We study the problem of devising a closed-loop strategy to control the position of a robot that is tracking a possibly moving target. The robot obtains noisy measurements of the target’s position. The measurement noise depends on the relative states of the robot and the target. We consider scenarios where the measurement values are chosen by an adversary, so as to maximize the estimation error. Furthermore, the target may be actively evading the robot. Our main contribution is to devise a closed-loop control policy for distance-dependent target tracking that plans for a sequence of control actions, instead of acting greedily. We consider a game-theoretic formulation of the problem and seek to minimize the maximum uncertainty (trace of the posterior covariance matrix) over all possible measurement values. We exploit the structural properties of a Kalman Filter to build a policy tree that is orders of magnitude smaller than naive enumeration while still preserving optimality guarantees. We show how to obtain even more computational savings by relaxing the optimality guarantees. The resulting algorithms are evaluated through simulations and experiments with real robots.