Nonlinear data observability and information
type: Item
instance of: scholarly article
title: Nonlinear data observability and information
zbMATH Open document ID: 0651.93015
DOI: 10.1016/0016-0032(88)90055-5
author: S. H. Smith
published in: Journal of the Franklin Institute
publication date: 1988-01-01T00:00:00Z
review text: For the deterministic system observability, two conditions, connectedness and univalence, are introduced and used. Depending on how the conditions are satisfied, observability is classified in three categories: observability in the strict sense, observability in the wide sense and the unobservable case. An underwater acoustical localization tracking example, the bearing-only information problem described in three different coordinates, and an array SONAR problem described in terms of a small number of sensors and various measurement policies are analyzed. For stochastic process observability, an information theoretic approach is introduced. Computed here, is the mutual information between the state and the observation. Since this quantity is expressed as an entropy difference between a priori and a posteriori processes, two densities are required for computation. Due to the difficulty in solving the density equation, an estimated second-moment approximation is considered. Then, mutual information is used as a criterion to determine the ``degree of observability''. Sensitivity with respect to various coordinate systems for an array SONAR, a combination of relative delay and Doppler measurements for up to three sensors are compared. Due to complexity of the computations, the tracking results, presented here, rely heavily on simulation.
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93E03
Mathematics Subject Classification ID: 78A55
zbMATH DE Number: 4062917
zbMATH Keywords: deterministic system observability
zbMATH Keywords: connectedness
zbMATH Keywords: univalence
zbMATH Keywords: underwater acoustical localization tracking
zbMATH Keywords: array SONAR problem
zbMATH Keywords: stochastic process observability
zbMATH Keywords: information theoretic approach
MaRDI profile type: Publication
full work available at URL: 0016-0032(88)90055-5
OpenAlex ID: W2053235293
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Wikidata QID: Q126350647
description: scientific article; zbMATH DE number 4062917