Williams Simon, Suvorov Arthur George, Wang Zengfu, Moran Bill
Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, VIC 3000, Australia.
Department of Theoretical Astrophysics, Eberhard Karls University of Tübingen, D-72076 Tübingen, Germany.
Sensors (Basel). 2021 Aug 4;21(16):5265. doi: 10.3390/s21165265.
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.
在从传感器数据进行参数估计的问题中，费希尔信息提供了一种衡量传感器性能的指标；实际上，从无穷小的意义上讲，就是能从测量中获取多少关于参数的信息。从几何观点来看，它是观测系统参数流形上的一种黎曼度量。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（改变传感器参数）以优化收集到的信息？”这一问题。传感器参数的变化会导致度量相应地改变。我们表明，由于重新配置而引起的信息变化恰好对应于参数流形上黎曼度量的无穷维空间中的自然度量，该度量限制在由传感器参数确定的有限维子流形上。结果表明，这种配置流形上的距离度量基于信息准则提供了最优的动态传感器重新配置。配置流形上的测地线被证明可以优化信息增益，但前提是要以一定的速率进行改变。详细给出了一个配置两个纯方位传感器以最优定位目标的示例，以说明数学机制，其中采用快速行进方法来高效计算测地线，并展示使用这种方法的实用性。
