Variational Bayesian Inference Based Direction Of Arrival Estimation in Presence of Shallow Water Non-Gaussian Noise
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摘要: 传统基于高斯统计特性的波达角(DOA)估计方法在高斯背景噪声中可以获得较好的估计性能，然而受脉冲噪声影响的浅海环境噪声不再服从高斯分布，若直接利用传统波达角估计方法会引入较大误差。为提升非高斯噪声环境下的波达角估计性能，该文提出一种浅海非高斯噪声下的基于变分贝叶斯推断的波达角估计方法。首先利用信号与脉冲噪声的稀疏性构建多测量向量稀疏信号恢复(SSR)模型；其次，考虑信号的共稀疏特性与脉冲噪声的独立稀疏性，构建层次化贝叶斯估计框架；然后利用变分贝叶斯推断估计信号与噪声的后验概率估计。稀疏信号模型中考虑离网格误差，利用根稀疏贝叶斯估计实现离网格误差修正，解决离网格误差引起的基失配问题；最后通过迭代更新获得较为精确的波达角估计，同时消除脉冲噪声的影响。仿真结果表明：所提方法在非高斯噪声环境下具有较好的波达角估计性能，同时对于脉冲噪声具有较强的抗干扰特性。Abstract: Conventional Direction Of Arrival (DOA) estimators achieve satisfactory performance with the common assumptions of Gaussian noise. However, the impulsive noise exists in the shallow water extensively and does not follow the Gaussian distribution, which induce undesirable biases and degrade the performance of the conventional estimators. In the paper, a new DOA estimation method based on variational Bayesian inference in presence of shallow water non-Gaussian noise is proposed to improve the DOA estimation performance. Firstly, the multiple measurement vectors Sparse Signal Representation (SSR) model is formulated utilizing the sparsity of signal and impulsive noise. After that, the hierarchical Bayesian estimation framework is formulated which considers the common sparsity of signal and the independent sparsity of impulsive noise. Subsequently, the variational Bayesian inference is utilized to achieve the posterior estimations for the signal and impulsive noise. The SSR model incorporates the off-grid bias, and the root sparse Bayesian learning realizes to refine the bias and mitigate the basis mismatches. At last, the accurate DOA estimation is achieved through iterative updates and the effects of impulsive noise are mitigated. Simulations are used to verify that the proposed estimator achieves superior performance compared with state-of-art benchmarks.
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表 1 浅海噪声参数拟合
噪声模型 参数 1 2 3 4 5 6 ${{{\rm{S}}\alpha {\rm{S}}} }$噪声 $ \alpha $ 1.3401 1.4369 1.3767 1.5134 1.1419 1.6236 $ \chi $ 0.0224 0.0455 0.0308 0.2085 0.0538 -0.0021 $ \gamma $ 0.8838 0.9349 0.9543 0.8637 1.1959 0.6863 $ \psi $ 0.0478 0.0567 0.0376 0.1197 0.1803 -0.0253 GMM噪声 $ \mu $ 0.0828 0.0735 0.0838 0.0962 0.1430 0.0632 $ \sigma _1^2 $ 1.7591 1.8785 1.9661 1.4830 2.9481 1.0192 $ \kappa $ 132 91.2 76.78 35.6 91.32 145 
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