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

For an interceptor that follows a Keplerian trajectory, 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 same guidance law has been applied to interceptors flying in a gravity field. In the presence of random navigation errors in the new guidance law, the numerically simulated 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. A trade-off in gain magnitude is required to prevent this degradation.