The Synthesis of Optimum Homing Missile Guidance Systems with Statistical Inputs

An analytical approach is presented which is applicable to the optimization of homing navigation guidance systems which are forced to operate in the presence of radar noise. The two primary objectives are to establish theoretical minimum miss distance performance and a method of synthesizing the optimum control system. The factors considered are: (1) target evasive maneuver, (2) radar glint noise, (3) missile maneuverability, and (4) the inherent time-varying character of the kinematics. Two aspects of the problem are considered. In the first, consideration is given only to minimization of the miss distance. The solution given cannot be achieved in practice because the required accelerations are too large. In the second, results are extended to the practical case where the limited acceleration capabilities of the missile are considered by placing a realistic restriction on the mean-square acceleration so that system operation is confined to the linear range. Although the exact analytical solution of the latter problem does not appear feasible, approximate solutions utilizing time-varying control systems can be found. One of these solutions - a range multiplication type control system - is studied in detail. It is shown that the minimum obtainable miss distance with a realistic restriction on acceleration is close to the absolute minimum for unlimited missile maneuverability. Furthermore, it is shown that there is an equivalence in performance between the homing and beam-rider type guidance systems. Consideration is given to the effect of changes in target acceleration, noise magnitude, and missile acceleration on the minimum miss distance.