  The conventional direction of arrival (DOA) estimation methods are performed
with multiple receiving channels. In this paper, a changeling DOA estimation
problem is addressed in a different scenario with only one full-functional
receiving channel. A new unmanned aerial vehicle (UAV) swarm system using
multiple lifted reconfigurable intelligent surface (RIS) is proposed for the
DOA estimation. The UAV movement degrades the DOA estimation performance
significantly, and the existing atomic norm minimization (ANM) methods cannot
be used in the scenario with array perturbation. Specifically, considering the
position perturbation of UAVs, a new atomic norm-based DOA estimation method is
proposed, where an atomic norm is defined with the parameter of the position
perturbation. Then, a customized semi-definite programming (SDP) method is
derived to solve the atomic norm-based method, where different from the
traditional SDP method, an additional transforming matrix is formulated.
Moreover, a gradient descent method is applied to refine the estimated DOA and
the position perturbation further. Simulation results show that the proposed
method achieves much better DOA estimation performance in the RIS-aided UAV
swarm system with only one receiving channel than various benchmark schemes.
