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The Information Geometry of Sensor Configuration
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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8400002/ https://www.ncbi.nlm.nih.gov/pubmed/34450705 http://dx.doi.org/10.3390/s21165265 |
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author | Williams, Simon Suvorov, Arthur George Wang, Zengfu Moran, Bill |
author_facet | Williams, Simon Suvorov, Arthur George Wang, Zengfu Moran, Bill |
author_sort | Williams, Simon |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-8400002 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-84000022021-08-29 The Information Geometry of Sensor Configuration Williams, Simon Suvorov, Arthur George Wang, Zengfu Moran, Bill Sensors (Basel) Article 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. MDPI 2021-08-04 /pmc/articles/PMC8400002/ /pubmed/34450705 http://dx.doi.org/10.3390/s21165265 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Williams, Simon Suvorov, Arthur George Wang, Zengfu Moran, Bill The Information Geometry of Sensor Configuration |
title | The Information Geometry of Sensor Configuration |
title_full | The Information Geometry of Sensor Configuration |
title_fullStr | The Information Geometry of Sensor Configuration |
title_full_unstemmed | The Information Geometry of Sensor Configuration |
title_short | The Information Geometry of Sensor Configuration |
title_sort | information geometry of sensor configuration |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8400002/ https://www.ncbi.nlm.nih.gov/pubmed/34450705 http://dx.doi.org/10.3390/s21165265 |
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