Miss analysis in Lambert interceptions with application to a new guidance law (Q5950076)

The Lambert problem is to determine an orbit that connects two given points in a given transfer time under the assumptions of the restricted two-body problem. This problem has received substantial attention in the literature because of its application to the interception of celestial bodies and ballistic missiles. In the paper, the position and the velocity of the target are assumed completely known. For an interceptor that follows a Keplerian trajectory and nominally intercepts a moving target, a closed form linear approximation for miss distance is obtained in terms of the perturbations of the orbital elements. Then a new guidance law is presented, which is developed using the Point of Closest Approach (PCA) miss vector. The results of numerical simulation show, that the predicted PCA miss decays quasi-exponentially in time and a large guidance law gain reduces the predicted PCA miss rapidly. But increasing the guidance law gain increases the rms of the predicted PCA miss, which results in a degradation of the interception performance, despite the fact that it reduces the nominal predicted PCA miss.