In this paper, we study an unmanned aerial vehicle (UAV)-enabled wireless sensor network, where a UAV is dispatched to collect the sensed data from distributed sensor nodes (SNs) for estimating an unknown parameter. It is revealed that in order to minimize the mean square error for the estimation, the UAV should collect the data from as many SNs as possible, based on which an optimization problem is formulated to design the UAV's trajectory subject to its practical mobility constraints. Although the problem is nonconvex and NP-hard, we show that the optimal UAV trajectory consists of connected line segments only. With this simplification, an efficient suboptimal solution is proposed by leveraging the classic traveling salesman problem and applying convex optimization techniques. Simulation results show that the proposed trajectory design achieves a significant performance gain in terms of the number of SNs whose data are successfully collected, as compared with other benchmark schemes.
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