Summary: This paper discusses the application of the theory of partially observable Markov decision processes (POMDPs) to the design of guidance algorithms for controlling the motion of unmanned aerial vehicles (UAVs) with onboard sensors to improve tracking of multiple ground targets. While POMDP problems are intractable to solve exactly, principled approximation methods can be devised based on the theory that characterizes optimal solutions. A new approximation method called nominal belief-state optimization (NBO), combined with other application-specific approximations and techniques within the POMDP framework, produces a practical design that coordinates the UAVs to achieve good long-term mean-squared-error tracking performance in the presence of occlusions and dynamic constraints. The flexibility of the design is demonstrated by extending the objective to reduce the probability of a track swap in ambiguous situations.