Projects per year
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 semi-Markov signals (HSMS), which generalize classical Markov chains by introducing explicit (possibly non-geometric) 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 semi-Markov model transition matrix that we define in the paper. Using this result, we show that the Neyman-Pearson 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 |
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Pages (from-to) | 1077-1092 |
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
- multi-state processes
- hidden semi Markov models
- explicit random duration
- hypothesis testing
- error exponent
- large deviations principle
- threshold effect
- Lyapunov exponent
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Profiles
Projects
- 1 Finished
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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
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REFIT: Electrical Load Measurements (Cleaned)
Murray, D. (Creator) & Stankovic, L. (Supervisor), University of Strathclyde, 16 Jun 2016
DOI: 10.15129/9ab14b0e-19ac-4279-938f-27f643078cec, 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