基于张量分解和Kullback-Leibler发散协方差拟合的矢量阵盲波达方向估计
Blind Direction-of-Arrival Estimation in Acoustic Vector-Sensor Arrays via Tensor Decomposition and Kullback-Leibler Divergence Covariance Fitting
摘要：
提出了一种基于矢量阵的窄带信号到达角盲估计方法。基于AVS测量的信号的特殊结构，我们证明了从阵列接收到的所有信号的协方差矩阵具有自然的低秩4向张量表示。因此，我们的估计不是直接从原始数据中估计DOA，而是从观测的二阶统计量（SOS）张量的唯一参数规范多矢分解（CPD）中产生的。通过利用基本统计和最近重新出现的张量理论的结果，我们得到一个一致的盲CPD为基础的DOA估计没有事先假设的阵列配置。我们表明，这个估计是一个等价的近似联合对角化问题的解决方案，并提出了一个特设的迭代解决方案。此外，我们推导出高斯信号的Cramér-Rao下界，并使用它来推导迭代Fisher评分算法，用于计算该特定信号模型中的最大似然估计（MLE）。然后，我们表明，高斯模型的极大似然估计实际上也可以用于获得非高斯信号的改进DOA估计（在温和的条件下），这在Kullback-Leibler散度协方差拟合准则下是最佳的，利用封装在SOS中的附加信息。我们的分析结果证实了模拟实验在各种情况下，这也表明了相当大的提高精度w.r.t.一个竞争的国家的最先进的盲估计AVS阵列，减少所产生的根均方误差高达一个数量级以上。
英文摘要：
A blind Direction-of-Arrivals (DOAs) estimate of narrowband signals for Acoustic Vector-Sensor (AVS) arrays is proposed. Building upon the special structure of the signal measured by an AVS, we show that the covariance matrix of all the received signals from the array admits a natural low-rank 4-way tensor representation. Thus, rather than estimating the DOAs directly from the raw data, our estimate arises from the unique parametric Canonical Polyadic Decomposition (CPD) of the observations' Second-Order Statistics (SOSs) tensor. By exploiting results from fundamental statistics and the recently re-emerging tensor theory, we derive a consistent blind CPD-based DOAs estimate without prior assumptions on the array configuration. We show that this estimate is a solution to an equivalent approximate joint diagonalization problem, and propose an ad-hoc iterative solution. Additionally, we derive the Cramér-Rao lower bound for Gaussian signals, and use it to derive the iterative Fisher scoring algorithm for the computation of the Maximum Likelihood Estimate (MLE) in this particular signal model. We then show that the MLE for the Gaussian model can in fact be used to obtain improved DOAs estimates for non-Gaussian signals as well (under mild conditions), which are optimal under the Kullback-Leibler divergence covariance fitting criterion, harnessing additional information encapsulated in the SOSs. Our analytical results are corroborated by simulation experiments in various scenarios, which also demonstrate the considerable improved accuracy w.r.t. a competing state-of-the-art blind estimate for AVS arrays, reducing the resulting root mean squared error by up to more than an order of magnitude.
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