In problems of parameter estimation from sensor data, the Fisher information provides a measure of the performance of the sensor; effectively, in an infinitesimal sense, how much information about the parameters can be obtained from the measurements. From the geometric viewpoint, it is a Riemannian metric on the manifold of parameters of the observed system. In this paper, we consider the case of parameterized sensors and answer the question, “How best to reconfigure a sensor (vary the parameters of the sensor) to optimize the information collected?” A change in the sensor parameters results in a corresponding change to the metric. We show that the change in information due to reconfiguration exactly corresponds to the natural metric on the infinite-dimensional space of Riemannian metrics on the parameter manifold, restricted to finite-dimensional sub-manifold determined by the sensor parameters. The distance measure on this configuration manifold is shown to provide optimal, dynamic sensor reconfiguration based on an information criterion. Geodesics on the configuration manifold are shown to optimize the information gain but only if the change is made at a certain rate. An example of configuring two bearings-only sensors to optimally locate a target is developed in detail to illustrate the mathematical machinery, with Fast Marching methods employed to efficiently calculate the geodesics and illustrate the practicality of using this approach.

中文翻译：

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传感器配置的信息几何

在从传感器数据估计参数的问题中，Fisher 信息提供了传感器性能的度量；有效地，在无穷小的意义上，可以从测量中获得多少有关参数的信息。从几何的角度来看，它是被观测系统参数流形上的黎曼度量。在本文中，我们考虑参数化传感器的情况并回答“如何最好地重新配置传感器（改变传感器的参数）以优化收集的信息？”的问题。传感器参数的变化导致度量的相应变化。我们表明，由于重新配置而导致的信息变化与参数流形上黎曼度量的无限维空间上的自然度量完全对应，仅限于由传感器参数确定的有限维子流形。该配置流形上的距离测量显示为基于信息标准提供最佳的动态传感器重新配置。配置流形上的测地线显示优化信息增益，但前提是更改以特定速率进行。详细开发了配置两个仅轴承传感器以最佳定位目标的示例，以说明数学机制，使用快速行进方法有效计算测地线并说明使用该方法的实用性。显示配置流形上的测地线以优化信息增益，但前提是更改以特定速率进行。详细开发了配置两个仅轴承传感器以最佳定位目标的示例，以说明数学机制，并采用快速行进方法有效计算测地线并说明使用该方法的实用性。配置流形上的测地线显示优化信息增益，但前提是更改以特定速率进行。详细开发了配置两个仅轴承传感器以最佳定位目标的示例，以说明数学机制，并采用快速行进方法有效计算测地线并说明使用该方法的实用性。