The focus of this article is to study methods for information-based planning of sensor configurations for use in source localization. Given a bounded region of interest, for each individual (plausible) source location, we define a performance measure as a scalar function (determinant) of the Fisher information matrix, which depends on the sensor-source geometry. This has been shown to be a useful measure of the localization performance of a given configuration of sensors. To establish a scalar numerical objective for optimizing the sensor configuration (for deployment of sensors), these measures must be aggregated over all the possible source locations. In this article, we study a variety of potential aggregation approaches through the generalized mean family of functions, which subsumes all common means, such as geometric, arithmetic, and harmonic means. We construct several examples, and show for bearings-only sensor schemes that there is a strong relationship between the choice of aggregation function and the structure of the optimal configurations, even with the assumption of a range-independent covariance structure. However, for two other sensor schemes for source localization, range-only and time difference of arrival, there is little or no effect on the optimal configuration as the aggregation is varied, when the covariance is range independent.

中文翻译：

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在确定用于源定位的最佳传感器配置中聚合的依赖性

本文的重点是研究基于信息的传感器配置规划方法，以用于源定位。给定一个感兴趣的有界区域，对于每个单独的（合理的）源位置，我们将性能度量定义为 Fisher 信息矩阵的标量函数（行列式），这取决于传感器-源的几何形状。这已被证明是对给定传感器配置的定位性能的有用度量。为了建立用于优化传感器配置（用于传感器部署）的标量数值目标，必须在所有可能的源位置上汇总这些度量。在本文中，我们通过广义平均函数族研究各种潜在的聚合方法，该函数族包含所有常见的方法，例如几何、算术、和谐的意思。我们构建了几个示例，并表明对于仅轴承传感器方案，聚合函数的选择与最佳配置的结构之间存在很强的关系，即使假设存在范围无关的协方差结构。然而，对于其他两种用于源定位的传感器方案，仅距离和到达时间差，当协方差与距离无关时，随着聚合的变化，对最佳配置的影响很小或没有影响。