Mathematical Problems in Engineering
Volume 6 (2000), Issue 2-3, Pages 225-265

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

Joonhyung Park, Richard G. Rhinehart, and Pierre T. Kabamba

Department of Aerospace Engineering, The University of Michigan, Ann Arbor 48109-2140, MI, USA

Received 10 September 1999

Copyright © 2000 Joonhyung Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.