# TSNetIQ: High-Resolution DOA Estimation of UAVs Using Microphone Arrays
## 1 Introduction  
In recent years, with the rapid development of the emerging low-altitude economy, angular position information of aerial vehicles such as unmanned aerial vehicles (UAVs) are drawing attention in various systems and services. Due to the poor adaptability of active radars in complex urban electromagnetic environments and the small radar scattering cross-sectional area of ordinary UAVs, which is difficult to capture, passive localization technology has gradually become the preferred solution for UAV localization [1]. Among the passive schemes, angle estimation based on sound source is regarded as a key method. Sound source localization using microphone array technology [2] has become an important way to obtain critical information in complex environments [3], which provides effective support for real-time localization by collecting signals through an array composed of multiple sensors, and then calculating the incidence angle of the sound source [4]. Traditional direction of arrival (DOA) estimation techniques can be categorized into four types: beamforming methods [5, 6], subspace decomposition methods, sparse reconstruction-based methods, and minimum variance-based methods. Beamforming methods are fundamentally constrained by the Rayleigh resolution limit, which restricts their ability to resolve closely spaced sources [7]. To overcome thislimitation and enhance the estimation accuracy, a class of algorithms based on eigenvalue decomposition (EVD) [8] has been developed, namely subspace decomposition methods including the well-known multiple signal classification (MUSIC) and the estimation of signal parameters via rotational invariance techniques (ESPRIT) [9; 10]. The MUSIC algorithm conducts EVD [11] on the covariance matrix of the received signals to separate the signal subspace and the noise subspace, which are mutually orthogonal [12]. By exploiting this orthogonality, MUSIC constructs a spatial spectrum in which the peaks correspond to the directions of arrival. The spectrum is searched to identify these peaks, thereby yielding high-resolution DOA estimates. In contrast, the ESPRIT algorithm [13] leverages a specially designed array geometry composed of two identical subarrays with a known and constant displacement between corresponding elements. This configuration ensures that the phase shift in an incoming plane wave across the subarrays is invariant to rotation. By solving the resulting generalized eigenvalue problem, the DOAs of the incident signals can be accurately estimated without the need for a spectral search [14]. Beyond subspace-based techniques such as MUSIC and ESPRIT, various other classes of algorithms [15] have been proposed to further improve DOA estimation performance under challenging conditions, such as a low signal-to-noise ratio (SNR), limited snapshots, or coherent sources. Sparse reconstruction-based methods, inspired by compressive sensing theory, exploit the inherent sparsity of signal sources in the angular domain [16]. By discretizing the angle space into a fine grid, DOA estimation is formulated as a sparse signal recovery problem [17]. Techniques such as the L1-norm minimization and orthogonal matching pursuit have been widely adopted in this context. These methods can provide super-resolution DOA estimates even with a limited number of array elements or snapshots. However, their performance heavily depends on the grid resolution, and they may suffer from basis mismatch errors when the true DOA does not align with the predefined grid. Minimum variance-based methods [18], such as the minimum variance distortionless response (MVDR) beamformer, aim to suppress interference and noise while maintaining unity gains in the desired signal direction [19]. MVDR constructs an adaptive spatial filter that minimizes the output power subject to a distortionless constraint in the steering direction. While MVDR offers improved resolution over conventional beamforming, its performance degrades in the presence of array calibration errors or coherent sources.