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

For an interceptor that follows a Keplerian trajectory and nominally intercepts a moving target, we have obtained a closed form linear expression for the miss distance in terms of the perturbations of the booster cut-off conditions, where the miss distance reflects the predicted miss at the point of closest approach (PCA) between the interceptor and the target. 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 numerical simulations of the performance of the guidance law show that, in the presence of gravity, an interception with a large gain yields a relatively tight engagement, while requiring approximately constant velocity of the interceptor. Finally, the performance degradation of the new guidance law in terms of the r.m.s. of the predicted PCA miss due to random navigation errors was numerically simulated. The results show that increasing the guidance law gain increases the r.m.s. of the predicted PCA miss, which results in a degradation of the interception performance. Thus a trade-off in gain magnitude is required to prevent the degradation