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Abstract
We study detection of random signals corrupted by noise that over time switch their values (states) between a finite set of possible values, where the switchings occur at unknown points in time. We model such signals as hidden semiMarkov signals (HSMS), which generalize classical Markov chains by introducing explicit (possibly nongeometric) distribution for the time spent in each state. Assuming two possible signal states and Gaussian noise, we derive optimal likelihood ratio test and show that it has a computationally tractable form of a matrix product, with the number of matrices involved in the product being the number of process observations. The product matrices are independent and identically distributed, constructed by a simple measurement modulation of the sparse semiMarkov model transition matrix that we define in the paper. Using this result, we show that the NeymanPearson error exponent is equal to the top Lyapunov exponent for the corresponding random matrices. Using theory of large deviations, we derive a lower bound on the error exponent. Finally, we show that this bound is tight by means of numerical simulations.
Original language  English 

Pages (fromto)  10771092 
Number of pages  16 
Journal  IEEE Journal on Selected Topics in Signal Processing 
Volume  12 
Issue number  5 
Early online date  29 Jun 2018 
DOIs  
Publication status  Published  31 Oct 2018 
Keywords
 multistate processes
 hidden semi Markov models
 explicit random duration
 hypothesis testing
 error exponent
 large deviations principle
 threshold effect
 Lyapunov exponent
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Profiles

Vladimir Stankovic
Person: Academic
Projects
 1 Finished

SENSIBLE: SENSors and Intelligence in BuiLt Environment (SENSIBLE) MSCA RISE
Stankovic, L., Glesk, I., Gleskova, H. & Stankovic, V.
European Commission  Horizon 2020
1/01/17 → 31/12/20
Project: Research
Datasets

REFIT: Electrical Load Measurements (Cleaned)
Murray, D. (Creator) & Stankovic, L. (Supervisor), University of Strathclyde, 16 Jun 2016
DOI: 10.15129/9ab14b0e19ac4279938f27f643078cec, http://www.refitsmarthomes.org and 3 more links, http://www.epsrc.ac.uk, http://reshare.ukdataservice.ac.uk/852366/, http://reshare.ukdataservice.ac.uk/852367/ (show fewer)
Dataset