Abstract
| Language | English |
|---|---|
| Pages | 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 |
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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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Optimal detection and error exponents for hidden semi-Markov models. / Bajović, Dragana; He, Kanghang; Stanković, Lina; Vukobratović, Dejan; Stanković, Vladimir.
In: IEEE Journal on Selected Topics in Signal Processing, Vol. 12, No. 5, 31.10.2018, p. 1077-1092.Research output: Contribution to journal › Article
TY - JOUR
T1 - Optimal detection and error exponents for hidden semi-Markov models
AU - Bajović, Dragana
AU - He, Kanghang
AU - Stanković, Lina
AU - Vukobratović, Dejan
AU - Stanković, Vladimir
PY - 2018/10/31
Y1 - 2018/10/31
N2 - 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.
AB - 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.
KW - multi-state processes
KW - hidden semi Markov models
KW - explicit random duration
KW - hypothesis testing
KW - error exponent
KW - large deviations principle
KW - threshold effect
KW - Lyapunov exponent
U2 - 10.1109/JSTSP.2018.2851506
DO - 10.1109/JSTSP.2018.2851506
M3 - Article
VL - 12
SP - 1077
EP - 1092
JO - IEEE Journal on Selected Topics in Signal Processing
T2 - IEEE Journal on Selected Topics in Signal Processing
JF - IEEE Journal on Selected Topics in Signal Processing
SN - 1932-4553
IS - 5
ER -