This paper considers the discrete time Kalman and H_∞ approach to the two-state α-β target tracking problem. A closed form steady-state solution for the α-β parameter selection for the H_∞ tracker, which is similar to the tracking index process for the MSE (Kalman) criterion, is presented. The H_∞ and Kalman processes model the radar/target system with the objective to keep the target within the radar beamwidth. The two trackers are compared, considering two cases that differ in the input maneuver disturbances, random maneuvers and constant acceleration. An example illustrates the performance of the α-β tracker with respect to keeping the target within the beamwidth in terms of probability of escape.