The 1991 Gulf War introduced an urgent need to intercept of a new type of target, namely the tactical ballistic missile (TBM) that is able to carry also non-conventional warheads. Successful interception of a TBM, much less vulnerable than an aircraft, requires a very small miss distance or even a direct hit (to hit a bullet with a bullet). Motivated by this challenge, a new guidance law was developed recently. It is based on the integration of several non-orthodox ideas: a pursuit-evasion game formulation, compensation of the inherent estimation delay and time varying velocity profiles, as well as time varying maneuver limits. The new interceptor guidance law provided a significant homing accuracy improvement. Nevertheless, it still fell short to guarantee a hit-to-kill accuracy because of the only partial compensation of the estimation delay and the non zero residual estimation error. The current new challenge is further improvement in guidance accuracy, which cannot be achieved, - since homing performance of a guided interceptor missile is limited by the accuracy of the estimator, - without minimizing the estimation errors against randomly maneuvering targets. It has to be remembered that the Separation Theorem is not valid for such a problem In this paper several options (such as multiple model adaptive estimators, dual control, unknown input detection, robust H-infinity estimator, etc.) are compared to the classical baseline of a Kalman filter with a shaping filter driven by white noise representing the random target maneuvers