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The theory of trackability with applications to sensor networks

Published: 04 June 2008 Publication History

Abstract

In this article, we formalize the concept of tracking in a sensor network and develop a quantitative theory of trackability of weak models that investigates the rate of growth of the number of consistent tracks given a temporal sequence of observations made by the sensor network. The phenomenon being tracked is modelled by a nondeterministic finite automaton (a weak model) and the sensor network is modelled by an observer capable of detecting events related, typically ambiguously, to the states of the underlying automaton. Formally, an input string of symbols (the sensor network observations) that is presented to a nondeterministic finite automaton, M, (the weak model) determines a set of state sequences (the tracks or hypotheses) that are capable of generating the input string. We study the growth of the size of this candidate set of tracks as a function of the length of the input string. One key result is that for a given automaton and sensor coverage, the worst-case rate of growth is either polynomial or exponential in the number of observations, indicating a kind of phase transition in tracking accuracy. These results have applications to various tracking problems of recent interest involving tracking phenomena using noisy observations of hidden states such as: sensor networks, computer network security, autonomic computing and dynamic social network analysis.

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    cover image ACM Transactions on Sensor Networks
    ACM Transactions on Sensor Networks  Volume 4, Issue 3
    May 2008
    210 pages
    ISSN:1550-4859
    EISSN:1550-4867
    DOI:10.1145/1362542
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 04 June 2008
    Accepted: 01 August 2007
    Revised: 01 April 2007
    Received: 01 July 2006
    Published in TOSN Volume 4, Issue 3

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    Author Tags

    1. Sensor networks
    2. multiple hypotheses
    3. tracking

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