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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    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 ORCID logoORCID: https://orcid.org/0000-0001-8251-7991, Stanković, Lina ORCID logoORCID: https://orcid.org/0000-0002-8112-1976, Vukobratović, Dejan and Stanković, Vladimir ORCID logoORCID: https://orcid.org/0000-0002-1075-2420;
    Item type:Article
    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:18 Sep 2020 05:00
    URI:https://strathprints.strath.ac.uk/id/eprint/64455
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