The problem considered in this paper is that of estimating the relative kinematics of a ballistic target tracked by a homing interceptor missile in a 2D scenario with the objective of minimizing the miss distance. The miss distance is the final relative range between the target and the interceptor and its minimization has traditionally been considered in guidance problems. In this work, an Extended H∞ Filter with a miss distance minimization objective (EHF-2) has been formulated to provide accurate estimates of the relative kinematics of the target and interceptor. The performance of this filter has been compared with those of the noise optimal Extended Kalman Filter (EKF) and the (noise) robust Extended H∞ Filter (EHF-1). It is observed that the proposed EHF-2 shows significant improvement in performance with respect to both miss distance as well as sightline rate (SLR) compared to EKF and EHF-1 over the total terminal range.