Present interceptor guidance research is frequently based on separating the design of the estimator and that of the guidance law, but the theorem is not proven valid and optimal. This article proposes a new way of integrating the guidance and estimation using the general separation theorem (GST). First, based on the consideration that the model for anti-missiles is a nonlinear and non-Gaussian problem, a model is built of guiding a missile towards an evading agile target in noisy environments. Second, the concept of a miss-set is introduced, and a geometric approach is utilized to incorporate the design of a guidance law into that of the optimal estimator under the guidelines of the general separation theorem. After an integrated guidance and estimation is derived, a miss-set centering guidance law (MSC) is proposed. Finally, a numerical study is provided which demonstrates the performance and viability of the proposed method in a realistic engagement scenario. A comparison between the proposed method and the augmented proportional guidance law (APN) is carried out to demonstrate a significant improvement of the former over the latter.