Optimal detection and error exponents for hidden semi-Markov models
Bajović, Dragana and He, Kanghang and Stanković, Lina and Vukobratović, Dejan and Stanković, Vladimir (2018) Optimal detection and error exponents for hidden semi-Markov models. IEEE Journal on Selected Topics in Signal Processing, 12 (5). pp. 1077-1092. ISSN 1932-4553
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Text (Bajovic-etal-IEEE-JSTSP-2018-Optimal-detection-and-error-exponents-for-hidden-semi-Markov-models)
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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 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.
Creators(s): |
Bajović, Dragana, He, Kanghang ![]() ![]() ![]() | Item type: | Article |
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ID code: | 64455 |
Keywords: | multi-state processes, hidden semi Markov models, explicit random duration, hypothesis testing, error exponent, large deviations principle, threshold effect, Lyapunov exponent, Electrical engineering. Electronics Nuclear engineering, Electrical and Electronic Engineering |
Subjects: | Technology > Electrical engineering. Electronics Nuclear engineering |
Department: | Faculty of Engineering > Electronic and Electrical Engineering |
Depositing user: | Pure Administrator |
Date deposited: | 14 Jun 2018 09:12 |
Last modified: | 24 Jan 2021 03:21 |
URI: | https://strathprints.strath.ac.uk/id/eprint/64455 |
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