用于立体阵定位的克拉美-罗界简单算法和分析

为了优化设计立体麦克风阵列，满足声学预警系统全空域定位的需求，推导了立体阵定位系统的克拉美-罗界。在此基础上，对比分析了均匀圆阵和几种立体阵（球形、圆柱、锥形和圆孤线阵）的定位性能，同时深入分析了选择不同参考基元对定位性能的影响。仿真结果表明，对方位角的估计，圆弧线阵的方差最小。对俯仰角的估计，几种立体阵的方差均小于均匀圆阵的方差。其中测向不耦合的立体阵方差略小于测向耦合的立体阵方差，圆柱阵的方差最小。同时在阵形、基元数目不变的情况下，改变参考基元的位置还可以进一步降低圆柱阵的俯仰角估计方差及距离相对方差。

Cramer-Rao Bound of Three-Dimensional Array

To satisfy the request of localization in full air space,the performance of three-dimensional array based on Cramer-Rao(CRB) bound was discussed.The CRB bound was derived.The performance of several geometric of array was analyzed,such as sphere,cylinder,cone and half cylinder compared with circle.The position of reference sensor was discussed to improve the performance using cylindered array.The simulation results show:(1) in azimuth estimation the bias of half cylinder is the smallest.(2) in elevation estimation,the bias of uncoupled three-dimensional arrays is smaller than that of coupled three-dimensional arrays,and the bias of all three-dimensional array is smaller than that of circle array.Moreover,the bias of cylindrical array is the smallest within these three-dimensional arrays.(3) Changing the reference senor from origin to z-axis can improve the performance of elevation and range estimation without altering the geometric of array.