This paper provides a direction-of-arrival (DOA) estimation method based on sparse Bayesian learning for a colored noise environment. In this method, the harmonic noise model is absorbed into the covariance matrix model to express the noise objectively. As such, the covariance matrix is parameterized with the signal powers and noise parameters. Given that the existing Bayesian models cannot be directly used for this covariance matrix model, this paper establishes a new probabilistic model. Different priors are assigned for signal power vector and noise parameter vector since signal power vector is sparse but noise parameter vector is not. Based on this probabilistic model, the variational Bayesian inference is applied to estimate signal powers and noise parameters. Moreover, first-order Taylor series expansion is applied to approximate the virtual steering vector as a function of the grid error between the true DOA and the closest grid point. Grid error is estimated in the Bayesian framework and applied to modify the grid, thus alleviating basis mismatch. Simulation results prove that the proposed method achieves high estimation accuracy with a mild computational complexity in a colored noise environment.

本文提出了一种基于稀疏贝叶斯学习的有色噪声环境下的到达方向估计方法。该方法将谐波噪声模型吸收到协方差矩阵模型中，以客观地表达噪声。这样，利用信号功率和噪声参数对协方差矩阵进行参数化。鉴于现有的贝叶斯模型不能直接用于该协方差矩阵模型，本文建立了一个新的概率模型。由于信号功率矢量稀疏而不是噪声参数矢量，因此为信号功率矢量和噪声参数矢量分配了不同的先验。基于该概率模型，将变分贝叶斯推断应用于估计信号功率和噪声参数。此外，一阶泰勒级数展开式的应用是根据真实DOA与最近的网格点之间的网格误差来近似虚拟转向矢量。在贝叶斯框架中估计网格误差，并将其应用于修改网格，从而减轻基础不匹配。仿真结果表明，该方法在彩色噪声环境下具有较高的估计精度和较低的计算复杂度。