## 1 Introduction  
Direction of arrival (DOA) estimation has been widely used in radar [1], sonar [2], wireless communication [3] and other systems. Typically, a fundamental premise in the domain of DOA estimation is that the array noise conforms to uniform Gaussian white noise. However, this premise may not always hold true, as non-ideal noise conditions (non-uniform or colored noise [4]) often occur in practical systems due to factors related to the sensor itself and external environmental influences. In the presence of colored noise, the performance of traditional DOA estimation techniques is significantly compromised, to a considerable extent. Unlike white noise, colored noise exhibits a non-uniform power spectral density across different frequencies, possessing specific frequency characteristics. This non-uniformity alters the statistical properties of the signal and noise, thereby interfering with the normal operation of DOA estimation algorithms. Specifically, colored noise may introduce additional interference terms, causing the received signal model to deviate from the ideal state, which increases the difficulty and error in parameter estimation. In extreme cases, if the spectral characteristics of colored noise overlap severely with the spectrum of the target signal, traditional DOA estimation algorithms may completely fail, unable to accurately identify the direction of the signal origin. Therefore, in the context of colored noise, the degradation in DOA estimation performance not only manifests in a loss of accuracy but also poses serious threats to the stability and reliability of the algorithms. Unlike the spatially uniform white noise model referenced in prior works [5; 6; 7; 8; 9; 10; 11; 12], practical applications often encounter varying noise covariance among sensors [13]. Consequently, classical subspace-based DOA estimation techniques, such as the MUSIC method [11], which rely on the eigen-decomposition of the array covariance matrix, experience significant performance degradation. Furthermore, DOA methods independent of eigendecomposition, like maximum-likelihood estimation [14], are also heavily impacted. Additionally, some recently proposed sparse representation methods [6; 12] share a dependence on the uniform white noise model. Given this, the challenge of DOA estimation in non-uniform noise environments has garnered increasing attention [7; 15; 16; 17; 18; 19; 20]. Deterministic and stochastic non-uniform maximum likelihood (ML) estimators have been developed to address noise non-uniformity [7; 15], albeit involving computationally intensive nonlinear optimization problems. A power domain approach [16] simplifies complexity by bypassing sensor noise variance estimation, yet it still entails solving highly nonlinear optimization issues. Another strategy [17] estimates the noise covariance matrix using the interrelationships within the array covariance matrix blocks, but necessitates a sensor count exceeding three times the source number. The iterative ML subspace estimation (IMLSE) and iterative least-squares subspace estimation (ILSSE) algorithms [18] iteratively estimate the signal subspace and noise covariance matrix, subsequently determining DOAs with traditional direction-finding methods. A method presented in [19] estimates DOA by vectorizing the covariance matrix (excluding diagonal elements) and applying sparse representation techniques. While this approach mitigates the impact of noise non-uniformity, the deletion of diagonal elements may lead to information loss. The augmented subspace MUSIC (ASMUSIC) method [20] demonstrates that the discrepancy in noise power between the acoustic pressure and velocity components of an AVS (Acoustic Vector Sensor) significantly impairs the DOA estimation performance of the MUSIC method, yet it does not resolve the issue of DOA estimation in arrays with unequal noise power among elements.