Miss distance analysis in homing and Lambert interceptions with application to a new guidance law.

Abstract

The purpose of guidance is to cause a collision between a missile and a specified target. Accordingly, the performance of guidance systems can generally be quantified in terms of the miss distance between the missile and target. This miss distance may be a deterministic or a stochastic quantity, depending on the phenomena that cause the miss. The common theme of this dissertation is the analysis of miss distances in guidance. Two guidance laws are considered here: a tactical homing guidance law that combines proportional navigation with pursuit guidance, and ballistic Lambert guidance. In the combined guidance law, we obtain an analytical expression for the mean square of the miss due to random navigation errors, explicitly in terms of the navigation constants. Generally, the mean square miss will then decrease as the navigation constants are increased in the case of a perfect autopilot. We also consider the effect of measurement noise in the presence of a first-order autopilot. Here, numerical simulations corroborate the findings of previous studies on proportional navigation, where it was shown that increasing the navigation constant shortens the engagement, but degrades accuracy in the presence of autopilot dynamics. Hence a trade-off is required for the optimal value of these navigation constants. In Lambert guidance, for an interceptor that follows a Keplerian trajectory, we have obtained a closed form linear expression for the Point of Closest Approach (PCA) miss distance in terms of the perturbations of the booster cut-off conditions. We use this analysis result to develop a new guidance law which, in the absence of gravity, ensures (1) that the magnitude of the predicted PCA miss decays exponentially, and (2) that the magnitude of the relative velocity is constant. The results of numerical simulations of the new guidance law show that, in the presence of gravity, an interception with a large gain yields a tighter engagement, while requiring approximately constant velocity of the interceptor as a function of time. The performance degradation of the new guidance law in terms of the rms of the predicted PCA miss due to random navigation errors was numerically simulated. The results show that increasing the guidance law gain increases the rms of the predicted PCA miss, which results in a degradation of the interception performance. Therefore a trade-off in gain magnitude is required to prevent this degradation.