Data-Efficient Quickest Change Detection in Sensor Networks
A sensor network is considered where at each sensor a sequence of random variables is observed. At each time step, a processed version of the observations is transmitted from the sensors to a common node called the fusion center. At some unknown point in time the distribution of observations at an u...
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| Published in: | IEEE transactions on signal processing Vol. 63; no. 14; pp. 3727 - 3735 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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IEEE
15.07.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1053-587X, 1941-0476 |
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| Abstract | A sensor network is considered where at each sensor a sequence of random variables is observed. At each time step, a processed version of the observations is transmitted from the sensors to a common node called the fusion center. At some unknown point in time the distribution of observations at an unknown subset of the sensor nodes changes. The objective is to detect the change in distribution as quickly as possible, subject to constraints on the false alarm rate, the cost of observations taken at each sensor, and the cost of communication between the sensors and the fusion center. Minimax formulations are proposed for the above problem and distributed algorithms are proposed in which on-off observation control and censoring is used at each sensor to meet the constraints on data. It is shown that the proposed algorithms are asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero. The asymptotic optimality of the proposed algorithms implies that an arbitrary but fixed fraction of data can be skipped without any loss in asymptotic performance as compared to the scheme where all the observations are used for decision making. It is also shown, via numerical studies, that the proposed algorithms perform significantly better than those based on fractional sampling, in which the classical algorithms from the literature are used and the constraint on the cost of observations is met by skipping a fixed fraction of observations either deterministically or randomly, independent of the observation process. |
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| AbstractList | A sensor network is considered where at each sensor a sequence of random variables is observed. At each time step, a processed version of the observations is transmitted from the sensors to a common node called the fusion center. At some unknown point in time the distribution of observations at an unknown subset of the sensor nodes changes. The objective is to detect the change in distribution as quickly as possible, subject to constraints on the false alarm rate, the cost of observations taken at each sensor, and the cost of communication between the sensors and the fusion center. Minimax formulations are proposed for the above problem and distributed algorithms are proposed in which on-off observation control and censoring is used at each sensor to meet the constraints on data. It is shown that the proposed algorithms are asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero. The asymptotic optimality of the proposed algorithms implies that an arbitrary but fixed fraction of data can be skipped without any loss in asymptotic performance as compared to the scheme where all the observations are used for decision making. It is also shown, via numerical studies, that the proposed algorithms perform significantly better than those based on fractional sampling, in which the classical algorithms from the literature are used and the constraint on the cost of observations is met by skipping a fixed fraction of observations either deterministically or randomly, independent of the observation process. |
| Author | Veeravalli, Venugopal V. Banerjee, Taposh |
| Author_xml | – sequence: 1 givenname: Taposh surname: Banerjee fullname: Banerjee, Taposh email: banerje5@illinois.edu organization: Dept. of Electr. & Comput. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA – sequence: 2 givenname: Venugopal V. surname: Veeravalli fullname: Veeravalli, Venugopal V. email: vvv@illinois.edu organization: Dept. of Electr. & Comput. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA |
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| References | ref13 ref12 ref15 ref14 ref11 ref10 ref17 ref16 ref19 ref18 siegmund (ref27) 1985 lai (ref25) 1998; 44 ref24 ref23 ref26 ref20 veeravalli (ref4) 2014 shewhart (ref5) 1931 ref22 ref21 ref29 ref8 poor (ref1) 2009 ref7 ref6 tartakovsky (ref28) 2011; 56 shiryayev (ref9) 1978 tartakovsky (ref2) 2014 basseville (ref3) 1993 |
| References_xml | – year: 2014 ident: ref4 publication-title: Quickest Change Detection – ident: ref13 doi: 10.1109/18.923755 – ident: ref29 doi: 10.1109/TPWRS.2015.2394246 – ident: ref14 doi: 10.1109/TIT.2005.850159 – year: 2014 ident: ref2 publication-title: Sequential Analysis Hypothesis Testing and Change-Point Detection doi: 10.1201/b17279 – ident: ref15 doi: 10.1080/07474940802446236 – year: 1978 ident: ref9 publication-title: Optimal Stopping Rules – ident: ref8 doi: 10.1137/1108002 – volume: 44 start-page: 2917 year: 1998 ident: ref25 article-title: Information bounds and quick detection of parameter changes in stochastic systems publication-title: IEEE Trans Inf Theory doi: 10.1109/18.737522 – ident: ref22 doi: 10.1109/TWC.2010.110510.091177 – ident: ref16 doi: 10.1109/TIT.2013.2272313 – year: 1931 ident: ref5 publication-title: Economic Control of Quality of Manufactured Product – ident: ref11 doi: 10.1214/aos/1176346587 – year: 1985 ident: ref27 publication-title: Sequential Analysis Tests and Confidence Intervals – ident: ref6 doi: 10.1214/aoms/1177729489 – ident: ref17 doi: 10.1109/ICIF.2002.1021129 – ident: ref21 doi: 10.1109/T-WC.2008.070808 – ident: ref10 doi: 10.1214/aoms/1177693055 – ident: ref18 doi: 10.1093/biomet/asq010 – ident: ref24 doi: 10.1080/07474946.2015.1030971 – ident: ref23 doi: 10.1080/07474946.2012.651981 – year: 2009 ident: ref1 publication-title: Quickest Detection – ident: ref7 doi: 10.2307/2333009 – ident: ref19 doi: 10.1109/ISIT.2011.6034390 – volume: 56 start-page: 534 year: 2011 ident: ref28 article-title: Third-order asymptotic optimality of the generalized Shiryaev-Roberts changepoint detection procedures publication-title: Theory Prob Appl – ident: ref12 doi: 10.1214/aos/1176350164 – ident: ref26 doi: 10.1137/1.9781611970302 – ident: ref20 doi: 10.1214/13-AOS1094 – year: 1993 ident: ref3 publication-title: Detection of Abrupt Changes Theory and Application |
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| SubjectTerms | Algorithm design and analysis Algorithms asymptotic optimality Delays False alarms minimax Monitoring multi-channel systems observation control outlying sequence detection Quickest change detection Random variables Sensors Signal processing algorithms Tin |
| Title | Data-Efficient Quickest Change Detection in Sensor Networks |
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