Miss Distance Analysis For A Terminal Guidance System Based On The Adjoint Method

In purpose of increasing the terminal guidance precision, a terminal guidance system is analyzed by establishing the mathematical relationship between the input signal and the miss distance based on the adjoint method. Based on the linear time varying terminal guidance system model, this thesis mainly focus on the mathematical relationship between system input and the miss distance, which is derived with the adjoint method. The analytical solution of miss distance is studied, based on which the influences on the terminal guidance precision from system parameters, target maneuvers, and the seeker noise are studied The main works are as followed:Firstly, under the small angle assumption, a two-dimensional time-varying linear model of the terminal guidance system is developed. The main influencing factors to the guidance precision are analyzed. By deriving the theory of adjoint method in mathematical way, the applicability of the adjoint method is discussed. An adjoint model of the terminal guidance system is established based on the on the procedural aspects of the adjoint method. Subsequently, in order to eliminate the restrictions to the input signals in the block diagram based adjoint model, the application of the adjoint method is extended to the state-space terminal guidance system model.Secondly, analytical solutions of the miss distance caused by typical target maneuvers are derived, with which the influences of the effective navigation ratio, the missile time constant and the time-to-go to the miss distance are analyzed. Also, a transfer function from target maneuver to the miss distance is derived. Regarding the miss distance caused by a target maneuver starting from a long distance as the steady state response of miss distance, the analytical solutions of target step maneuver and sinusoidal maneuver to the miss distance steady state response are obtained. And the analytical solutions are applied in improving the parameters of the terminal guidance system. Thereafter, in the state space model of the terminal guidance system, the analytical solution of the miss distance caused by a non-typical target maneuver is derived and analyzed. The target maneuver type which will cause the maximum miss distance of a terminal guidance system is obtained. The accuracy of the results are proved with simulations.Finally, taking the root mean square miss distance as the criteria, the influence by the stochastic input to the terminal guidance precision is analyzed based on the adjoint method. For the aspect of seeker noise, the analytical solutions of the miss distance caused by the glint noise and the line-of-sight angle noise are derived. For the aspect of target maneuver, taking the starting time of a target maneuver as a random variable, the analytical solutions of the miss distance caused by random target maneuvers are obtained. And to forward the study, the statistical analysis is extended by applying the adjoint method into the calculation of the miss distance cumulant function. The analytical solutions of the miss distance high order moments caused by random target maneuvers are derived. The accuracy of the miss distance probability distribution obtained with the high order moments is compared with Monte-Carlo in simulation.