Joint Gain-Phase Errors Calibration and 2D DOA Estimation for Sparse Planar UAV Arrays

With the gradual development of the unmanned aerial vehicle (UAV) swarm electronic reconnaissance research, multi-target localization of UAV arrays has become a research hotspot. In UAV arrays, the uniform linear array (ULA) of multiple UAVs equivalents can only estimate 1D DOA, and the swarm of UAV of approximately the same height can be equivalent to the arbitrary sparse planar array (SPA), which can be used to directly estimate 2D DOA and locate the radiation source. But due to the complexity of the planar array, the estimation and calibration of the gain-phase errors face challenges such as multi-target overlap, limited accuracy owing to suboptimal convergence, and high computational cost. In this paper, for the problem that subspace-based and sparse reconstruction-based DOA methods are difficult to balance the degree of freedom (DOF) and estimation performance, we use the decoupled atomic norm minimization (DANM) method to avoid spectral peak search combined with the gradient descent method to minimize the gain-phase errors. The method can simultaneously estimate the errors and the initial 2D DOA and further accurately estimate the 2D DOA based on the error calibration. The simulations are evaluated using a representative coprime planar array (CPPA) and the results show that the method can achieve higher estimation accuracy compared to the other mainstream methods.

I. Introduction

The problem of the direction of arrival (DOA) estimation is an important area of research in array signal processing and has been widely used in navigation, underwater sonar and multiple-input multiple-output (MIMO) communication systems, etc. Although high-resolution subspace-based [1] and sparse reconstruction-based [2], [3] DOA methods have been proposed, the effectiveness of these methods still depends on an accurately known array response matrix. But in practical sparse planar UAV arrays, gain-phase errors inevitably occur due to factors such as fading delays in signal propagation and channel inconsistencies [1], which leads to deviations of the array manifold from the ideal model.