基于目标高斯分布的定位系统节点最优部署方法

针对三维空间定位系统中目标位置服从高斯先验分布假设条件下节点最优部署问题, 分析了纯方位目标定位算法中估计误差的费希尔信息矩阵, 推导出基于目标先验分布的克拉美罗界(Cramer-Rao bound, CRB)。为了解决目标位置在任意高斯分布时, 协方差矩阵为非对角阵的问题, 提出了基于三维坐标旋转的最大后验概率估计方法, 将协方差矩阵转化为对角阵以实现最小化CRB的迹, 从而得到定位系统中节点的最优部署。最后, 通过梯度下降算法对节点最优部署问题的理论推导进行仿真, 验证了该部署方法的有效性，同时仿真结果中不同节点部署方法的对比也表明了该方法可有效降低定位误差。

Optimal deployment method of sensors in localization system based on targets with Gaussian distribution

The optimal deployment of sensors problem is considered when the target location obeys Gaussian prior distribution in three-dimensional space positioning system. The Fisher information matrix of the estimation error in bearings-only localization algorithm is analyzed and Cramer-Rao bound (CRB) based on the target prior distribution is derived. Then, the maximum posterior probability estimation method based on three-dimensional coordinate rotation is discussed to convert a non-diagonal covariance matrix into a diagonal matrix, which aims to minimize the trace of the CRB, and the optimal sensor deployment is obtained. Finally, the gradient-descent algorithm is adopted to simulate effectiveness of the method is verified. Simulation results also show that the method can effectively reduce the localization error compared with the different sensor deployment.