the dominant dynamics and stochastic error sources of a missile is developed. The two dimensional, nonlinear missile target terminal engagement problem is modeled in state dependent coefficient form, to generate a set of truth data. Dominant missile dynamics regarding the miss distance, such as the missile airframe response, and the seeker tracking response is accounted for in the system dynamics. The linear time varying counterpart of the nonlinear engagement model is formed by utilizing the state dependent coefficient form. The nominal state history of the nonlinear model is obtained through numerical solution, and the linear time varying model system matrix, input matrix and the output matrix are populated by linearization around the nominal state history. The resulting linear time varying model is validated under stochastic disturbances such as range dependent seeker line of sight rate noise and initial heading error against the truth data. The adjoint counterpart of the linear time varying model is shown to generate realistic mean and root mean square values, when compared to the original nonlinear model.