For effective interception of ballistic missiles with large velocity and screw maneuverability in their falling course, focused research should be carried out on guidance filter techniques. In this paper, a novel Laplace transform was used to design a four-state filter and the target acceleration, first and second derivatives of acceleration were estimated. The results are more accurate with short latency compared with three-state filter estimation. Meantime, combined with the given Weave guidance law, the four-state filter with weave guidance law is proved to have advantages in smaller miss distance compared with the three-state filter with proportional guidance law and three-state filter with optimal guidance law.