Motivated by a fixed-speed, fixed-altitude Unmanned Aerial Vehicle (UAV), we seek to control the turning rate of a planar Dubins vehicle that tracks an unpredictable target at a nominal standoff distance. To account for all realizations of the uncertain target kinematics, we model the target motion as a planar random walk. A Bellman equation and an approximating Markov chain that is consistent with the stochastic kinematics is used to compute an optimal control policy that minimizes the expected value of a cost function based on the nominal distance. Our results illustrate that the control can further be applied to a class of continuous, smooth trajectories with no need for further computation.

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