论文标题
Ziv-Zakai限制DOAS估算
Ziv-Zakai Bound for DOAs Estimation
论文作者
论文摘要
均方根误差（MSE）的下限在评估到达方向（DOA）估计性能中起着重要作用。在众多DOA估计的界限中，局部Cramer-Rao结合（CRB）仅渐近。相比之下，现有的全局紧密Ziv-Zakai Bound（ZZB）适用于仅评估单一源估计。在本文中，我们得出了适用于评估混合相干/不相互分多个来源DOA估计的明确ZZB。首先表明，从单源估计到多个来源估计的ZZB直接概括不能保持在先验性能区域中的界限。为了得出全局紧密的ZZB，我们引入了订单统计信息，以描述MSE计算过程中通过订购过程引起的doas的先验分布的变化。派生的ZZB首次是相干来源之间连贯系数的函数，并揭示了A先验性能区域中MSE融合与来源的数量之间的关系。此外，派生的ZZB还为过度确定和不确定的DOA估计提供了统一的紧密界限。仿真结果证明了派生的ZZB比CRB的明显优势在评估和预测多种源的估计性能方面具有明显的优势。
Lower bounds on the mean square error (MSE) play an important role in evaluating the direction-of-arrival (DOA) estimation performance. Among numerous bounds for DOA estimation, the local Cramer-Rao bound (CRB) is only tight asymptotically. By contrast, the existing global tight Ziv-Zakai bound (ZZB) is appropriate for evaluating the single source estimation only. In this paper, we derive an explicit ZZB applicable for evaluating hybrid coherent/incoherent multiple sources DOA estimation. It is first shown that, a straightforward generalization of ZZB from single source estimation to multiple sources estimation cannot keep the bound valid in the a priori performance region. To derive a global tight ZZB, we then introduce order statistics to describe the change of the a priori distribution of DOAs caused by ordering process during the MSE calculation. The derived ZZB is for the first time formulated as a function of coherent coefficients between coherent sources, and reveals the relationship between the MSE convergency in the a priori performance region and the number of sources. Moreover, the derived ZZB also provides a unified tight bound for both overdetermined and underdetermined DOA estimation. Simulation results demonstrate the obvious advantages of the derived ZZB over the CRB on evaluating and predicting the estimation performance for multiple sources DOA.
