Explicit Ziv-Zakai lower bound for bearing estimation
Explicit Ziv-Zakai lower bound for bearing estimation
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DOI：
10.1109/icassp.1996.550148
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发表时间：
1996-05
期刊：
影响因子：
--
通讯作者：
K. Bell;Y. Ephraim;H. V. Trees
中科院分区：
文献类型：
--
作者：
K. Bell;Y. Ephraim;H. V. Trees
扩展的Ziv-Zakai界矢量参数的开发下界的均方误差（MSE）估计的二维方位的窄带平面波信号使用任意几何形状的平面阵列。该边界具有简单的封闭形式的表达式，其是信号波长、信噪比（SNR）、数据快照的数量、阵列中的传感器的数量以及阵列配置的函数。边界的分析表明，有几个区域的操作，并提供分离的区域的阈值的表达式。在快照数和/或信噪比较大的渐近区域中，该界接近逆Fisher信息。在先验性能区域中，当快拍数或信噪比较小时，该界接近先验协方差。在过渡区，边界在两个极端之间平滑地变化。最大似然估计（MLE）的模拟结果表明，该界密切预测的MLE在所有区域的性能。
The extended Ziv-Zakai bound for vector parameters is used to develop a lower bound on the mean square error (MSE) in estimating the two-dimensional bearing of a narrowband planewave signal using planar arrays of arbitrary geometry. The bound has a simple closed form expression which is a function of the signal wavelength, the signal-to-noise ratio (SNR), the number of data snapshots, the number of sensors in the array, and the array configuration. Analysis of the bound suggests that there are several regions of operation, and expressions for the thresholds separating the regions are provided. In the asymptotic region where the number of snapshots and/or SNR are large, the bound approaches the inverse Fisher information. In the a priori performance region where the number of snapshots or SNR is small, the bound approaches the a priori covariance. In the transition region, the bound varies smoothly between the two extremes. Results from simulation of the maximum likelihood estimator (MLE) demonstrate that the bound closely predicts the performance of the MLE in all regions.