We propose a fully Bayesian approach to wideband, or broadband, direction-of-arrival (DoA) estimation and signal detection. Unlike previous works in wideband DoA estimation and detection, where the signals were modeled in the time-frequency domain, we directly model the time-domain representation and treat the non-causal part of the source signal as latent variables. Furthermore, our Bayesian model allows for closed-form marginalization of the latent source signals by leveraging conjugacy. To further speed up computation, we exploit the sparse ``stripe matrix structure'' of the considered system, which stems from the circulant matrix representation of linear time-invariant (LTI) systems. This drastically reduces the time complexity of computing the likelihood from $\mathcal{O}(N^3 k^3)$ to $\mathcal{O}(N k^3)$, where $N$ is the number of samples received by the array and $k$ is the number of sources. These computational improvements allow for efficient posterior inference through reversible jump Markov chain Monte Carlo (RJMCMC). We use the non-reversible extension of RJMCMC (NRJMCMC), which often achieves lower autocorrelation and faster convergence than the conventional reversible variant. Detection, estimation, and reconstruction of the latent source signals can then all be performed in a fully Bayesian manner through the samples drawn using NRJMCMC. We evaluate the detection performance of the procedure by comparing against generalized likelihood ratio testing (GLRT) and information criteria.

翻译：本文提出了一种完全贝叶斯方法用于宽带波达方向估计与信号检测。与以往在时频域建模信号的宽带波达方向估计与检测研究不同，我们直接对时域表示进行建模，并将源信号的非因果部分视为潜变量。此外，我们的贝叶斯模型通过利用共轭性，实现了对潜源信号的闭式边缘化。为加速计算，我们利用了所考虑系统特有的稀疏"带状矩阵结构"，该结构源于线性时不变系统的循环矩阵表示。这将计算似然的时间复杂度从$\mathcal{O}(N^3 k^3)$显著降低至$\mathcal{O}(N k^3)$，其中$N$为阵列接收的样本数，$k$为信源数量。这些计算改进使得通过可逆跳转马尔可夫链蒙特卡洛方法进行高效后验推断成为可能。我们采用RJMCMC的不可逆扩展形式，该版本通常比传统可逆变体具有更低的序列相关性和更快的收敛速度。通过NRJMCMC抽取的样本，可对潜源信号进行完全贝叶斯框架下的检测、估计与重构。我们将该方法的检测性能与广义似然比检验及信息准则进行对比评估。