Department of Computer Science and Automatic Control, National Distance Education University (UNED), Madrid 28040, Spain.
Sensors (Basel). 2013 Aug 16;13(8):10674-710. doi: 10.3390/s130810674.
The problem of determining the optimal geometric configuration of a sensor network that will maximize the range-related information available for multiple target positioning is of key importance in a multitude of application scenarios. In this paper, a set of sensors that measures the distances between the targets and each of the receivers is considered, assuming that the range measurements are corrupted by white Gaussian noise, in order to search for the formation that maximizes the accuracy of the target estimates. Using tools from estimation theory and convex optimization, the problem is converted into that of maximizing, by proper choice of the sensor positions, a convex combination of the logarithms of the determinants of the Fisher Information Matrices corresponding to each of the targets in order to determine the sensor configuration that yields the minimum possible covariance of any unbiased target estimator. Analytical and numerical solutions are well defined and it is shown that the optimal configuration of the sensors depends explicitly on the constraints imposed on the sensor configuration, the target positions, and the probabilistic distributions that define the prior uncertainty in each of the target positions. Simulation examples illustrate the key results derived.
确定传感器网络的最佳几何配置以最大化多个目标定位可用的与范围相关的信息的问题在许多应用场景中都至关重要。在本文中，考虑了一组测量目标与每个接收器之间距离的传感器，假设范围测量受到白高斯噪声的干扰，以便搜索能够最大程度提高目标估计精度的配置。使用估计理论和凸优化工具，通过适当选择传感器位置，将该问题转换为最大化每个目标的 Fisher 信息矩阵的行列式的对数的凸组合，以确定产生任何无偏目标估计器的协方差最小的传感器配置。解析和数值解都有明确定义，结果表明传感器的最佳配置显式取决于对传感器配置、目标位置以及定义每个目标位置先验不确定性的概率分布的约束。仿真示例说明了得出的关键结果。
