Unmanned aerial vehicles (UAVs) can provide wireless access to terrestrial users, regardless of geographical constraints, and will be an important part of future communication systems. In this paper, a multi-user downlink dual-UAVs enabled covert communication system was investigated, in which a UAV transmits secure information to ground users in the presence of multiple wardens as well as a friendly jammer UAV transmits artificial jamming signals to fight with the wardens. The scenario of wardens being outfitted with a single antenna is considered, and the detection error probability (DEP) of wardens with finite observations is researched. Then, considering the uncertainty of wardens' location, a robust optimization problem with worst-case covertness constraint is formulated to maximize the average covert rate by jointly optimizing power allocation and trajectory. To cope with the optimization problem, an algorithm based on successive convex approximation methods is proposed. Thereafter, the results are extended to the case where all the wardens are equipped with multiple antennas. After analyzing the DEP in this scenario, a tractable lower bound of the DEP is obtained by utilizing Pinsker's inequality. Subsequently, the non-convex optimization problem was established and efficiently coped by utilizing a similar algorithm as in the single-antenna scenario. Numerical results indicate the effectiveness of our proposed algorithm.

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