Ordering for Shift-In-Mean of Gauss-Markov Random Fields with Dependent Observations
Previous work on ordered transmission approaches showed significant transmission savings but focused entirely on cases with statistically independent observations at a set of sensor nodes. Here we take the first steps toward applying ordering to cases with statistically dependent observations. While we focus on a particular signal detection problem, we choose one of the most well studied problems, detection of a shift-in-mean for a multivariate Gaussian distribution. We employ the well developed theory of decomposable graphical models, and focus on cases where the observations are taken at a set of sensor nodes which can be grouped into a set of cliques. We assume the nodes within a clique are physically close, so that inner-clique communications can be considered extremely inexpensive. We present the computation of the overall likelihood ratio as a new sum, distinctly different from the sum over a set of independent variables, which implies it is possible to employ ordering over the cliques in an attempt to limit the number of communications from each clique to the place where the clique data will be combined. We present results that imply we can often save a significant portion of these transmission, which is lower bounded by half of the number of cliques. We describe necessary conditions for the result to hold and provide numerical results indicating these conditions are satisfied in many cases of practical interest.
J. Zhang et al., "Ordering for Shift-In-Mean of Gauss-Markov Random Fields with Dependent Observations," Proceedings of the IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (2012, Hoboken, NJ), pp. 65-68, Institute of Electrical and Electronics Engineers (IEEE), Jun 2012.
The definitive version is available at https://doi.org/10.1109/SAM.2012.6250563
IEEE 7th Sensor Array and Multichannel Signal Processing Workshop, SAM 2012 (2012: Jun. 17-20, Hoboken, NJ)
Electrical and Computer Engineering
Keywords and Phrases
Decomposable Graphical Models; Detection Problems; Gauss-Markov; Independent Variables; Likelihood Ratios; Multivariate Gaussian Distributions; Numerical Results; Random Fields; Statistically Dependent, Gaussian Distribution; Sensor Nodes; Sensors; Signal Processing, Speech Recognition
International Standard Book Number (ISBN)
International Standard Serial Number (ISSN)
Article - Conference proceedings
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